THE THEORY OF THE MEASUREMENT OF THE
INCOME OF TRADING ENTERPRISES
ROBERT RAYMOND STERLING
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
UNIVERSITY OF FLORIDA
3 1262 08552 2398
Robert Raymond Sterling
I Introduction .. . . . .. .. .
The Definition of Income.....
Statement of the Problem . .
The Model . . . . . .
Income Within the Model . . .
The Nature of the Enterprise .
The Timing of the Measurement .
II Information and Communications
Information . . . . .
III Measurement ..........
The Definitional Dispute . .
General Propositions of Measurement . . .
Sum m ary . . . . . . . . . . .
IV Measurement (continued) . . . . . . .
Conditions Attending the Operation of Measurement
The Temporal Conditions of the Operation. . .
Measurements, Predictions and Retrodictions
. . . . 10
. . . . 27
. . . . 31
. . . . 41
. . . . 44
. . . . . 47
. . . . . 48
. . . . . 59
. . . . . 76
Intensive versus Extensive Dimensions . .
Objective Versus Subjective Measurements .
V The Theoretical Construct . . . . . .
The Value Dimension ..............
The Problematic Situation . . . . . .
Decision Theory of the Trader . . . . .
Decision Theory of Other Interested Receivers .
Summ ary .. . .. . . .. .. .. .
VI The Constructs Applied . . . . . . .
Information in the Model . . . . . .
Measurement in the Model . . . . . .
Summary of Part I ...............
VII Boulding's Constant . . .
VIII The Fisher Tradition ............
Discounting Under Conditions of Certainty
Valuation Under Uncertainty . . . .
IX The Accounting Tradition . . . . .
The Fundamental Principle of Valuation.
The Fundamental Rule of Valuation . .
. . 286
. . 296
. . 314
. . 339
. . 351
. . 361
Arguments for the Cost Rule . . . ... 370
Summ ary .... ... ... .. .. .... . 412
X Present Market .................. 416
XI The Assumptions Relaxed . . . . . . 422
Perfect Market . . . . . . .... .422
Stable Price Level ............... 434
Summary ................... 457
This study is the first step toward an attempt to develop
a general theory of the measurement of enterprise income. We
emphasize "measurement" because we will not be concerned with
the definition of income; instead we will utilize a commonly ac-
cepted definition and reduce its implementation to a problem in
We call this a "first step" because we will limit our dis-
cussion to only one type of enterprise under severely simple con-
ditions. Thus, our goal is modest:
The development of a theory of the meas-
urement of the income of trading enter-
The methodology is critical, analytical and eclectic. Dif-
ferent implementations of the accepted definition will be analyzed
and criticized. Concepts from several disciplines will be used
when they are germane to the problem. The underlying theme is
pragmatism. The criteria flow from a consideration of the de-
sired ends and, when the concepts permit, the development is
The Definition of Income
For the purpose of this study we will use the definition
presented by Hicks, Simons, Haig, Alexander, et al., as the
fundamental basis for our discussion of the measurement of
Probably the most well-known of these definitions is
The purpose of income calculations in
practical affairs is to give people an indi-
cation of the amount which they can consume
without impoverishing themselves. Following
out this idea, it would seem that we ought to
define a man's income as the maximum value
which he can consume during a week, and still
expect to be as well off at the end of the week
as he was at the beginning. Thus, when a
person saves, he plans to be better off in the
future; when he lives beyond his income, he
plans to be worse off. Remembering that the
practical purpose of income is to serve as a
guide for prudent conduct, I think it is fairly
clear that this is what the central meaning
This definition is almost ideal for our purposes because of the
explicit statement that income is to be a "guide for prudent con-
duct." We shall lay a considerable amount of emphasis upon in-
come being a guide for prudent conduct, or, in the more modern
and Americanized terminology, we shall emphasize that income
should be useful for decision-making purposes. The decisions in
1J. R. Hicks, Value and Capital, 2nd ed. (London: Oxford
University Press, 1946), p. I7Z.
this paper, however, will be considerably broader than the general
decision-theory type of problem. The literature on "Decision
Theory" is aimed primarily at managerial profit maximization;
the decisions which we will be concerned with will not be so re-
stricted. We will include the decisions of other people who are
interested in the enterprise.
Hicks continues to discuss several approximations to the
central meaning of his notion of income. Even though we have
accepted Hicks' definition of income, we will not necessarily con-
cur with his analysis of approximations to the central meaning of
his income concept. For example, we will specifically quarrel
with his statement that:
S.. ex post calculations of capital accumu-
lation have their place in economic and
statistical history; they are a useful meas-
uring-rod for economic progress; but they
are of no use to theoretical economists,
who are trying to find out how the economic
system works, because they have no signifi-
cance for conduct. 3
We will argue that an interpretation of the ex post calculation is
a necessary datum for correct decisions and thus that it does
have "significance for conduct."
2Much of the current literature is devoted to variants on the
maximum-profit theme. Some concentrate on minimizing costs
with an assumed, often tacit, demand level. Others concentrate
on time minimization with the implicit notion of the opportunity
costs attached to time. We consider these, and other like devel-
opments, to be nothing more than special cases of profit maxi-
3Hicks, p. 179, second emphasis supplied. Hayek also denies
Taxation theory, with its emphasis on income tax, ha s of
necessity been an area which has made the closest scrlitiny of
concepts of income. One of the earliest attempts in the Unit ed
States was made by Professor IIaig. Ile defines income as the
...increase or accretion in one's power to
satisfy his wants in a given period in so far
as that power consists of (a) money itself,
or, (b) anything susceptible of valuation in
terms of money. '
It is interesting to note the striking similarity between Itaig's
and Hicks' concepts of income, althollgh it is quile clear that their
basic assumptions about the use of that income were very dissim-
ilar. Haig was working on a problem of .. tting an equitable nmethxi
of levying income taxes; Hicks was concerned not with equity but
with the practical conduct of affairs. Neverthel ess, they ciamer to
the same conclusions as to thi definition of income. This should
be an important datum bearing on the prevailing notion that there
is no single measurement of inonme that is proper for all pur-
poses.5 The notion of different income for different purposes is
the usefulness of "income" in e conon i anal is. (See F. A.
IIayek, Pure Theory of Capital (London, l 19,1i) p. 33b.)
4Robert Murray Haig, "The ( oncept of Income Economic
and Legal Aspects. reprinted in N sgrai and Shoup, Alterican
E conomi A *c t on ', I i .. .. f I : l : l .*,
IX (H om '.' ..... il 11 1 ,, ~- i '.
5For example, Boulding state "ihe concept of profit (in-
come) will quite rightly differ dc ..ndi( n the purpose for
which we need it. The definition of pro it for tax purposes, for
instance, may differ considerably from the definition which is
required for other forms of decision-nmaking. What we need here
quite the vogue in this day and age, but, surprisingly enough, in-
come definitions derived for these different purposes do not neces-
Professor Simons, writing contemporaneously with both
Hicks and Haig, 6 defines income as follows:
Personal income connotes, broadly, the exer-
cise of control over the use of society's scarce
resources. It has to do not with sensations,
services, or goods but rather with rights which
command prices (or to which prices may be
imputed). Its calculation implies estimate (a)
of the amount by which the value of a person's
store of property rights would have increased,
as between the beginning and end of the period,
if he had consumed (destroyed) nothing, or (b)
of the value of rights which he might have exer-
cised in consumption without altering the value
of his store of rights. In other words, it implies
estimate of consumption and accumulation. 7
Clearly, this definition is consistent with those of Hicks and Haig.
A secondary purpose of Simon's statement is to reject Fisher's
is not a single definition of profit applicable to all cases, but a
spectrum of definitions, in which the relationship of the various
concepts is reasonably clear and in which the definition is fitted
to the purpose for which it is to be used. Kenneth E. Boulding,
"Economics and Accounting: The Uncongenial Twins, Studies in
Accounting Theory, eds., W. T. Baxter and S. Davidson (Home-
wood, Ill.: Richard D. Irwin, Inc., 1962), p. 45.
61938-39 seems to have been a vintage year for income defin-
ition. Unfortunately, the edicts of these authors have either been
forgotten or deliberately ignored.
7Henry C. Simons, Personal Income Taxation (Chicago: Uni-
versity of Chicago Press, 1938), p. 49.
concept of income. The phrase "sensations, services or goods"
is obviously, albeit tacitly, a quarrel with Fisher.
This quarrel (and others about Fisher) is not relevant to
this study. This paper has been restricted to the consideration of
enterprise income while Fisher's analysis is of personal income.
Fisher's concept is almost exclusively psychic and since, by defin-
ition, an enterprise can have no psyche, both the problems and the
method of approach are different. Fisher disqualifies himself in
the consideration of enterprise income by writing:
It is interesting to observe that a corporation
as such can have no net income. Since a
corporation is a fictitious, not a real, person,
each of its items without exception is doubly
entered. Its stockholders may get income
from it, but the corporation itself, considered
as a separate person apart from these stock-
holders, receives none.8
If we accepted Fisher's notion this study would end at this point,
and therefore it is clear that we must disagree in order to con-
tinue. The point of disagreement, however, is at the premise,
not in the analysis. Fisher assumes that a psychic experience
must occur before there is "income. We make no such assump-
tion in our definition, and appeal to the linguistic fact that some-
thing called "income" has been utilized for many years, both in
common parlance and scientific inquiry, as a measure of the
"success" of an enterprise.
8Irving Fisher, The Theory of Interest (New York: MacMillan,
1930), p. 23. For a full explanation of the "double entry" see
Even Fisher's disciples disagree with him on this issue.
Lindahl, who has probably done more than any other person in
advancing Fisher's thesis, takes him to task:
Irving Fisher's analysis is carried out in a
masterly fashion, but all his attempts to
demonstrate that this concept of income is the
usual one and that it is the only logical one,
must be considered unsatisfactory. In neither
popular nor scientific terminology are income
and consumption equated.... 9
Lindahl, after the basic disagreement has been stated,
proceeds to develop a theory of income based upon Fisher's anal-
ysis, particularly upon the concept of ertrag or yield. However,
Lindahl's theory is concerned with the valuation of wealth, not
with a different definition of income. He is in agreement with the
definitions presented above; his quarrel is with the method of
valuation. He continues:
...income is generally taken to include saving
(either positive or negative), and the crux of
the matter is to decide gust what this saving
may be taken to cover. 0
That is, the "crux" is capital valuation, not the definition.
In a more modern context, Professor Alexander writes:
A year's income is, fundamentally, the
amount of wealth that a person, real or
Irving Fisher, The Nature of Capital and Income (New York:
MacMillan Co., 1906), especially pp. 159-164.
9Erik Lindahl, "The Concept of Income" in Economic Essays
in Honor of Gustav Cassel (London, 1933), p. 400.
corporate, can dispose of over the course
of the year and remain as well off at the
end of the year as at the beginning. 11
Again, the definition is equivalent to the several presented above,
except for the minor change of the time period from one week to
one year. As Alexander states:
Another set of problems, which concern the
question of what is meant by "as well off at
the end of the year as at the beginning" is
the principal subject of the present monograph. 12
Thus Alexander is concerning himself with the problem of valua-
tion at two time periods. His conclusion is essentially the same
as Boulding's, that ".. .many variant concepts tof income] can be
conceived, each of which has certain advantages for a particular
The above definitions of income are all by economists.
Much ado has been made in recent years about the difference be-
tween the economists' and the accountants' concept of income.
The quarrel is semantic. Accountants also accept the definition;
their method of valuation is the variant.
A reference to the basic accounting equation--assets equal
equities--proves the point. Accountants array the assets and
11Sidney S. Alexander, "Income Measurement in a Dynamic
Economy, Studies in Accounting Theory, eds., W. T. Baxter
and S. Davison, revised by David Solomons (Homewood, Ill.:
Richard D. Irwin Press, 1962), p. 127.
liabilities of a given enterprise at a point in time and "value'14
them. At a subsequent point in time, usually a year, the account-
ants repeat the process. The difference between the proprietor-
ship or owner's equity at these two points, properly adjusted for
investment and dis-investment, is equal to the owner's income for
that period. Almost every basic textbook in accounting has a
problem which can be stated mathematically as:
A1 L1 = P1; A2 LZ = P2; P2 P1 71
77is equal to the income of the enterprise for the period
(tl to t2) if there had been no investment or dis-investment.
Montgomery makes this explicit by remarking:
If an absolutely accurate balance sheet
could be prepared at the beginning and
the end of a period, the difference would
constitute the net profits or the net loss
for the term. 15
More recently and more directly Gordon has stated:
. we all agree with Hicks who defined
"a man's income as the maximum value
which he can consume during a week, and
still expect to be as well off at the end of
14 There is a quarrel whether the accountant "values" assets
or does something else. The entire rationale of "unexpired costs"
has been attacked and the debate has been over whether "costs"
are "values." Simons has taken the position that the accountant
does not value because there exist different costs for the same
goods. For a more complete discussion, see infra.
15Robert H. Montgomery, Auditing (New York: Ronald Press,
1916), p. 206. He rejects the method, however, because "the valu-
ation and revaluation of capital assets involves too much specula-
tion... (p. 206).
the week as at the beginning." Disagree-
ment arises as to the operational meaning
to be given to the phrase "as well off. "16
In summary, the definition or concept of income as being
"the difference between wealth at two periods of time plus con-
sumption" is agreed upon by almost all writers. We will utilize
this definition in this study as a fundamental premise.
Statement of the Problem
The above section pointed out the concurrence of opinion
about the definition or concept of income, among economists as
well as between economists and accountants. The problem then
is not with the definition of income, but with the application of the
income concept in a specific instance. The basic disagreement
centers around the phrase "as well off" in the definition. There
are at least four17 different approaches to the measurement of
how "well off" a person or enterprise is.
16Myron J. Gordon, "Scope and Method of Theory in Research
in the Measurement of Income and Wealth, Accounting Review,
XXXV, No. 4 (October 1960), p. 606, emphasis supplied.
17There are almost as many ways of classifying income concepts
as there are writers on the subject. For example, Hicks lists
three (Hicks, pp. 171-177). Hansen lists three different concepts
of the Fisher Tradition and refers to a fourth presented by Krist-
enson (Palle Hansen, The Accounting Concept of Profit, Amsterdam:
North-Holland Publishing Co., 1962, p. 21), Kerr lists three which
are sub-classifications of the Accounting Tradition (Jean Kerr.
"Three Concepts of Business Income, in Davidson, Green, Horn-
gren and Sorter, An Income Approach to Accounting Theory,
The Fisher Tradition18
In the absence of dividend payments and
new contributions by stockholders, income
is measured at the end of the period by adding
up the discounted values of all net receipts
which the managers then expect to earn on the
firm's existing net assets and subtracting from
this subjective value a similar computation
made at the beginning of the period.... The
development of this concept, stated here in
extremely simple terms, has been largely the
work of Erik Lindahl, Studies in the Theory of
Money and Capital, . . 1
The key word in the above quotation is "expect. In the Fisher
tradition, expectations about the future are the basis of the meas-
urement of income.
Since the future, by definition, cannot be measured, what
we are measuring under this tradition is the owner's and/or
manager's expectations or feelings about the future. In the case
Englewood Cliffs, N. J.: Prentice-Hall, 1964, pp. 40-48), Wueller
discusses a great many without ever bothering to classify them
except in the most general terms (P. H. Wueller, "Concepts of
Taxable Income, Political Science Quarterly, Part I, LII (March,
1938), 83-110, Part II, LIII (December 1938), 577-583, Part III,
LIV (December 1939), 555-576). In brief, this classification is
not natural or infallible, it is only convenient. However, the
attempt has been to state each one broadly enough to include all
the extant concepts.
18Although, as noted above, Fisher disqualified himself from
the measurement of enterprise income, Lindahl, Cassell, Hansen,
and others have developed a concept of income which springs
directly from Fisher's ertrag. Thus, we classify this concept as
being in "The Fisher Tradition. "
19E. O. Edwards and P. W. Bell, The Theory and Measurement
of Business Income (Los Angeles: University of California Press,
1961), pp. 24-Z5, emphasis supplied.
of personal income these feelings are part of the psychic benefits
received by the individual. In the case of enterprise income,
since the enterprise cannot have feelings, what we are measuring
are the feelings or expectations of the managers. Thus, the
measurement of well-offness is dependent upon management's
prognostication of what the future holds.
Criticism of this concept usually falls into two categories:
(1) it is subjective, and (2) the future is uncertain.
The first criticism--subjectivity--appears to be the crucial
one for most writers. The concept is usually rejected out of hand
because it is subjective. An extended discussion of subjectivity
versus objectivity would be much beyond the scope of this paper
and would lead us into a philosophical discussion that is as yet un-
resolved.20 Suffice it to say at this point that these "subjective"
20If what is meant by subjectivity is the antonym of objectivity
which is defined as "being, or regarded as being, independent
of the mind; real; actual. (From Webster's New World Diction-
ary of the American Language), then the so-called "objective"
method of measuring assets by their cost would be subject to the
same criticism. That is, the determination of costs and their
amortization are no more "free from the mind" than is the sub-
jectivity of the expectations of the managers. If what is meant by
subjectivity here is that it is not verifiable, then "descriptive
propositions are statements about fact, and are theoretically
verifiable by any competent observer as either true, false, or
having a certain degree of probability. Normative propositions
are assertions of value: their truth or falsity may therefore legit-
imately vary for different individuals." (Philip Wheelwright,
A Critical Introduction to Ethics, revised edition, New York:
Odyssey Press, 1949, p. 49). Since the valuation by expectations
of the owners appears to be descriptive rather than normative--
what ought to be--it would appear that they would be equally
valuations must be made, as will be demonstrated below, and, if
they are to be rejected for the purpose of income determination,
they must be rejected on grounds other than their subjectivity.
The second criticism--uncertainty--is not directed against
the concept but,instead, that certainty does not conform to reality.
That is, most writers seem to take the position that if the future
were certain there would be no problem of income determination
under the Fisher tradition. For example, Moonitz goes through
"a valuation experiment" in which he assumes complete certainty
of the future. He concludes by saying:
How much of the data shown for each year can
be reflected in a matching of cost and revenue
under the practical difficulties with which we
are forced to contend under ordinary circum-
stances? That these difficulties stem mainly
from the fact that we cannot know what the
events will be during the entire future life
of an enterprise is now apparent. 21
Moonitz implies that if the future were known with certainty
there would be at least fewer, and perhaps no, problems of income
determination. Such a sanguine view of this method under certainty
is not taken by those people who are directly working with the
verifiable as any other method of valuation. See, for example,
Ray Lepley, Verifiability of Value, especially Chapter 2, "The
Nature of Value Verification. We will discuss the problem in a
little more detail in connection with metrics. See infra.
21Maurice Moonitz and Louis H. Jordan, Accounting: An
Analysis of its Problems, revised edition, (New York: Holt,
Rinehard and Winston, 1963), I, p. 135.
development of this theory. Hansen notes at least four possibili-
ties for adjusting the capital. He states:
The profit according to method (1) conforms
closely to the concept of gains and is there-
fore encumbered with the theoretical defects
of this concept of profit (see above).
Profit according to method (2) corresponds
to the above-mentioned concept of adjusted
anticipated capital interest. Consequently,
the sum of the period-profits will not be equal
to the ideal profit. 22
Note that these difficulties in Hansen's determination of
income would not disappear even if the future were known with
certainty. We will deal with the problem of uncertainty below
from a different approach.
The Accounting Tradition
"In keeping with the principle that accounting is primarily
based on cost, ... 23 this approach appears to be antithetical to
that presented above. That is, the Fisher Tradition was concerned
with future expectations while accounting, based on cost, is con-
cerned with past acts. The fact that accounting is concerned with
the past is one major source of criticism. If we accept Jevon's
dictum that "in commerce bygones are bygones, this criticism
22Hansen, p. 29.
23Accounting Research and Terminology Bulletins, final edition
(New York: American Institute of Certified Public Accountants,
1961), p. 28.
seems to have validity. However, if there are other purposes for
the measurement of income, e.g. the administration of working
capital, 24 then the criticism can be met by stating a variance in
purposes of the measurement.
In addition, accounting is sometimes criticized because it
is not a valuation method. 5 This depends upon the definition of
"valuation." Moonitz takes the view that the problem is one of
valuation and that cost is one method of expressing value and,
further, it is the desirable method.
Accounting literature of the past quarter-
century is replete with discussions of a
supposed conflict between cost and value
as a leading postulate in accounting. The
preceding discussion has shown that there
can be no conflict because the two concepts
are not co-ordinate. The concept of value
is the major one; cost is one method or
24Devine makes the administration of working capital an explicit
objective of income. That is, income should have something to do
with the ability to pay dividends. See Carl Thomas Devine, "Loss
Recognition, from Accounting Research, VI (October 1955), 310-
320, reprinted in Davidson, Green, Horngren and Sorter, An In-
come Approach to Accounting Theory (Englewood Cliffs, N.J.:
Prentice-Hall, 1964), p. 163.
If one pursues Devine's concept he finds himself in the position
of arguing for the cash basis of income measurement. It may even
further entail the cash position of the enterprise because of the
inability to pay dividends from assets that were once cash.
25"One might say that he Caccountantsj often eschews valuation
entirely. At least, one finds difficulty in the idea that an inventory
is being "valued" when different parts of an inventory of identical
goods are priced differently--as is approved practice." (Simons,
Personal Income Taxation, p. 80, footnote 54.)
formula for expressing value. In many cases,
cost is probably the most useful formula to
follow, but it is still only one procedure. In
brief, the "conflict" raises a false issue.26
Simon objects to calling "cost" valuation because identical
items receive different unit values. The lack of comparability
within the firm is Simon's concern. Accountants are also con-
cerned with identical items receiving different values but their
emphasis is on inter-firm comparability. The deviation in the value
of identical items is the basis of the continuing argument over uni-
formity of accounting principles. If the principles were uniform,
the values would be identical. For example, Mr. Bows criticizes
the lack of uniformity in current accounting practice by positing
two identical firms and noting a value deviation of several hundred
The lack of uniformity in accounting principles and its differ-
ent valuations for identical assets should raise some questions about
"objectivity" in accounting. For example, Mr. Alexander states:
Another very powerful factor operating on
the development of accounting methods has
been the attempt to minimize the accountant's
responsibility for the human judgments which
must be made in passing from a consideration
of the accounts to the conduct of business
affairs. This desire to avoid responsibility
6Moonitz and Jordan, I, p. 169.
27Albert J. Bows, "The Urgent Need for Accounting Reform, "
The National Association of Accountants Bulletin (September 1960),
has led accountants to set up two require-
ments for sound accounting that somewhat
limit the choice of methods. These are the
requirements of objectivity and conservatism. 28
Again, without going beyond the scope of this paper into a philo-
sophical discussion of objectivity versus subjectivity, it would
appear reasonable to cast a doubt upon the "objectivity" of a method
that allows such deviations in the results. If one means by objec-
tivity the verifiability, then cost may be more readily verified than
some subjective value, but it is certainly not "objective."
This point is so often misunderstood that it deserves repe-
tition. Most writers outside the field of accounting consider that
the word "cost" closes the discussion of objectivity. Nothing could
be further from the truth. Most of the writing about accounting
could be classified as explaining what accountants mean by cost
and how it is determined. To state the proposition of "cost" with-
out further explanation is meaningless even to the accountant.
Voluminous tomes have been written concerning the definition of
"cost." Paton has made the matter explicit by criticizing his
colleagues as some of the worst offenders in considering cost ob-
jective. He writes:
Accountants are supposed to be thoroughly
familiar with this situation Cdifficulty of
determining cost] and hence the faith that
some of them seem to have in the objectivity
ZAlexander, p. 128, emphasis supplied.
and reliability of complied cost data is
something at which to marvel. 2-)
Regardless of difficulties of this kind we take the position
that the assignation of dollar amounts to assets is "valuation."
Obviously then, accountants value under r ourr definition. However,
the point is not central to the analysis. If one wants to call what
the accountant does non-valuation, it will not affect the conclusion
of this study.
The notion that present market values are the correct
method of valuation does not have such a body of theory supporting
it as the two previous notions. It is true, that, for example,
It is probably obvious to most people
that market value is the appropriate
measure of well-being associated with
each item of wealth in a man's possession. 30
Nevertheless, Alexander does not support this view in the rest of
his theoretical analysis. His conclusion, as we stated above, is
that there can be different income for different purposes. Several
other writers take a similar position, 31 but none develop a body
29William A. Paton and William A. Paton, Jr. Asset Acc mont-
ing (New York: Macrnillan Co., 1952), p. 54.
30Alexander, p. 137.
31For example, Joel Dean, "Measurement of Real Economic
Earnings of a Machine Manufacturer. Accounting Review, XXIX,
(April 1954), p. 257.
of theory about it with the single exception of Edwards and Bell. 32
Certain accountants also take the position that present
market value is a proper method of valuation. MacNeal, in Truth
in Accounting, set forth this position in great detail in the 1930's.
More recently, the so-called revolution in accounting has been
taking the same position. For example, a recent article takes the
position that valuation of current assets at cost is not only "tradi-
tional" but also "treacherous. "33
The primary criticism against current market value is its
lack of objectivity. This stems mainly from accounting circles
who, subject to Mr. Paton's criticism above, feel that cost is com-
A second criticism of present market value is approached
by the taxation theorists as the distinction between the "ability to
pay" and the "capacity to pay, that is, the "separation problem."
The argument runs that income is not "earned" until it is separated
by receipt of cash. 34 This is very similar to Devine's position on
32E. 0. Edwards and P. W. Bell, The Theory and Measurement
of Business Income (Los Angeles: University of California Press,
1961). However, their interpretation of market value is replace-
ment cost. Also, they utilize an entirely different methodology
and thus their analysis is not pertinent.
33Robert T. Sprous, "Historical Costsand Current Assets--
Traditional and Treacherous, Accounting Review, XXXVIII
(October 1963), pp. 687-695.
34The architect of this view, which is the basis of modern
accounting, is Professor Seligman's argument before the Supreme
Court (Eisner vs. Macomber 252 U. S. 289, 1919) that stock
the administration of working capital. However, accountants are
usually concerned about the capacity to pay dividends, whereas
capacity in this context is concerned with the payment of taxes.
Otherwise they seem to be identical notions. We will discuss this
Professor Boulding seems to be in a class by himself in his
suggestion for the use of a constant. While there are many other
writers in economics and accounting who would agree with the basic
proposition that income is essentially unmeasurable in any com-
pletely unassailable fashion, there are a few who would go so far
as to say that it is so arbitrary that a constant might well be used.
Because of the arbitrary element, Boulding suggests a constant.
All valuation thus seems to possess a
certain unavoidable arbitrary element,
as long as the asset structure remains
heterogeneous....A possible method of
escape from this dilemma is to perform
all valuations at a constant valuation ratio,
independent of the market price.35
Boulding is alone in this suggestion and there is no extant
criticism of his method. We will deal with it below.
dividends are not taxable because they are not "separated. "Sep-
aration" here means clearly the receipt of cash, i.e., the "cash
basis accounting. "
35Kenneth E. Boulding, A Reconstruction of Economics (New
York: John Wiley and Sons, Inc., 1950), p. 45.
Although there is general agreement on the definition of
income, there are four alternative methods of determining "well-
offness" which yield widely varying results. Each of these methods
has supporters and detractors, advantages and disadvantages.
Several authors take the position that the purpose of the income
measurement will determine which of the methods should be used
and that more than one method should be used concurrently.
We will examine the alternative methods below and attempt
to set forth generalized criteria that will allow us to select one
(or more) of the methods as better than the others.
The model used in the analysis is essentially the same as
the one presented by Boulding.36 A cursory review of the neces-
sary assumptions and conditions will be presented below. The
interested reader will find a more complete description by Boulding,
especially in A Reconstruction of Economics.
36Kenneth E. Boulding, Economic Analysis, 3rd ed. (New York:
Harper and Bros., 1955), p. 277 et passim.; Kenneth E. Boulding,
A Reconstruction of Economics (New York: John Wiley and Sons,
Inc., 1950), pp. 39 ff; Kenneth E. Boulding, "Economics and Account-
ing: The Uncongenial Twins, Studies in Accounting Theory, eds.,
W. T. Baxter and S. Davidson (Homewood, Ill.; Richard D. Irwin,
Inc., 1962), pp. 44-55.
In Figure 1 the model is presented in its entirety. "Dollars"
or "money" are measured on the y-axis and "wheat" on the x-axis.
The simplicity of using only two commodities, although money is a
"general" commodity, allows us to picture the "trader"37 in all
possible positions and also to trace the path from one position to
the next. This is the value of the model. In a simple two-dimen-
sional diagram the present position, as well as all past positions
and all possible future positions are presented visually, and cast
the problem of valuation in strong relief. 38
0 I Wheat (bushels)
37Boulding refers to this model as a "pure marketer." "Trader"
has been selected here to differentiate between two kinds of "mar-
keters"--as opposed to "producer. In a later study an inventory
holding marketer --"merchandiser"--will be considered.
38It is also possible, as Boulding shows, to present "negative
wheat" and "negative money, i.e., short selling and debt, by
utilizing two other quadrants. However, the existence of debt or
short contracts, while real and interesting problems for other pur-
poses, are excluded from consideration in this study because they
are only tangential to the central problem.
The Transformation Coefficient
The line in Figure 1 is a "transformation coefficient" or the
market price that exists at the present moment. It defines all the
trader's opportunities in this market. The trader, at the present
moment, can move to any point on this line from M1 to W1 in the
ratio implied by the slope of the curve. Note that the trader cannot
move to any point away from the curve and remain in the market.
This is the difference between this transformation coefficient and
the production-transformation function more generally used in
The model further simplifies considerations by placing
severe restrictions upon the activities of the trader. There are
only two courses of action open to the trader: He can (1) exchange,
or (2) hold (the negative of, or refusal to, exchange). If he is at
some point away from the axes, he can move in two directions:
toward the y-axis (money) or toward the x-axis (wheat). Within
the model there is no provision for additions (savings, investment)
or deductions (consumption or shifting investments). Moreover, the
linearity of the curve implies, and we make explicit, that the trader
39The production-transformation function allows for movements
to points below the curve (toward the origin) by underemployment
of the resources. Under- or un-employment concepts are not
useful in this context of pure exchange and the curve defines all
the possibilities. If commodities are removed or destroyed it
simply moves the curve back toward the origin and changes all
the opportunities by the same amount.
is operating in a perfect market where his decisions do not affect
either the present or future transformation coefficients.40 Thus,
an exhaustive statement of the trader's alternatives within this
market is that he may (1) hold, or (2) exchange along an externally
determined and completely defined route.
The Valuation Coefficient
In order to determine the "net worth" or "total value of
assets"41 when heterogeneous assets42 are held, it is necessary
to express one asset in terms of the other. That is, it is neces-
sary to measure one asset with the other43 in order to sum the two.
In Figure 2 the trader has moved along a transformation curve
(not shown) to point Pl, and we wish to calculate the value of his
net worth. In order to do so we will draw off a valuation curve
(arbitrary in this case) Vm to Vw. 44
40We mean by perfect market simply that the changes in price
are exogenous. The other requirements for a perfect market, such
as perfect knowledge, are not germane so long as the trader cannot
affect the present or future price by his actions.
41The two terms are equal magnitudes since we have excluded debt.
42As we will see below, heterogeneity is not the cause of the
problem, but it is usually stated in this context.
430f course a third "measuring" asset could be used, but this
would not add anything to the analysis; it would simply require a
third dimension on the graph.
44We also assume the valuation curve to be linear. If it is not,
there are serious difficulties from the theory of measurement.
For example, the units are not additive.
0 W1 V
The value of the enterprise can now be expressed as OVm
in money or as OV, in wheat. This is made up of two parts: OW1,
amount of wheat, multiplied by the slope of the curve, and the
product added to OM1 (multiplied by unity since money is the meas-
uring agent in this case) to arrive at OVm, and the same process
for OVw if wheat were selected as the valuing agent.
The problem--and it is the prime problem of this study--
is that the "proper" or "correct" valuation coefficient is not immed-
iately apparent. Indeed, it is the subject of much debate and con-
45We can agree with Boulding when he says:
Without knowing a set of valuation coefficients, there-
fore, we cannot tell whether the point P is "larger" or
"smaller" than P1. ('Twins,"p. 48)
If, then, we are to say whether any given change represents
In a previous section we presented four competing methods
of valuation. The Fisher Tradition; the Accounting Tradition;
Present Market value; and Boulding's Constant. In terms of the
model these are simply different valuation coefficients. Note also
that three of the four valuation coefficients are, have been, or are
expected to be, transformation coefficients. The Fisher Tradition
valuation coefficient is an expected (future) transformation
a gain or a loss, and even more if we are to be able
to measure the gain or loss, we must have a system
of valuation. .. .(Reconstruction, p. 43, emphasis
However, when he says:
It is clear that, as the various transformations are
made and the speculator traces out the path POPI1
P7, he reaches certain positions which are quite
obviously superior to his starting point.... P5 is
unquestionably a preferable position to P0, for it
represents a greater quantity of both assets than
does P0. (Idem.)
it is neither clear, obvious, or unquestioned, that simply because
a position represents a greater quantity of both assets that it
should also represent a preferable position.
A preferred position requires the positing of certain
assumptions about the motive of the trader or his enterprise. It
may be that the trader is trying to maximize something, but it is
not clear that the maximization vector is necessarily in the dir-
ection of a point between the axes. The vector may be along one
axis or nearer one axis than the other. Also, it is difficult to
speak of a superior position without some knowledge of the trader's
expectations, even if we have identified the maximization vector.
If Boulding is speaking only of a greater quantity repre-
senting a greater value, then we must agree, if the valuing agent
has a constant valuation coefficient. Obviously then, a greater
quantity of the valuing agent would yield a greater value so long
as the other commodity's value was not less than zero.
coefficient. The Accounting Tradition is a past (entry, cost)
transformation coefficient and the present market value is the
existing (present) transformation coefficient.
Recognizing this fact we could classify our alternatives as
(1) Using a valuation coefficient that is inde-
pendent of transformation coefficients, or
(2) Using a valuation coefficient that is either
(a) past (b) present or (c) expected trans-
Other Assumptions in the Model
The valuing agent (the commodity selected to express the
total value) will be assumed to have a constant valuation coefficient
(unity). This assumption implies that if money is selected as the
valuing agent, a stable price level is assumed. We will later re-
lax the assumption of a stable price level. In addition, we will
assume that there is no problem in ascertaining the physical quan-
Income Within the Model
In the analysis of the model we will use the generally
accepted definition of income, viz., income is the difference be-
tween wealth at two periods of time plus consumption (dividends
for an enterprise). Specifically, we will value the enterprise's
assets (equal to net worth) at two periods and take the difference.
The limitation of "enterprise income" avoids the problem
of utility measurement since, by definition, an enterprise can have
no wants to be satisfied and hence no "utility." If the trader's util-
ity is relevant to the question of enterprise income, we will assume,
along with Pigou, 46 that the utility varies in the same direction as
the wealth. However, only the "wealth" (value of assets of the
enterprise) will be measured; any adjustment necessary because
of the declining marginal utility of wealth is outside the scope of
Income from a Complete Exchange
If at any time the enterprise has all of its assets in the form
of the valuing agent, the exchange will be defined as "complete."
Following the assumption above--the valuing agent has a valuation
coefficient of unity--the value of the enterprise is unequivocal
when the exchange is complete. Hence, it follows that the meas-
urement of the income is unequivocal between two instants when
the exchange is complete at both instants.
In Figure 3 the trader holds W1 quantity of wheat (the valu-
ing agent in this example) at instant t1 and W2 quantity at t2. The
income of the enterprise is W2 minus W1, for the time tI to t2.
46Pigou states it in different terms: "When we have ascertained
the effect of any cause on economic welfare, we may... regard this
effect as probably equivalent in direction, though not in magnitude,
to the effect on total welfare..." A. C. Pigou, The Economics of
Welfare, 4th ed. (London: Macmillan and Co., Ltd., 1950), p. 20.
There is no problem of valuation coefficients when the exchange is
complete. Note, however, that if the enterprise were at M2 at t2
the problem of valuation coefficient selection is met although the
assets held at t2 are homogeneous.
This is a slight disagreement with Boulding. He states
that the problem arises only when heterogeneous assets are held.
This may mean heterogeneous assets over time, i.e., an incom-
plete exchange, and if so, we agree. However, it is clear that the
assets may be homogeneous at one instant in time without solving
the problem of valuation. Also, if the asset is held in homogen-
eous form over time and is not in the form of valuing agent, the
problem would still arise. The point is that the asset must be
homogeneous in the form of the valuing agent instantaneously and
intertemporally before the measurement can be unequivocal.
Wheat was selected as the valuing agent in the above ex-
ample and we arrived at an unequivocal measure. However, it is
obvious that the valuing agent needs to be more than a chance
selection if the income is to be of maximum usefulness. The
selection of either commodity as the valuing agent is not dictated
by the model; exogeneous criteria must be employed. The selec-
tion will be made below.
Income from an Incomplete Exchange
If the enterprise holds any portion of its total assets in a
form other than the valuing agent, the exchange is defined as "in-
complete." In this case, and only in this case, the problem of
valuing one commodity in terms of the other arises. Thus, the
principal problem of this essay may be stated simply as the prob-
lem of valuing assets under the condition of an incomplete exchange.
It should again be noted that the problem is not one of valu-
ing heterogeneous assets. The valuation coefficient of the valuing
agent has been assumed to be unity, and hence there is no difficulty
in valuation. The problem is one of valuing the other assets) in
terms of the valuing agent.
This entire problem could be avoided by simply waiting
until the "incomplete" exchange became "complete." Thus, the
trivial solution to the problem of income measurement is evident:
Wait until the exchange is complete. The problem arises only
when the measurement is desired prior to the completion of the ex-
change. An examination of this desire--the impetus of the prob-
lem--is beyond the model and requires specific criteria. This
will be discussed below.
A two-commodity trader model has been presented to facil-
itate discussion of the problems of income measurement. Income
was defined as the difference between wealth at two instants in
time and the problem was stated as being the selection of a valu-
We noted that the problem arose only when the measurement
was desired prior to the completion of the exchange. Two subsidi-
ary problems were pointed out:
1. The selection of the valuing agent.
2. The impetus of the desire for the measurement.
The Nature of the Enterprise
In the above section we identified two separate, although
related, problems that arise because of considerations outside the
model. The purpose of this section is to resolve these problems.
However, prior to such a resolution, a general discussion of the
nature of the enterprise and the trader is necessary in order to
make the assumptions and the criteria which follow from those
The Motive Force of the Enterprise
It is clear that the "enterprise, being an inert thing and
an abstraction, can have no motive force. Any motivation imputed
to the enterprise, therefore, must spring, ultimately, from humans.
The question of what motivates humans (individuals or
groups) is one that is the subject of much disagreement and debate.
The "economic man" has long been discredited and utility theory
subjected to bitter attack concurrent with elaborate refinements.
In light of this, the wonder of utility theory is not its fidelity with
reality, but rather its tenacity and resilience. Since Jevons'47
original charge that economics must be grounded in utility, the
concept has been inescapable.
The author, aware of the attacks and personally having
some reservations about its adequacy, assumes that the maximand
of humans, or groups of humans, is utility.
Moreover, this assumption is not restricted to the narrow
notion that utility can arise only by consumption. This, in the
author's opinion, is the basic flaw in the otherwise brilliant works
of Fisher. It appears reasonable to assume that a man can gain
satisfaction from the mere fact of being able to consume rather
than the actual act of consumption. The act of consumption is
generally agreed to be want-satisfying. The problem is one of
timing: Does the ability to satisfy a future want (future consump-
tion) produce the satisfaction of a present want? Fisher's answer
is no; any delay in consumption must be compensated for by future
470r, as Schumpeter would have us believe, since Aristotle.
Joseph A. Schumpeter in Elizabeth Boody Schumpeter, ed.,
History of Economic Analysis (New York: Oxford University
Press, 1954), p. 1054.
consumption that is greater than the present consumption foregone.
The author's answer is yes, because of the declining utility of
present consumption, a delay in consumption may increase the
totality of the satisfactions.
Certainly in the reduction ad absurdum case of zero con-
sumption in the future with 100 per cent consumption now, there
would be greater utility by waiting. It may be true that the con-
sumers' "telescopic faculty is defective, "48 but this does not ne-
gate the fact that if a consumer decides to wait, he will increase
his utility. The command that he has of the future will avoid the
disutility of anxiety in addition to the power, prestige and security
(and accompanying utility thereof) that is accorded him because of
that command. Consideration of these factors can build a strong
case for the willingness of a rational consumer to pay negative
interest in order to insure future consumption. (This is exactly
the situation that the Swiss Banks find themselves in today. They
charge their depositors, instead of paying, interest.) Thus, the
mere fact of being able to command goods and services, regard-
less of whether the command is ever exercised by consumption,
is productive of utility. 49
48Pigou, p. 25.
490bviously, this cursory statement is not intended to refute
Fisher. The intention is simply to make clear the assumptions
of this study by using Fisher as a relief.
Thus, we assume that there are two (relevant) sources of
utility: (1) consumption and (2) command over goods.
Selection of the Valuing Agent
Undoubtedly, it is apparent that money will be selected as
the valuing agent. Nevertheless, we consider it imperative that
we go through the selection process for two reasons: First, to
point up the criteria used for the selection, and second, to clear
up the existing confusion. Surprising as it may seem, the valuing
agent is presently a hotly-debated issue, and further, some writers
shift from one valuing agent to another, apparently without ever
recognizing what they have done.
The selection of the 'valuing agent arises from considera-
tions outside the model. The model of the enterprise has no inher-
ent preference for any particular position or commodity. It is
indifferent. However, if the trader were truly indifferent, as the
model suggests, between the two commodities, we would arrive at
the anamolous position of the impossibility of losses.
Suppose that the trader enters the market with 100 bushels
of wheat and purchases 100 dollars. If the price of money (in
terms of wheat) now goes to zero, the trader still holds the 100
dollars and has suffered no absolute loss. 50 In the same fashion,
501t is true that he has suffered an opportunity loss by not wait-
ing until the dollars could be obtained without the sacrifice of the
wheat, but his position has not been diminished by the price change.
if the trader enters the market with 100 dollars and purchases 100
bushels, and the price of wheat (in terms of money) then goes to
zero, he still holds the wheat and has lost nothing.
The only thing that is being said in the above example is
that the quantity of a commodity held is not affected by a price
change. It would appear reasonable to assert that if the trader has
a given amount of utility associated with a given quantity of a com-
modity and that quantity remained constant, then the utility would
remain constant. That is, if utility is associated with the quantity
of a commodity there is no possibility of diminishing the utility and
hence no possibility of a loss.
Obviously, this is not the case. The trader undoubtedly has
satisfaction from holding a consumable good, such as wheat, but
due to the declining marginal utility of the consumption of a parti-
cular good, his total utility is increased by exchanging for some
good which has a higher utility.51 Thus, the decline in price of a
held good directly causes a decline in the utility of the holder.
Moreover, the magnitude of decline in utility varies directly with
the quantity of the commodity held; the greater the quantity held,
the greater the decline in utility if the price of that commodity
51The exchange will, of course, continue until all the marginal
utilities of all goods have been equated. Cf. any basic economics
It is true that a consumable commodity has an absolute floor
of utility which is positive while the floor of a price is zero. Thus,
in some cases, a price decrease would be greater than the utility
decrease. This is a genuine problem in personal income measure-
ment, but it is not a problem of enterprise income measurement.
When this floor is reached, the "trader" would become a "consum-
er" of the commodity and thus subject to the Fisher analysis.
This problem is avoided in the pre sent analysis for two reasons:
First, the model has restricted the activities to exchanging and
holding, and has excluded consumption; and second, we are here
trading wheat contracts which have negligible consumption
The point is a simple one. The process of exchange out-
side the model increases the utility of the trader qua consumer.
Money is the general expression of the ability to exchange in a
market economy. In an "n" dimensional diagram, the money sur-
face relates all the goods to money which then allows the relation
of all goods to one another. Money is the single numeraire which
performs this relational function and is therefore superior to
wheat as a valuing agent.
It is true that money has no value except in exchange, but,
in the model, the wheat contract has no value except as it relates
to money. Money has value as it relates to all other wants of the
trader, but wheat is one step removed from "value" to the trader
qua consumer. For this reason, money is riskless (assuming a
stable price level) because there can be no decline in its ability
to yield utility, but wheat has a definite risk attached to it since its
ability to yield utility depends on its ability to be exchanged for
For these reasons we draw the obvious conclusion that
money is the superior valuing agent. Money is the general expres-
sion of the command over goods. We assumed above that there
was utility in the very act of being able to command goods, and
here we find money to be the proper expression of the utility, albeit
money increments may not equal utility increments.
The Maximand of the Enterprise. --We assumed above that
the maximand of the trader was utility. Further, we pointed out
that the enterprise's motive force was provided by the trader and
hence could also be stated as the maximization of utility, and then
we concluded that the vehicle for maximization was money. It fol-
lows that the maximand of the enterprise is money or the ability
to command money.
This conclusion is neither startling nor significantly differ-
ent from the more common assumption of profit maximization. It,
however, does state precisely the profit maximization assumption
and leaves no room for, say, the maximization of a quantity of
52Again, the holding of money has an opportunity risk attached
insofar as the trader might miss a profitable exchange, but there
is no risk of any utility decrease if there is a stable price level.
wheat with a zero price.53
The author is aware of the contribution by the empiricists
and behaviorists to motivation theory and the consequent weakening
of the strict interpretation of profit maximization. There is no
quarrel with these contributions in this study. On the contrary,
our total understanding that has been enriched by Burnham's "sep-
aration of ownership and control, Lester's questionnaires, 54
Simon's "satisficing, ,55 Boulding's insistence upon a return to
utility56 and a host of other contributors and concepts.
Three separate (but related) arguments may still be ad-
vanced in spite of these contributions.
53Many authors state the assumption as maximization of "money
profit" (e.g., Alfred W. Stonier and Douglas C. Hague, A Text-
book of Economic Theory, New York: Longmans, Green and Co.,
1953, pp. 87-88), or "financial profits, and in one case at least
"make money" (Lawrence Abbott, Economics and the Modern
World, New York: Harcourt, Brace and World, Inc., 1960,
p. 137). The vast majority state the maximization of profit with-
out a modifier, which leads Boulding to note that "the quantity
which is supposed to be maximized does not exist!" (Boulding,
The Skills of the Economist, Cleveland: Howard Allen, Inc., 1958,
p. 56). Perhaps profit in the abstract doesn't exist, but money
increments do, and that, for better or worse, is our assumption.
54Richard A. Lester, "Shortcomings of Marginal Analysis for
Wage-Employment Problems, American Economic Review,
XXXVI (March 1946).
55Herbert A. Simon, "Theories of Decision-Making in Econom-
ics and Behavioral Science, American Economic Review, XLIX
56Boulding, Skills, p. 28.
First, one can assume cet. par. That is, if all other things
to be maximized or satisficed (e.g., leisure of trader, customer
goodwill, potential entrants and competitors, taxation, empire
building, management-owner -creditor-taxing authority-consumer -
labor conflicts, prestige, etc.) remain constant, it is reasonable
to assume that a larger profit will be preferred over a smaller
Second, if some maximand is not posited, it is impossible
to make either preferential or determinate statements about any-
thing. That is, a theory or construct must be set up about the nature
of the thing described before a meaningful description can be made.57
Without the positing of profit maximization, all of the recent ad-
vances in decision theory, and most particularly in capital budget-
ing, would be invalid. The irony of invalidating decision theory is
that it would no longer be available to help entrepreneurs maximize
profits because of the assumption that they don't maximize profits.
Finally, and most important for this study, is the fact that
we made this assumption only for the purpose of selecting a valuing
57This, it should be emphasized, is not peculiar to, and a limi-
tation on, the social sciences as many would have us believe. It
is equally true of the queen of the physical sciences, physics, as
Caws so eloquently points out. Peter Caws, "Definition and Meas-
urement in Physics, Measurement: Definitions and Theories,
eds., C. West Churchman and P. Ratoosh (New York: John
Wiley and Sons, Inc., 1959), pp. 3-17, esp. pp. 3, 8, 14, 15, 16.
See the section on "measurement" in this study for an elaboration.
agent, a selection which the reader would probably have granted
without the analysis. Once the valuing agent has been agreed on,
the decision model that is presented below can be equally well
utilized for minimizing the money profits if that is what is desired.
The above arguments should not be interpreted as an attempt
to negate other goals of the enterprise. Solvency, for example, is
obviously a prerequisite for the continuity of operations. Thus, if
the objective of continuity of the enterprise exists, solvency is
necessarily a sub-objective of continuity. Likewise, however,
continuity is a sub-objective of money-profit maximization. It may
be necessary to make the objective more precise by adding the
modifier "long-run, '58 but the fact remains that there is "one
overriding goal: the maximization of money profits. "59
Continuity, per se, may very well be the overriding goal
of a sub-group, such as management, but it is inconceivable that
even the managers would continue if there was a "better" (more
profitable) alternative available cet. par. It is certain that the
58This may become a dead issue as the distinction between the
"runs" becomes less clear through further research and refine-
ment. For example, Eirik G. Furubotn ("Investment Alternatives
and the Supply Schedule of the Firm, unpublished paper presented
at the Annual Conference of the Southern Economic Association,
Roanoke, Va., November 15, 1963), takes the position that the
entrepreneur, in a complex industrial society, must constantly be
working in a mixture of "runs" for his investment decision.
59George J. Stigler, The Theory of Price, revised edition
(New York: MacMillan Co., 1952), p. 148.
owner would not continue if there was, cet. par., a better alterna-
tive. In short, the author casts his lot with Berle when he observes:
...it is still true that a non-Statist economic
organization cannot continue to exist and
enjoy power (let alone enhance its position)
unless it makes profits. Therefore the operation
of such organizations must be directed toward
reaping profits, and they must move within the
general limitations of the profit system ....
Increased capital for a corporation means in-
creased power. Capital losses mean loss of
power and eventual extinction. 60
In summary, we assume:
1. The trader's maximand is utility.
2. The raison d'etre of the enterprise is to
maximize the trader's maximand.
3. Utility varies in the same direction as the
ability to command goods and services.
4. Money is the appropriate expression of
the ability to command goods.
5. Therefore, the prime maximand of the
enterprise is money (or ability to
command money) and the correct valuing
agent is money.
The Timing of the Measurement
As noted above, the problem of selecting a valuation coef-
ficient arises only when the exchange is incomplete. The meas-
urement can be stated as two alternative times:
60Adolph A. Berle, Jr., Power Without Property: A New Devel-
opment in American Political Economy (New York: Harcourt,
Brace and Co., 1959), p. 90.
1. The timing of the measurement is
determined by the state of the exchange,
i.e., income is measured (assets valued)
at the time the exchange becomes complete.
2. The timing of the measurement is deter-
mined by an external desire at some
particular instant in time regardless of
the state of the exchange.
Alternative (1) is the trivial solution: since the valuing
agent has a valuation coefficient of unity (by assumption) and the
state of a completed exchange is when the assets are homogeneous
in the form of the valuing agent (by definition), there is no prob-
lem in the measurement of income.
Alternative (2) embodies the significant problems. Indeed
the underlying problem of this study can be stated as a desire for
income measurement when the exchange is incomplete.
The impetus of this desire is obvious: information is wanted.
Information is required because time has reached some specified
instant, because time has elapsed since the last information was
received. Thus, the concept of income has a vital, indispensable,
temporal dimension. The desire for information is the prime
cause of the measurement, and this desire occurs at some instant
in time. We may say then, that time is the fundamental, independ-
ent variable of the measurement of income. The advent of a spe-
cific temporal location triggers the measurement. Moreover,
income is a concept bounded by time; it is within a time interval;
contained between two specified instants of time. Simons has
cautioned against neglecting this relationship:
The relation of the income concept to the
specified time interval is fundamental--
and neglect of this crucial relation has been
responsible for much confusion in the rele-
vant literature. The measurement of income
implies allocation of consumption and accumu-
lation to specified periods. In a sense, it
implies the possibility of measuring the results
of individual participation in economic relations
for an assigned interval and without regard for
anything which happened before the beginning
of that (before the end of the previous) interval
or for what may happen in subsequent periods.
All data for the measurement would be found,
ideally, within the period analyzed. 1
Unfortunately, Simons' charge has been ignored, forgotten or mis-
understood. Neglect of the temporal dimension is still a problem
and confusion is still the result.
Information is desired at an instant in time about the events
within a time period. A measurement is made and the results are
transmitted in accordance with this desire. If the exchange is com-
plete, there is no problem. If the exchange is incomplete, the meas-
urement is made by means of a valuation coefficient. One overall
criterion for the selection of a valuation coefficient is its "infor-
mational content." The valuation coefficient that contains the most
information is the one that should be selected. Thus, our first
Criterion I: A valuation coefficient which yields more
information is superior to a valuation
coefficient which yields less information.
61Simons, Personal Income Taxation, p. 50.
As it stands this criterion is much too general to be of use
in this study. "Information" is a complex concept. In order to
make the criterion applicable to the problem at hand, it is neces-
sary to examine the concept of information in some detail. That
examination is the purpose of the next chapter.
The purpose of this study is to develop a theory of meas-
urement of income for a trading enterprise. Hicks' definition of
income is accepted by most scholars and we will utilize it as a
basic premise in this work.
The problem lies in the various implementations of the def-
inition in the measurement of wealth. There are four competing
concepts of valuation: (1) The Fisher Tradition, (2) The Account-
ing Tradition, (3) Market Value, and (4) Boulding's Constant.
A trading model will be utilized to analyze the problem.
Such a model has the virtue of simplicity and will allow us to pic-
ture all possible positions that the trader can obtain. The activi-
ties of the trader in this model are restricted to holding or ex-
changing along a completely defined and externally determined
route. We call this route the "transformation coefficient."
The position of the trader must be expressed as a value in
order to determine his wealth. We call this value expression the
"valuation coefficient." There are four alternative valuation coef-
ficients, three of which are transformation coefficients:
1. The Fisher Tradition--Future trans-
2. The Accounting Tradition--Past
3. Present Market--Present trans-
4. Boulding's Constant.
When all assets are held in the form of the valuing agent
we will call this "a complete exchange." The valuing agent is
assumed to have a value of unity and thus the income is subject to
an unequivocal measurement under conditions of a complete ex-
change. An incomplete exchange is defined as assets held in a
form other than the valuing agent. Thus, the problem was recast
as selecting the correct valuation coefficient under conditions of
an incomplete exchange.
After a consideration of the nature of the enterprise, money
was selected as the proper valuing agent. This was done by assum-
ing that the trader's motivation is utility. We noted that there are
two sources of utility: (1) consumption and (2) command over
goods. Money is the general expression for command over goods
and is the media for obtaining consumption. The trader furnishes
the motive force for the enterprise, hence the maximand of the
enterprise is money profits.
An inquiry into the reason for the valuation of assets led
us to the obvious conclusion that information was desired prior
to the completion of the exchange. Thus, our first criterion for
selection of a valuation coefficient is the information which it
furnishes. The concept of information is the subject of the next
INFORMATION AND COMMUNICATIONS
In the preceding chapter we pointed out that the general
criterion for the selection of a particular valuation coefficient is
its information content. A possible reformulation of the problem
is as follows:
Determination of the informational content
of the alternative valuation coefficients.
If we could determine the informational content of each valuation
coefficient, we could apply Criterion I and the problem of this study
would be solved. Before this can be done we must review some of
the general characteristics of the concept of information. Such a
review is the purpose of this chapter.
In the succeeding chapter the concept of "measurement"
will be discussed. The two concepts--measurement and informa-
tion--are difficult to delineate in any meaningful fashion, hence
the discussion will overlap at several points. For purposes of
clarity, however, we will attempt to separate the concepts and dis-
cuss them seriatim.
The terms "information" and "communications" are used
synonymously in the literature. 1 We will break with the traditional
1For example, Claude Shannon's pioneering work was entitled
The Mathematical Theory of Communications, (Urbana, Ill.:
usage in an attempt to be more precise. We will use "communi-
cations" as a general term describing the transmission of unevalu-
ated messages. "Information" will be restricted to the description
of useful messages.
If a message is to be useful there are two essential prere-
quisites: (1) verity and (2) relevance. If a message does not des-
cribe reality, it is obvious that its usefulness is, at least, severely
limited. Likewise, the message must be relevant to the problem
under consideration before it can be of use to that problem.2
University of Illinois Press, 1949) and Stanford Goldman's "thorough
discussion of that work" was entitled Information Theory (New York:
Prentice-Hall, 1953). This is because of the simple expedient of
including one's self in the category of those to be communicated
with. The elementary definition is "self-information, and the
theorists conceive of communicating with the self as well as with
other interested parties.
Likewise, in measurement theory the notion is that one meas-
ures in order to communicate with himself as well as with others.
Churchman argues that all measurements fall in the category of
communications. He writes:
Robinson Crusoe cannot bring along his hut as he
searches for a flagstone for his hearth. But he does
need to compare an expreience on the beach with a
past experience in his hut .. .Even if there were but
one mind in all the world, such a castaway would need
to compare the experience of one moment and place
with that of another moment and place. He would have
to communicate with his own past. C. West Church-
man, "Why Measure?" Measurement Definitions and
Theories, eds., C. West Churchman & P. Ratoosh,
(New York: John Wiley & Sons, Inc., 1959), p. 89.
2McDonough describes information as having two basic attri-
butes, validity and value:
The concept of verity may be described as "conformance
with reality. In its simplest form it is nothing more than "truth. "
The nature of reality and truth has been the subject of extended
analysis in the philosophical literature. It is not our purpose either
to resolve or review these discussions. The dispute over what is
"real" as opposed to a "product of the mind" or the Kantian reversal
would lead us too far astray at this point. We will take the easy
way by briefly describing the attributes that are germane to this
Reality is subject to distortion by (1) perception errors and
(2) deliberate misrepresentations. Both are fundamental and both
are intertwined. One can be certain of misrepresentation only if
he is certain of his perception of reality. However, it is easy to
define intent to misrepresent, albeit it may be impossible to prove.
Difficulties of proof aside, we submit that intent to inform rather
Validity implies that one can have confidence in
a statement whereas value indicates that the state-
ment is worthwhile knowing. (p. 87)
Validity in his context must be a synonym for "truth. This is an
odd use of "validity. It usually applies to arguments, not infor-
mation. Perhaps he was also trying to avoid a metaphysical dis-
cussion by avoiding truth concepts. We use verity and explicitly
skirt the metaphysics.
We disagree with McDonough when he describes "validity tver-
ity] as the prime characteristic inasmuch as it is a prerequisite
to value" (p. 87). We see no reason to rank the two attributes.
Irrelevant information is valueless regardless of its verity. Adrian
M. McDonough, Information, Economics and Management Systems
(New York: McGraw-Hill Book Co., Inc., 1963).
than to deceive is a prerequisite of verity and hence of information.
If the intent is to deceive, it should be named misinformation.
Errors of perception are not so easily resolved. There
has been sufficient experimentation to shake one's confidence in
perception reports regardless of the honesty of the reporter. The
classic cases from psychology texts are too well known to be re-
peated here. Suffice it to say that the best intentions do not neces-
sarily guarantee a veritable message.
Our concern is with quantitative data and thus any errors
of perception would be matters of degree. If the intent is to in-
form, but the reporter misperceives the data, there will be some
lack of verity. The usefulness of data that have only a degree of
verity is not amenable to generalization: It would depend upon the
requirements of the specific situation. Note, however, that in the
absence of other information the misperceived report is the only
basis for action and therefore should be classified as "information."
That is, some description of reality is better than none, even if
the description has some degree of error.
Metricians often list errors of perception as one of the
causes of imprecision in measurements. A more complete dis-
cussion is left to a later chapter, but, in this connection, we must
point out that precision has little to do with verity.
"Absolute" precision is impossible to conceive, much less
achieve. Limitations of precision are caused by the instrument
of measurement as well as the perception of the scale by the
metrician. In addition, the limitation of the unit is crucial when
the data are continuous. It is possible to conceive of an "absolutely
precise" measurement in a given unit, but it is always possible to
use smaller units and hence a more precise measure. A given unit
may be halved and then halved again until it becomes very small,
but this unit is always subject to a further fractioning and is, there-
fore, always imprecise in terms of the smaller unit.
This has caused some metricians to complain that no mes-
sage is ever completely veritable because it is never absolutely
precise. We take a more generous and a more pragmatic view.
The message "that water is hot" lacks precision. It may be that
it is so imprecise as to be useless. The state of being useless,
however, is not a result of veritableness (perhaps all would agree
that it was hot) but a result of the lack of precision. The degree of
precision required to be useful depends upon the specific problem-
atic situation. As a warning to a child, "hot" would be enough, but
in a scientific experiment it would not be.
The same could be saidof a more precise transmission,
say, "It is 900F. It is almost certain that the "true" temperature
is different from 90. 000 and thus it may be useless for certain
problems. However, if the transmitter was trying to inform rather
than deceive, we would classify the message as "veritable."
The point is that a message, measurement, may be veritable
but not precise. The contrary condition does not hold. If the meas-
urement is "precise, it is veritable. A measurement that is both
precise and veritable may still be useless, but to be useful, it must
be veritable. Hence, the first information criterion.
Information Criterion I: Messages must be veritable.
One attribute of verity is the
intent of the informant.
The second attribute of information as presented by
McDonough is its "value. We have here selected the word "rele-
vance" to replace "value" because we have already overworked the
latter and, more importantly, we intend to argue that relevance is
a more appropriate term.
A strong case can be made that all information is valuable
simply because it presents the individual with a more complete
picture of reality. At the psychological level, an individual is re-
ceiving information at all times. He is immersed in an environ-
ment which is continually sending messages (stimuli) to his per-
ceptors. One can argue, a priori, that it is valuable for an indi-
vidual to have knowledge of his environment and transitively, all
information is valuable.
The sequence begins with the environment
of the perceiver considered at the level of
The individual does not utilize all the messages which are received
at the ecological level, however. Most of them are shunted off
3\. I. Gibson, "On the Nature of Total Perception, Unpub-
lished Manuscript, p. 10, emphasis supplied.
as "unimportant, "uninteresting, or "irrelevant, and only a few
are allowed through to the reasoning process. The response--if it
is deliberate--will depend upon the selection of the "appropriate"
neurallyy determined) stimuli. This may be visualized in an over-
simplified diagram as in Figure 4.
P contains process Response
The number of appropriate messages is considerably
smaller than the total number of messages sent. The appropriate-
ness of the messages is determined by the problematic situation
in which the organism finds itself. If the organism is hungry, it will
not "hear" (i.e., the message will be shunted aside) the ticking of
a clock. If the organism is interested in getting out of the woods
when it is lost, it probably will not "perceive" the beauties of
nature. One is probably capable of receiving, in some sense,
all the messages, but the particular situation will determine the
relevance and the irrelevant will be sidetracked.
The reasoning process in the organism is set up to handle
problematic situations as they occur. If there were no problems
in the environment, the organism would remain in a state of nir-
vana which would not require responses. The organism is, how-
ever, continually required by changes in the environment to adjust,
respond, so that it will maintain its homeostasis. That is, we may
say that all information is valuable but not all information is rele-
vant to the particular problem at hand. Thus, when Mr. Goldman
The quantitative theory of information which
we have been developing may appear incomplete
and perhaps disappointing to the reader because
it does not treat the value of information. There
are just as many binits in the information which
tells whether John Smith's wife had a boy or a
girl, as in the information which tells whether your
own wife had a boy or a girl.
The question must be the relevance of the information to the re-
ceiver and his problem. If the message that Smith's wife had a
boy was received by Jones, it would be difficult to argue that this
information was completely valueless to Jones, but it is apparent
that it is irrelevant to Jones' problem.
We can sympathize with the information theorists who did
not even attempt to set forth a general theory of the value of
4Goldman, Information Theory, p. 63.
information. It certainly wasn't an oversight, as Mr. Goldman's
statement shows; it was simply impossible. The relevance of the
information to a particular problem will determine its relational
value to the receiver and thus no general statement about value is
Knowledge of the specific problem is required in order to
ascertain relevance. That is, we must state our goal, our prob-
lem, the desired end, before we can make a judgment about rele-
vance. This pragmatic end-directed view is the basis for our
distinction between communications and information.5 All messages
are classified as communications, information is restricted to
those messages which are relevant (useful) to a specified end.
Thus, our second criterion.
Information Criterion 2: Messages must be relevant.
Relevance refers to a particular
The Theoretical Construct. --Knowledge of the problem is
a requisite for relevance judgments, but it is not sufficient. An
additional requirement is necessary, viz., the theoretical construct.
5British theorists employ a distinction between selective infor-
mation-content and semantic information-content. The semantic
content refers to structure and meaning, i.e., communications
qua inter-personal understanding. Compare for example, W. R.
Ashby, Introduction to Cybernetics (London: Chapman and Hall,
1956), passim. Our distinction is problem-directed rather than
In the above diagram the filter-selector is controlled by the reason-
ing process. Messages of search must be sent to the filter-selector
from the reasoning process to determine which of the substantive
messages get through. The reasoning process must then set forth
the criterion of relevance so that it receives messages pertinent
to the problem at hand.
The above can be restated as: The mind needs a theory.
One of the functions of such a theory is to select the relevant data
as well as to arrangethose data in a meaningful fashion. To say that
the world is too complex to be perceived in its entirety has become
a cliche, but it remains true. It is necessary to set up a theory
which rejects the irrelevant complexities and allows one to concen-
trate on the communications that can be handled by the limited
capacity of the mind.
Several philosophers have taken this construct formulation
one step further, and argue that the conception is a prerequisite of
the information. Caws writes:
Cassirer makes the point that all measure has
to be "conceived and sought" before it can be
found in experience, i.e., one has first a con-
cept of some quality and looks afterwards for
quantitative expressions of it.6
Peter Caws, "Definition and Measurement in Physics, in
Measurement: Definitions and Theories, eds., C. West Churchman
and P. Ratoosh (New York: John Wiley & Sons, Inc., 1959), p. 8.
The conception comes first and then the information. Some psy-
chologists would argue that the "beginnings" of concept formulation
are from observations. However, they are talking about the devel-
opment, from infancy, of the reasoning process and are not quarrel-
ing with the central point of Caws' assertion.
Hempel devotes an entire book to the primacy of concept
formulations. He goes through an interesting reduction ad absurdum
argument in which he calculates the "hage" of every member of the
Concepts with empirical import can be readily
defined in any number, but most of them will be
of no use for systematic purposes. Thus, we
might define the hage of a person as the product
of his height in millimeters and his age in years.
This definition is operationally adequate and the
term 'hage' thus introduced would have relatively
high precision and uniformity of usage; but it lacks
theoretical import, for we have no general laws
connecting the hage of a person with other char-
Hempel does not say that the hage of a person is not information;
he simply proves that it has no known theoretical import. That is,
hage is a communication which is not relevant to any extant theory
and, therefore, is without value in any problematic situation.
Koivisto delineates facts and observations in his discussion
of a theory.
7C. G. Hempel, "Fundamentals of Concept Formation in Em-
pirical Science, International Encyclopedia of Unified Science, II,
No. 7 (Chicago: University of Chicago Press, 1952), p. 46.
How important a theory is to our understanding
cannot be overemphasized. In fact, we cannot
assert that something is a 'fact' unless we have
an adequate theory. Without a theory we have
only observations. .. Facts do not consist merely
in observations; they consist in a strategic com-
bination of observation and theory. 8
"Facts" for Koivisto do not exist separate from a theory; "obser-
vations" do, but are without value to our understanding. In our
terminology the facts are "relevant information"; observations are
The functions of a theory are (1) to select the relevant infor-
mation from a myriad of complex observations and (2) to arrange
the information in comprehensible combinations.9 The former is
the basis for our proposition.
8William A. Koivisto, Principles and Problems of Modern
Economics (New York: John Wiley & Sons, Inc., 1957), p. 13.
90f course this is a theoretical construct about theoretical con-
structs on which disagreements are legion. There are many differ-
ent schools on the nature and functions of theories. All of them,
however, except the pure positivists, would accept this statement.
The pure positivists would insist that the selection of data was a
"result" instead of a "function, but they would not deny that induc-
tive theories eventually serve as selectors. For example, compare
Alfred J. Ayer, Language, Truth and Logic (New York: Dover,
1946). N. R. Campbell is not as "pure" a positivist as Ayer and he
freely admits the primacy of construct.
For less general discussions that are specifically directed
toward the social sciences, see Robert K. Merton, Social Theory
and Social Structure, especially Chapter 9 on collective terms.
On economics, see for example, J. N. Keynes, Scope and Method
of Political Economy (London, 1890); Joseph Schumpeter, Economic
Doctrine and Method (New York, 1954); T. W. Hutchison, A Review
of Economic Doctrines, 1870-1929 (Oxford, 1953); Alan G. Gruchy,
Modern Economic Thought (New York, 1947). Specific criticism of
operationalism may be found in Andreas Papandreous, Economics
Information Proposition 1: The theoretical construct
is the locus of the criterion
The quantitative theory of communication is a solution to an
allocation problem. Messages are outputs that have costly inputs.
The problem is to maximize the quantity of information and mini-
mize the cost of that information. That is, the scarcity and con-
current allocation-efficiency problems are met. Shannon's work
was an attempt at a general solution to this problem.
As Goldman points out in several places, information theory
measures "the quantity of information, not its value. "10 More
directly, communications theory assumes, for purposes of the
theory, all information to be valuable and the attempt is to maxi-
mize the amount available. In the quote about the sex of the child
(supra p. 54) the number of "binits" in a particular message is the
important datum with no method of ordering those binits by value.
Regardless of this serious limitation, the concepts and terms of
as a Science (Philadelphia, 1958), and Fritz Machlup, "Operational
Concepts and Mental Construct in Model and Theory Formation, "
Giornale Degli Economists Annali di Economia, September 1960,
10Goldman, Information Theory, p. 300.
quantitative communication theory are helpful in the present con-
The prime difference between communications theory in
this context and the psychological view presented above is the
spatio-temporal separation of the environment and the receiver.
Contrary to the psychological situation where the receiver is im-
mersed in the environment and continually receiving unlimited
messages without cost, the receiver in this situation has a cost
and/or a limitation attached to the binits received. It may be help-
ful to visualize this as follows:11
Environment Transmitter Channel Receiver
This diagram is useful because it points up two important facets in
l1This is a simplification of Shannon's presentation. He set up
five basic elements: (1) Information Source; (2) Transmitter; (3)
Channel; (4) Receiver; (5) Destination. (Claude Shannon and Warren
Weaver, The Mathematical Theory of Communications (Urbana, Ill.:
University of Illinois Press, 1949), p. 5.
1. The limitation of the channel, or conversely,
the additional cost of increasing the channel
2. The selection of relevant information has been
shifted from the internal logical process
(theory) of the receiver to the transmitter.
The limitation of information imposed by the channel capac-
ity is all the more reason for insisting on the relevance of the in-
formation to be transmitted. Suppose that the channel was limited
to x binits of information and there were two messages to be sent,
both containing exactly x binits. A choice is enforced but there is
no criterion in communication theory for making that choice. For
example, if the two messages were:
(1) The sex of Smith's child is a boy.
(2) The sex of Jones' child is a boy.
There is no way of choosing which message to transmit unless the
transmitter knows the identity of the receiver. In more general
terms, the transmitter needs to know the problem of the receiver
before he can make an intelligent choice of the message to be
An obvious "solution" to the problem is either to reverse
the origin of the message or to select one randomly and wait for
the "feedback." Note, however, that this solution solves the "prob-
lem" by denying the existence of the problem. Admittedly, feed-
back is a valuable method of controlling transmissions, but note
that it utilizes some of the channel's scarce capacity. Thus, it
would either require the addition of capacity and the corollary costs
or the omission of at least part of the substantive message. The
solution is trivial because it disregards the constraints which are
the cause of the problem. 12
The limitation of channel capacity places an extremely
heavy burden on the transmitter. This is the problem that the news-
caster faces daily. He has a severely limited channel (time) and
must select for transmission from a vast array of things, all of
which may be classified as "news." His problem is compounded by
having a great many receivers with a wide variety of interests
(purposes) and hence the "value" (relevance) of the information
selected will probably be different for each.
It is appropriate to reiterate that quantitative information
theory is of no help in the newscaster's dilemma. For example,
assume that the probability of a presidential assassination is great-
er than the probability of snow in Miami Beach. The calculation of
12This is precisely the author's reaction to the "Different in-
comes for different purposes" notion. If it is economically feas-
ible for each receiver to feedback his particular "purpose" and
then the transmitter to prepare and transmit all of the information
requested, there is no problem. If the channel has such a large
capacity, and the corollary large costs, the non-problem has
been solved in such a trivial fashion that it should never have
the quantity of information is determined by the formula:13
I(x) = -log2P(x)
Here P(x) is the probability of event x occurring and I(x) is the
measure of the quantity of binits. Thus, the smaller the probabil-
ity the greater the number of binits. On this basis, snow in Miami
Beach would be transmitted. Obviously, something is wrong. The
quantity I(x) needs a "valuation coefficient" based upon the relevance.
Also, as above, feedback is not the solution. In addition to
the capacity constraint, there are two other criticisms of feedback.
First, the old saw that "nothing is as dead as yesterday's
news" is an indication of the time value of information. Since feed-
back requires the additional time necessary to transmit at least
two additional messages, the value of information obtained through
feedback is considerably less than that obtained in the initial trans-
mission. It is true that feedback may aid the newscaster in devel-
oping a criterion of relevance for use in the future, but the immed-
iate use of feedback is the result of either wrong or incomplete
data in the transmission. That is, feedback is used to correct
errors and obviously it would be better to avoid errors.
The second criticism of feedback is even more fundamental.
Feedback is a function of the information possessed by the receiver.
13H. Bierman, L. Fouraker, R. Jaedicke, Quantitative Anal-
ysis for Business Decisions (Homewood, Ill.: Richard D. Irwin,
Inc., 1961), p. 308. In this work, I(x) is called the "value" of
information. They use value in its mathematical sense; it means
"quantity of binits. "
If the receiver has inadequate information, he is very likely to ask
the wrong questions. For example, suppose that Jones receives a
message informing him of the sex of Smith's child. If Jones did
not know that his wife was pregnant, he would have no basis for
feedback. In the case of our newscaster, the receivers do not ask
specific questions, such as "Was the president assassinated today?"
or "Was there snow in Miami Beach?" The number of such ques-
tions is infinite and the capacity is finite. The question that the
receivers implicitly ask is, "What's new?" and the transmitter
makes the judgment. If all the transmitters decided to transmit
snow in Miami Beach and omit the assassination, it is extremely
unlikely that any receiver would feedback a question about the un-
known assassination. It is clear that in such a case the transmit-
ter(s) have complete control over what they transmit and therefore
have a high degree of control over the feedback. The transmission
determines the knowledge of the receiver and thus delineates the
area that feedback will be concerned with. Reliance upon feedback
as a criterion of relevance is thus clearly impossible.
The conclusion is inevitable: In a communication system
the criterion of relevance is located at the transmission source.
The transmitter must select what is to be transmitted. 14 Thus,
14This is not an attempt to justify such a situation. We can note
the Cybernetics situation in which a low-energy information system
has absolute control of a high-energy power system and join with
Parsons in viewing the analogous social systems with alarm. We
can join with the general outcry against the manipulation possible
our first communication proposition.
Communication Proposition 1: The locus of the theoretical
construct (which determines the
relevance criterion) is at the
The above proposition is concerned only with the locus of
the relevance criterion at the time of transmission. A legitimate
question can be raised about the origin of that criterion. It is nec-
essary for the transmitter to possess the criterion, but how does
he come by it? Does he ask the receiver? If he does, he will
utilize some of the scarce channel capacity, but, more importantly,
he is very likely to get different answers from different receivers
and thus be in no better position than before. That is, the receivers
are likely to have different purposes and different levels of sophis-
tication which will result in a wide variety of requests.
The "ask the receivers" notion makes the implicit assump-
tion of de gustibus non disputandem and this should be examined.
in the discretion allowed the transmitter and deplore the nefarious
effects of an ill-motivated transmitter. The above analysis is an
attempt to present the inevitable result of a limited channel com-
munication system. Although the purpose and methodology is dif-
ferent, our conclusion is, at the core, the same as Carr's, "Prop-
aganda is as essential a function of mass democracy as advertising
of mass production, (Edward H. Carr, The New Society (Boston:
Beacon Press, 1957), p. 69) and we join with him in his reluctance
to announce such a conclusion. The broad social consequences of
that conclusion are beyond the scope of this essay.
This assumption would not allow us to ask about the origin of the
construct. Instead, it takes it as a given datum and proceeds from
there. The notion is pervasive in present society and is given an
honorific aura by associating it with other honorific terms like
"democracy" and "consumer sovereignty." We could agree that if
tastes were given--original with the individual--a strong case could
be made for not tampering with those tastes, and this could be done
in the name of democracy. However, this ignores completely the
philosophers', semanticists', social psychologists', sociologists',
and cultural anthropologists' insistence that such tastes are "soc-
ialized, "acculturized, "environmentally determined, "linguis-
tically determined, and so on. In short, learned from the cultural
milieu in which the individual finds himself.
The newscaster who currently spends a considerable portion
of the channel capacity reporting football scores is responding to
the relevance criterion of the receivers. The reason that he does
not report chess or bridge results is that the receivers are not
"interested" (irrelevant). One finds this interest in football a little
strange since there are certainly a great many more bridge players
(and therefore people who are actively interested in bridge) than
football players. In another culture the capacity would be used for
chess, cricket, bull fights, or opera for the same reason, i.e.,
receiver's interests. The result is not commonly recognized. By
broadcasting football scores, the transmitter is continuing the
interest of receivers in football. The transmitter is a significant
part of the cultural milieu from which the tastes are learned.
Transitively, the transmitter is, to a large extent, the determin-
ant of tastes.
In the particular case at hand, no one would deny that the
receiver has an extant construct. However, this construct was
learned previously in some sort of an education-communication
process. If we now ask the receiver what his construct is in order
for the transmitter to establish a criterion of relevance, we have
made a circle which is not complete, but certainly it is vicious. 15
The moral is clear. The transmitter plays a major part in
concept formation whether he likes it or not. He is forced into the
position of making a choice between alternative roles:
1. Reinforcing the current construct by
transmitting in accordance with it.
2. Changing the construct.
The escape alternative of being neutral is not available. A posi-
tion of neutrality is a positive decision to continue the current
15This is the position of certain income transmitters. For ex-
ample, Carl Nelson (unpublished paper presented at the annual
meeting of the Northeastern Accounting Association, New York,
April 18, 1964) suggests that we survey the users of accounting data
and the results be used as a criterion of relevance. It is almost
certain that the responses would be interpreted as evidence for the
status quo because the construct of the receiver has been previously
(partially) determined by the transmitter. Mr. Nelson further sug-
gests that the survey should not include alternative concepts because
of the introduction of bias. What he must mean is that the survey
be biased in favor of the status quo by the process of the trans-
mitter giving the receiver only one "alternative."
construct. The refusal to make a decision is, ipso facto, a decis-
ion to continue the status quo. Thus, the transmitter must select.
Communication Proposition 2: The transmitter must choose
the appropriate theoretical
Proposition two does not solve any problems. On the con-
trary, it creates very knotty problems which were previously
thought to be non-existent by the "neutrality of transmissions."
These problems may be roughly divided into two categories:
1. The transmitter and the receiver
with different constructs.
2. Receivers with a variety of constructs.
In the first case, the transmitter must know or be able to
determine the receiver's construct. If the transmitter does not
know that the receiver has a different construct, he has no prob-
lem. If, however, the transmitter knows that the construct of the
receiver is different, the problem must be faced. The transmitter
may then elect to transmit information in accordance with either:
1. The receiver's erroneous construct. 16
2. The transmitter's correct construct.
16Presumably if there is a difference in constructs, the trans-
mitter considers his correct and the other erroneous. If he did
not, and were rational, he would accept the receiver's construct
and there would be no difference and no problem.
The consequence may be:
A. Erroneous decision either from:
1. Using the wrong information in the
wrong construct, or
2. Using the right information in the
B. Correct decision which can come only from
using the right information in the right
However, consequence B has been ruled out. The receiver has
the wrong construct by definition of the problem. Still, it is
tempting to prove syllogistically that the only way to get correct
decision is with correct information and thereby decide that issue.
Unfortunately, the world is not that simple. It is very likely that
the degree of error in the erroneous decisions varies with the infor-
mation received. It is quite possible that the wrong information
in the wrong construct will yield a more correct decision than the
right information in the wrong construct. This is a melancholy
fact that cannot be avoided. No simple criterion can be laid down
for the solution of the problem. Instead, it must rest in that nebu-
lous area of personal judgment.
One word of warning is in order however. Disciplines often
become so introverted that they think technical terms are broadly
understood. Scientists are inclined to impute understanding to
people who are outside of the reference group which normally em-
ploys the term. We are likely to become provincial enough to think
that our everyday language is intelligible to everyone simply because
of our facility. Upon reflection we would all deny that other groups
understand our terms, particularly if we have recently tried some
interdisciplinary communication. Nevertheless, a physicist and an
economist, for example, will liberally sprinkle their communica-
tions with "entropy, "utility, "equilibrium, "acceleration, and
similar terms when it is clear to a third party that the referent for
these symbols is vastly different for each. 17
In the second case--receivers with a variety of constructs--
the problem is one of maximizing the total information received.
Once again, however, upon analysis, this raises some unresolvable
problems. Is one maximizing information when the largest number
of receivers can utilize the information or when a smaller number
of receivers can more fully utilize the information?
Both approaches are taken in practice. Several years ago
the Air Force issued a communication memorandum which forbade
the use of some words (e.g., feasible, orient, secular) because
17This basic fact is often forgotten by accountants who argue
that a change of income measurement would not be understood by
the receivers. At the same time they lament the fact that such
well-worn words as "depreciation, "surplus, "reserve, "asset,"
"expense, are not understood in their technical sense by the re-
ceivers. It is clear that misunderstanding now exists, yet they
resist change, not because of fear of more misunderstanding, but
because they think it would cause misunderstanding!
this eliminated a number of receivers. Obviously, one could push
this principle to the absurd. If the number of receivers is the sole
criterion we can continue to omit "difficult" words until we have
been reduced to grunts or sign language. Since a large vocabulary,
including jargon, enriches the communications of individuals, there
is a sacrifice made each time a receiver is added. This can be
visualized as a "demand curve, in Figure 6.
R u \
W U \
Number of receivers
The marginal receiver determines the level of enrichment and
results in an "enrichment deficit" of all previous receivers. It
would be nice now if we could measure "information" on the y-axis
and pull off the marginal information curve and stop adding receiv-
ers when it crossed the x-axis. The difficulty is that "enrichment"
is not amenable to "binit" analysis so that the exercise would be
The curve illustrates the opposite extreme also. As com-
munications become richer, the receivers are cut off untilthere
is only one receiver left. Both extremes are undesirable except
in rare cases. We might want to communicate to all receivers on
occasion, such as civil defense warning, or only to one in a highly
personal situation. Unfortunately, the vast majority of communi-
cation problems fall between these extremes. Churchman makes
the point nicely.
In sum, the language of measurement does
entail a decision problem. The more precise
a language the less broadly is it understood.
To put it otherwise--if one wanted to be cute
about it--the clearer a language the more con-
fusing it is to most people. Precise languages
narrow the class of users but increase the de-
gree of refinement that any user can attain.
The proper balance between breadth and depth
is the linguistic decision problem of measurement. 18
The final criterion for this situation will be, at least in part, deter-
mined by the theoretical construct in which the information is
applied. Obviously, if the construct specifies precision that is not
available, our level of confidence in the outcome will be lowered.
If we pursue this, however, we will simply begin a search for a
criterion for confidence levels and eventually wind up in an infinite
regression. Suffice it to say at this point that we have pointed up
the language problem without solving it.
One implication of both problems--different construct and
different receivers--is the need for the use of at least some of the
channel capacity for educational purposes. If progress is going to
be made, erroneous constructs will have to be replaced and the
18Churchman, "Why Measure, p. 87.
sophistication of the receivers will have to be raised. Clearly, an
allocation of channel capacity to this function has a high priority.
Higher than the communication of binits if those binits are to pro-
duce dangerously erroneous decisions. Perhaps not so high if they
produce only slightly erroneous results. This is a difficult judg-
ment for the transmitter, but it must be made.
We agree with Ogden and Richards. As early as 1923 they
The old view that the only access to a subject
is through prolonged study of it, has, if it be
true, consequences for the immediate future
which have not yet been faced. The alternative
is to raise the level of communication through
a direct study of its conditions, its dangers and
its difficulties. The practical side of this under-
taking is, if communication be taken in its widest
sense, Education. 19
Thus, our third proposition.
Communication Proposition 3: Education has a high priority
in the allocation of channel
Binit Maximization. --Once all the requirements set forth
above have been met, we can return to the simpler problem of
maximizing the number of binits. We agree with the implicit
assumption that cet. par. binits should be maximized, but we
19C. K. Ogden and I. A. Richards, The Meaning of Meaning
(New York: Harcourt, Brace and Co., 1948), p. x.
consider verity and relevance to be essential prerequisites.
Recognition of these prerequisites presents us with some problems
which communications theory in its present state cannot handle.
The theory in its present state is concerned with economiz-
ing channel capacity by statistical theorems. It allows one to
maximize the binits transmitted under various channel conditions--
noisy, lossy, etc. This is a great contribution, but we note
Brillouin's warning as well as his hope.
Information has received a purely statistical
definition from which all human elements are
excluded: moral import, scientific significance,
artistic quality, even speculative value in busi-
ness...Not one of these concepts, essential
though they are to the usual meaning of the word
"information, comes within the ambit of our
definition... It is essential to emphasize these
restrictions, which correspond to the present
state of affairs in the theory. We may hope
one day to be able to discard these barriers
but we cannot, at the moment, foresee how it
will be possible.20
Unfortunately these restrictions have not always been
heeded. Guilbaud cites cases where popularizers have calculated
the "worth" of a daily newspaper" and finds it to be a hundred
thousand hartleys."21 ("Hartley" is a binary choice.) He points
out that it is "absurd" to make such calculations and that communi-
cations theory was not designed for this purpose. For this reason,
20Quoted by G. T. Guilbaud, What is Cybernetics? (New York:
Criterion Books, 1959), p. 59.
21Ibid., p. 60.
it is clear that we cannot meaningfully calculate the binits per
message for each valuation coefficient. On the other hand, it is
clear that, if we could specify the problems and constructs of the
various receivers, we could make some relational judgments about
the competing concepts. Once this has been done, we can then
maximize the information per message without cardinally meas-
uring the binits.
The concept is both simple and familiar.
...information in cybernetics is not concerned
with what we actually say in our messages, but
rather with what we could say. What is of interest
to our theory is the choice, the range of possible
The theory of choice is not an unfamiliar topic in economic tracts.
Rogers brings this even closer to home by an analogy.
Just as entropy of a source was likened to the out-
put of a steel mill, so, as Shannon has remarked,
can capacity of a channel (in bits /signal or bits/
second) be likened to the maximum load capacity
of a conveyor belt (in tons/day). If entropy (steel
output) is below channel capacity (belt capacity) we
know that the information (steel) produced can be
satisfactorily transported, provided that it is
properly coded (cut up, arranged and packed onto
the moving belt).23
We can speak of more or less steel without ever measuring it or
even specifying what a ton is. We can conceive of flexible capacity
and minimize it without measuring the output.
2Ibid., p. 59.
23Hartley Rogers, Jr., "Information Theory, Mathematics
Magazine, XXXVII, No. 2 (March 1964), p. 73.
This is the framework which we will utilize below when we
speak of binit maximization. In our context it is an unspecified
unit that we use to order or rank the quantity of information.
It has been pointed out that a desire for information was
the impetus for a measurement prior to the completion of the ex-
change. This necessitates a discussion of the concepts of infor-
mation and communications.
We defined communications as unevaluated data and restricted
information to useful data. Information, so defined, has two funda-
mental attributes. It must be veritable and relevant. Verity re-
fers to "conformance with reality" but for our purposes the intent
of the transmitter is the overriding requisite. Relevance refers
to the applicability of data to a particular problem. Theoretical
constructs serve the function of specifying what data is relevent.
In communications there is a spatio-temporal separation
of the transmitter and receiver. This results in a shift of the cri-
terion of relevance from the receiver to the transmitter. Thus,
the transmitter must select the appropriate construct. This
causes some difficult problems for the transmitter and necessi-
tates the allocation of some capacity to the explanation of the con-
structs. In the succeeding analysis we will utilize the terms and
concepts of communication theory without necessarily assigning
them numerical values.
One obvious conclusion of this discussion is that we must
carefully spell out the theoretical construct(s) appropriate to the
trader model before we can make informational judgments about
the various valcos. Luckily, there is no controversy over the
correct constructs in our simple model. We will present them
This chapter has been unable to avoid completely the prov-
ince of measurement theory. A more complete discussion is the
object of the next chapter.
The purpose of this study is to develop a theory of the
measurement of enterprise income. It was noted that the impetus
of the measurement was a desire for information and the first
criterion of "informational content" was developed. Thus, we
discovered the cause of the problem--to provide information--but
we neglected the question of why provide "measurement-type"
information. There are other kinds of information--e.g., "quali-
tative"--that could be provided and there is no a priori reason
for deciding on the measurement type. An examination of that
question and a review of the concept of measurement is the pur-
pose of this chapter.
The Definitional Dispute
A burgeoning literature on metrics has appeared in recent
years. Much of it has been concerned with the proper definition
of measurement and a major debate has arisen. The term "meas-
urement" is defined and used by physicists, psychologists and
philosophers of science sometimes in strikingly different, some-
times in subtly different ways. Whoever expects to find a single,
well-established definition current among specialists in all these
fields will be disappointed. Disputes as to the possibility of the
"measurement of sensations" (sensory events) have been suffic-
iently acute, so that one learned society--The British Association
for the Advancement of Science--appointed a special committee
to study the matter. This committee devoted much of its time to
a discussion of the meaning of the term "measurement. It has
been said that "they came out the same door that they went in."
Its reports revealed striking disagreement among its members. 1
In a passage which probably contains reference to the work
of this committee, Campbell (a physicist), who served briefly as
a committee member, says:
A philosopher will suppose that the logical
analysis of measurement is familiar to every
physicist who actually measures, and he will
not expect me to say anything that is not to be
found in every competent textbook. He is
reminded therefore that most physicists have
a horror of logic and regard an accusation
that their doings conform to logical principles
as a personal insult. The most distinguished
physicists, when they attempt logical analysis,
are apt to gibber; and probably more nonsense
is talked about measurement than about any
other part of physics. When an international
congress meets to discharge the dull but
necessary duty of finding the conventions of
measurement (which duty it performs admirably),
a flood of incomprehensible verbiage about
1A.Ferguson, et al., "Quantitative Estimates of Sensory
Events, British Association for the Advancement of Science,
1938: pp. 277-335, and 1939-1940: pp. 331-349.
'units and dimensions' is let loose, which
leaves everyone even more muddled than
they were before. The only conclusion that
can be drawn from 'competent' textbooks is
that there are no principles of measurement. 2
Opinion as to the nature of measurement may be divided
roughly into two categories. On the one hand, there are those
writers (few psychologists or psychological philosophers are
found in this group) who maintain that only those dimensions which
permit a physical operation of addition are measurable. On the
other hand, there is a small but prolific group (physicists or
physical science philosophers are rarely found in this group) who
deny that this is a requirement for a measurable dimension. Fol-
lowing Stevens3 we will refer to the former as the "narrow view"
and to the latter as the "broad view. However, we use these labels
as a shorthand description of the two views, not in any pejorative
Several broad views of measurement may be distinguished
but the differences among the writers in the broad view are much
less than the difference between the two groups. Stevens is prob-
ably both the broadest and the most prolific writer on measurements.
2Norman R. Campbell, "Measurement and Its Importance for
Philosophy, Aristotelian Society Supplement, Vol. 17, 1938,
3".. some practitioners of the physical sciences prefer to
cling to the narrower view..."
S. S. Stevens, "Measurement, Psychophysics and Utility" in
Churchman, Measurement: Definitions and Theories, p. 19.
Hempel differs in some fundamental, some minor, ways but still
may be classified as broad.
By contrast, differences among those writers who hold
the narrow view are of a minor, often minuscule, character. We
can say with little fear of distortion that there is only one narrow
view of measurement. N. R. Campbell is the architect of this
view and probably the most important single writer on the subject.
The fundamental treatise is his Physics: The Elements. Other
writers who follow him are Nagel, Bergman, Pap, Guild, Caws
and a host of others.
Resolution of this debate is beyond the scope of this study
and also beyond the ability of the author. One is tempted to
plague both their houses. The broad view is sometimes so broad
that it fails to offer any distinction between measurement and a
host of other activities while the narrow view is sometimes so
narrow that it would exclude every dimension except length and
weight. For example, Stevens holds that "...the assignment of
numerals4 to objects or events according to rule--any rule" is a
4In another context, Stevens says: "Measurement is...in its
broadest sense...the assignment of numerals to objects or events,
according to rules." S. S. Stevens, "Mathematics, Measure-
ments and Psychophysics, Handbook of Experimental Psychology,
ed., S. S. Stevens (New York: John Wiley & Sons, 1951), p. 23a.
Campbell says: "Measurement is the process of assigning
numbers to represent quantities...." Norman R. Campbell,
Physics: The Elements (Cambridge: Cambridge University
measurement.5 Upon first encounter with this definition it is
tempting to present a reduction ad absurdum rule and ask Stevens
if the results are measurements. This would be of no effect,
however, because Stevens lists as examples of "measurements"
things that are intuitively absurd. It is quite likely that everyone
who has not been influenced by Stevens would agree that it is ab-
surd to call the numbering of football players a measurement. It
violates a well-worn, if ill-defined, linguistic concept that is
common to almost all members of the community. Yet Stevens
lists the "numbering of football players" as a measurement on a
Press, 1920), p. 267.
The strongest reason for saying that measurement is the
assignment of numbers, rather than numerals, has been nicely
stated by Hempel. He says that "quantitative or metrical concepts
or briefly quantities...attribute to each item in their domain of
applicability a certain real number, the value of the quantity of
that item. In a footnote to this passage, he points out that it
would be improper to speak of the attribution of numerals, rather
than numbers, for the following reason:
"... the values of quantitative concepts have to be con-
strued so as to be able to enter into mathematical
relationships with each other, such as those expressed
by Newton's law of gravitation, the laws of mathematical
pendulum, Boyle's law, etc.; ...and all these operations
apply to numbers, not to numerals. Similarly, it is
impossible to speak significantly of the distance, or
difference, of two numerals."
C. G. Hempel, "Fundamentals of Concept Formation in Empirical
Science, International Encyclopedia of Unified Science, Vol. II,
No. 7 (Chicago: The University of Chicago Press, 1952). The
text reference is to page 55. The footnote, footnote 61, is found
on page 85. We will ignore this nicety and use the two terms
interchangeably in this work.
5Stevens in Churchman, Measurement: Definitions and
Theories, p. 19, emphasis supplied.
"nominal scale. "
Stevens notes our objection but he implies that it is of no
The nominal scale is a primitive form, and
quite naturally there are many who would
urge that it is absurd to attribute to this
process of assigning numerals the dignity
implied by the term measurement. Certainly
there can be no quarrel with this objection,
for the naming of things is an arbitrary busi-
ness. However we christen it, the use of
numerals as names for classes is an example
of the 'assignment of numerals according to
But the absurdity objection is important. We hesitate to call a
nominal scale one of measurement, in either scientific or ordi-
nary parlance, because its values do not represent the order or
rank of the objects scaled. To assign numerals to football play-
ers is simply to give them convenient names. Surely measuring
is to be distinguished from naming. If not, the author is reminded
of Charlie Brown's new neighbors who were named numbers. If
Lucy was familiar with Stevens' work she could say that the
mother measured the children. One child was measured twenty-
three, all were measured numbers. The substitution of "named"
6Stevens in Churchman, Measurement: Definitions and
Theories, p. 25, Table I.
7S. S. Stevens, "Mathematics, Measurement and Psycho-
physics, Handbook of Experimental Psychology, ed., S. S.
Stevens (New York: John Wiley & Sons, 1951), p. 26a, and S. S.
Stevens, "On the Theory of Scales and Measurement, Science,
Vol. 103, 1946, p. 679a.
for "measured" is required before the preceding sentence makes
sense. Surely "measured" and "named" are not synonyms regard-
less of how hard Mr. Stevens tries to make them so.
A common method of coding is to substitute numbers for
names according to a rule. Under the nominal scale this is a
measurement but of what dimension? What dimension does the
Social Security Office measure ? Stevens says that
The oft-debated question whether the
process of classification underlying the
nominal scale constitutes measurement
is one of those semantic issues that de-
pends upon taste.8
The dimension question shows this is not true. Stevens' defini-
tion is useless in addressing the question of which dimensions
are measured and which dimensions are capable of being meas-
ured. Whether a given definition has this important use is neither
a "semantic issue" nor a "matter of taste. "
Except for Stevens' nominal scale, 9 all writers agree that
some dimensions (properties, characteristics) can be measured
and that some cannot. All agree that weight and length can be
measured and that shape and color cannot. Shape cannot be meas-
ured because objects cannot be ranked or ordered with respect to
8Stevens in Churchman, Measurement: Definitions and
Theories, p. 25.
9His other scales--Ordinal, Interval, Ratio--meet the require-
ment of ranking objects in a dimension.
shape. We can say that X is less than, greater than, or equal to
Y in the dimension of length; but we cannot meaningfully say that
X is less than, greater than, or equal to Y in shape.10
Color is similar although a little more complex. We can
say that an object is redder than, less red than, or equal in red-
ness to another red object, but we cannot meaningfully say that a
red object is redder than, etc., a blue or green object. One re-
quirement then for a measurable dimension and one on which all
writers agree is that object in the dimension must be capable of
being ordered, ranked. The explanation for this, presumably, is
that in measuring the objects in a dimension we wish to express
their relation to one another in that dimension in degree numer-
There are, however, many dimensions, the objects of
which are capable of being ordered, which many writers would
1They may be "identical" or "congruent" but not "equal" in
the usual linguistic usage. Whorf argues that this is a restriction
on both our thinking and communication that is caused by the
structure of our language. See in particular, "Thinking in Primi-
tive Communities" for his hypothesis on comparitive aspects of
"We even have to think and boggle over the question for some
time, or have it explained to us, before we can see the difference
in the relationships.. whereas the Hopi discriminates these re-
lationships with effortless ease, for the forms of his speech have
accustomed him to doing so." B. L. Whorf, Language, Thought,
and Reality (New York: John Wiley & Sons, 1956), p. 85.
In this paper, we take the language as a given constraint, and
while we may envy the Hopi his verbal ability to relate, our lan-
guage requires numbers to make such relationships. Thus,
shape is either identical or different, and such either/or concepts
are not rankings, although they may be comparisons.
deny to be measurable. Consider, for instance, hardness, densi-
ty, pitch, sweetness, etc. For each of these dimensions we can
meaningfully say that the objects are greater than, less than, and
equal to one another, and we can assign numbers to the objects
in those dimensions to represent their relative magnitude. Moh's
scale of hardness of minerals is a system for such assignment.
Mineral X is said to be harder than Y if X scratches Y; X is said
to be equal to Y if neither scratches the other and if X and Y
scratch and are scratched by the same minerals. Ten minerals
of unequal hardness are selected and ranked, and labelled 1, 2,
..., 10. A number can then be assigned to any other mineral by
comparing it with the scale. The numbers thus assigned will
represent relative hardness.
Many writers (the narrow view) maintain that the above
procedure cannot be regarded as measurement for roughly the
following reasons. Although X receives the number 1 and Y the
number 2, we may not infer from this that Y is twice as hard as
X. In general, ratio comparisons of this kind are meaningless
when numerals are assigned by procedures like that involved in
Mohs' scale. This can be seen from the fact that letters of the
alphabet--which have an understood order--could have been used
instead of numbers; and from the fact that the choice of numbers
for the scale was arbitrary. Instead of 1 through 10, 1, 10, 100,
... 1, 000, 000, 000 might have been used, although this would have
been more cumbersome.
Although we can admit that the lack of ratio comparisons
is a serious limitation of Mohs' scale, we must also appreciate
that an ordinal scale is an extremely useful conception. We will
freely admit that a cardinal scale is more useful but to exclude
the ordinal scale simply because it is less useful seems to be an
arbitrary classification of those concepts which can be termed
"measurement." A strong argument can be made that one has
the right to define any word any way he chooses as long as he
makes that definition explicit. That is, the definition of meas-
urement is a "matter of taste. On the other hand, this approach
is likely to cause serious difficulties in inter-personal communi-
cations. If everyone has a unique definition, the convenience of
using a single label--word--for a complex abstraction has been
lost. In addition, a different referent for the same word is al-
most certain to cause misunderstanding no matter how carefully
the definitions are drawn.
In the following analysis we will assiduously avoid the
definitional dispute. We will present some germane propositions
of measurement which all writers would accept in spirit if not in
detail. Criticism of our propositions, in the language of the
logician, would be that they are necessary but not sufficient. The
narrow school would accept each proposition as necessary to
measurement but they would say that the set of propositions was
insufficient because it did not include the additive axiom. The
broad school would likewise accept the propositions but criticize
the set as being insufficient because it does not include the nom-
In a later section we will present some more specific
characteristics of measurement. That section will include a dis-
cussion of the additive axiom, not as a general requirement for
measurement, but as that axiom relates specifically to the meas-
urement of income. In this fashion we can have the best of both
worlds; we can avoid a dispute that would lead us far astray while
at the same time utilizing the concept that is the basis of that
General Propositions of Measurement
I often say that when you can measure what
you are speaking about and express it in
numbers, you know something about it, but
when you cannot measure it, your knowledge
is of a meager and unsatisfactory kind. Lord
The objective of metrics has been well put by Lord Kilvan.
We can all agree that our knowledge is richer, more satisfactory
when we can express it in numbers. Or, in terms of the above
discussion, our information is more informative if it can be ex-
pressed as a measurement. The purpose is clear: measurements
make information more informative, but the interesting questions
11Quoted by H. T. Davis, The Theory of Econometrics (Bloom-
ington, Ind.: Principia Press, 1941), pp. 2-3.
are yet to come. What are the characteristics of measurement
that give it this higher status?
Churchman answers this question in one context in terms
of "precision. "
The contrast between quantitative and non-
quantitative seems to imply a contrast
between "precise" and "vague" information.
Precise information is information that en-
ables one to distinguish objects and their
properties to some arbitrarily assigned
degree of refinement...the reason that pre,-
cision is useful is that precise information
can be used in a wide variety of problems. 12
Churchman's concern appears to be with precision. Not-
ice, however, that precision is a second order concern. More
fundamental is enabling "one to distinguish objects and their
properties." Obviously, if there was no need to distinguish,
there would be no need to distinguish precisely. Thus, the more
fundamental aspect of measurement is its concern with the dis-
tinction between properties, characteristics of objects.
In more general terms, measurement is a process of com-
parison. We say that objects are longer, heavier, more resistant,
etc., than other objects. We use the comparative form of the
words in order to distinguish certain properties, characteristics
of objects. This basic and simple-minded fact is sometimes
overlooked because the results of measurement are ordinarily
12Churchman, Measurement: Definitions and Theories,
stated in a positive form of speech. The very fact that we tend
to forget that it is a comparison is testimony to its conceptual
significance. "Three feet long" brings forth an image that is so
definite that we think of it as a positive, black or white, descrip-
tion. Upon reflection, however, it is obvious that the statement
is a comparison: more importantly, it is a general comparison.
It means that this rod is longer than all objects that are less
than three feet, equal to all objects that are exactly three feet,
and shorter than all objects that are greater than three feet.
Thus, the fundamental purpose of measurement is to allow us to
distinguish, discriminate, compare, objects. For convenience,
we call this the comparative proposition.
Measurement Proposition 1: The purpose of measurement
is to relate, order, compare
objects, events, to other objects,
Comparison of objects can be achieved in many different
ways. The examination of any particular object will reveal a
multitude of properties, characteristics that can be utilized to
discriminate between that object and others. It will have length,
volume, color, density, hardness, sweetness, shape, etc., any
one or all of which can be utilized to compare. Even the simplest
of objects possess a bewildering array of different characteristics
and the complete description'of all these characteristics may be
well nigh impossible. An attempt to describe all the character-
istics of, say, a simple stone would require an enormous amount
of time and effort.
Ordinarily, however, all the characteristics of any par-
ticular object are not desired. The comparison is made between
only certain selected characteristics of the objects. The purpose
of the comparison will determine which characteristics should be
measured and which should be ignored. Crusoe's problem of
finding a flagstone to fit his hearth specified the characteristics
that were relevant. Shape, length and perhaps smoothness were
relevant characteristics. Sweetness, specific gravity, carbon
half-life and perhaps color were not. But, our discussion over-
laps. The selection of the characteristic to be measured employs
the same relevancy criterion as the selection of the binit to be
transmitted. The metrician has a problem and that problem,
along with the theoretical construct for its solution, specifies
which characteristic should be measured.
The primacy of the theory, construct, conception is stated
by almost all investigators of the subject of measurement. It be-
comes even clearer here than in the writings on information.
Churchman refers to the efficient use of the information in "any
problem-situation"13 and in another context the generation of "a
13"The scaling of a property of an object provides information
as to the most efficient use of that property in any problem-situ-
ation." C. West Churchman, "A Materialist Theory of Measure-
ment" in Philosophy for the Future, eds., Sellars, McGill and
Farber (New York: MacMillan, 1949), p. 490.
class of information that will be useful in a wide variety of prob-
lems (Supra). Stevens, who has several fundamental disagree-
ments with Churchman, is in complete agreement on this point.
lie puts the question as "What purposes are we trying to serve?"11
instead of referring to the solution of problems, but the difference
is only in the choice of words. The purpose served is clearly the
solution of a problematic situation.
But all of this has been said in the information chapter.
The construct provides the criterion of relevance for the metrician
in the same manner as it did for the transmitter. In addition,
however, in measurement theory the construct performs the in-
dispensable service of describing, explaining the dimension
(property, characteristic) that is to be measured. As Cassier
puts it, all measurements must be "conceived and sought. l15
14"As I see this issue, there can surely be no objection to any-
one computing any statistic that suits his fancy, regardless of
where the numbers came from in the first place. Our freedom to
calculate must remain as firm as our freedom to speak. The only
question of substantial interest concerns the use to which the cal-
culated statistic is intended. What purposes are we trying to
serve?" Stevens in Churchman, Measurement: Definitions and
Theories, p. 29.
15Quoted by Peter Caws, "Definition and Measurement in Phys-
ics" in Churchman, Me sure ment: Definitions and Theories, p. 8.
Caws presents a coi,- rt argument for thl prior conception notion:
"This operationismm) is a neat solution to the problem of the iden-
tity of the measured and the defined, since the same operation
serves for both purposes. But it leaves the problem of the nature
of what is measured and defined untouc ed. Suppose we measure
a length by the familiar device of putting a standard measuring
rod against it, and obtain a numerical result; does this tell us
That is, we do not discover dimensions, we mentally conceive
them and then seek to perform an operation which allows us to
express that conception as a measurement. 16 The conception of
the dimension is fundamental. One cannot measure an unconceived
dimension. The juxtaposition of a meter stick to an object in the
absence of a conception of the dimension of length would be point-
less. There are philosophical disputes over the existence of a
dimension prior to its conception--some say that a dimension
does not "exist" until it is "conceived" while others argue that the
conception was simply a "discovery" of a pre-existing dimension--
but this is not germane. It is plain that one cannot seek an expres-
sion of something that he has not conceived.
anything about length as such? What it does yield is something
that may be called "specific length, by analogy with specific
gravity; but when the process is complete we know nothing about
length as it applies to the case in question that we did not know
about it as it applied to the standard measuring rod that we used.
We would know something about length operationally only if the
measuring rod itself had no length. ...one first has a concept of
some quality and looks afterward for quantitative expressions of
it. (p. 8)
16Guild refers to a creation of a magnitude instead of a con-
ception: "It is probably usual to regard the experimental proces-
ses of determining equality and of adding as something which we
have just found to be a convenient method of determining quanti-
tative relations inherent in the nature of the magnitudes, whereas
the processes are the necessary connecting links between phe-
nomena and number without which there would be no basis of
comparison between the laws of the former and those of the latter.
The experimental criteria do not merely enable us to measure a
magnitude, they create the magnitude-by defying the fundamental
relations which are to be the basis of the classification."
(Ferguson, p. 298)
The "definition of the fundamental relation" is a mental
Of course numbers can be generated for a wide variety of
things, some of which may be quite abstract and difficult to des-
cribe. Length is a conception common to almost everyone and
thus "two yards" brings forth an immediate mental image. En-
tropy is not so common, and therefore a measurement of entropy
would be totally meaningless to many people. It requires extended
explanation of the constructs of physics before entropy brings
forth any kind of mental image, much less a meaningful mental
Measurement is concerned with a process of comparing,
ranking, ordering, objects in a dimension. Obviously, the dimen-
sion must be amenable to comparison or we cannot measure it.
More fundamental is the conception, the definition of the dimen-
sion. "Dimension" is a convenient name for a mental construct
of a relevant property of an object.
Measurement Proposition 2: The construction and definition
of a dimension is a prerequisite
to the operation of measurement.
Given the conceived dimension we can then relate, com-
pare objects to objects with respect to that dimension. We can
align one object to another and discover which is longer without
further refinements. This is a crude form of comparison
conception which must come prior to the operation. "Create"
seems to be tantamount to "conceive. "