!"#$%#&#'()$*+,-../0/)/12$-3$4-'+(1/5#$677-8&1/&9$:1(&;(';. 681"-'$?-#)$:@$A#+.B/ :-8'7#>$!"#$677-8&1/&9$C#5/#DE$F-)@$GHE$4-@$G$0. This has the convenient effect of placing all recording, transmission, and similar errors in the state partition; and it allows viewing the information system as defining a function from S into Y: y =(s). Within this framework, the standards are viewed as defining a function, m, from H into the real line such that m(8) m(77') That is, the standards if and only if 77R77'. are used to single out a most preferred alternative. Using the standards, we are able to compare any two accounting alternatives and decide which of the two is superior or whether they are equally desirable. Presumably, the comparisons are also transitive. One way of describing such a choice process, which we adopt, is to view the standards as providing a hypothetical numerical ranking for each of the alternatives. Note, however, that the domain of this ranking function is limited to E itself, without any reference to the individual's preferences and beliefs. A fundamental question now arises: does any such function, m(.), exist? In selected settings the answer is, no doubt, affirmative. But, in general, the answer is negative. This is discussed below.
THE IMPOSSIBILITY RESULT

max A E(U I y, 7, ay*)D(y |
X7EXc YEY

(2) (2)

Observe that this characterization of the choice, or specification, of an accounting alternative is but an expected utility variant of the situation initially discussed. We provide for comparison of any pair of alternatives; and our comparisons are transitive. We place these comparisons in an expected utility format simply because it is convenient. Reliance on standards to specify the most preferred accounting alternative follows a somewhat different tack. The purpose is to select the preferred alternative, but the method of analysis does not rely on subjective opinions and preferences regarding outcomes; rather, it relies on extrinsic properties of the accounting alternatives per se. The authors of ASOBAT, for example, state:
These standards provide criteria to be used in evaluating potential accounting information. They constitute a basis for inclusion or exclusion of data as accounting information. If these criteria, taken as a whole, are not adequately met, the information is unacceptable. On the other hand, economic data which adequately fulfill these criteria represent accounting material that must be considered for reporting.6

One way of characterizing this standards, or criteria, approach is to regard the standards as reflecting the basic qualities of the accounting alternatives irrespective of the individual's beliefs or preferences. For example, objectivity refers to the accounting measurement process per se; similarly, usefulness and relevance refer to the partition induced by the system, irrespective of its cost. To make this precise, we now assume, without loss of generality, that each sqlH 6 A Statement of Basic Accounting Theory (American partitions the state set. That is, for all AScH Accounting Association, 1966), p. 8.

In this section we formally state the assertion that, in general, no set of standards exists that will single out the most preferred accounting alternative without specifically incorporating the individual's beliefs and preferences. We shall focus on an , I individuals, arbitrary set of i = 1, and assume each to be Savage rational. Then individual i's action choice problem is described by state set Si, action set Ai, outcome function pi(*), utility function Ui(*) and probability measure cIi(.). We

Demski: Accounting Standards now have the following result, which is proven in the Appendix.
THEOREM: Let i= 1, , I index a set of Savage rational users of information. Further let m(-) denote a mapping from the set of information system alternatives into the real line that is independent of the individuals and their choice problems. No measure of information quality m(-) exists such that m(77)>m(r') if and only if E(Uif77) ? E(Ui 7q') for all individuals and choice problems and any arbitrary pair of information system alternatives, vq and ti'. DISCUSSION

721 that any set of standards will single out the most preferred accounting alternative. Moreover, a less stringent interpretation of standards does not eliminate the impossibility result. That is, we might interpret the standards as, say, circumscribing the feasible list of alternatives. But this merely amounts to specifying a set of indifferent alternatives (in a feasible sense); and the Theorem goes through with equal force. We can strengthen, in fact, the result in several respects. Adding beliefs to the analysis does not circumvent the negative result. For example, we might apply objectivity only to those situations we thought might occur with "reasonable probability." This extends the domain of m(.) to systems and beliefs, with m(, 1?) being the basic mapping. But the Theorem's proof is totally unaffected by such an addition. We could also extend the Theorem to ex post performance evaluation systems as well, where the measurements are designed to motivate subordinate decision makers.'0 But the fundamental conclusion remains: no such ranking function, in general, exists.
SUMMARY

The major significance of this result is to ensure that, generally speaking, we cannot rely on standards to provide a normative theory of accounting. No set of standards exists that will always rank alternatives in accordance with preferences and beliefs -no matter what these preferences and beliefs are, as long as they are consistent in admitting to the expected utility characterization. This negation is, in fact, far reaching. It applies to the use of measure or aggregation theory, as discussed by Ijiri,7 the use of information theory, as discussed by Lev,8 as well as the more typical sets of standards, as in ASOBAT. It also applies with equal force to so-called managerial and financial reporting areas. Allocation criteria, such as physical identification, facilities provided, and benefits received do not universally work, nor does a criterion of statistical correlation. Further observe that the basic difficulty does not rest with a multiperson orientation. We might have a single-person situation or a multiperson setting in which only a dictator's preferences and beliefs counted. Either way, I= 1 and the Theorem remains.9 Without restricting the nature of the decision problem faced or the nature of the controlling preferences and beliefs, we simply cannot guarantee

We have interpreted accounting theory as providing a complete and transitive ranking of accounting alternatives at the individual level. It was then proven that
7 Y. Ijiri, "Fundamental Queries in Aggregation Theory," Journal of The American Statistical Association (December 1971). 8 B. Lev, Accounting and Information Theory (American Accounting Association, 1969). 9 Indeed, another fundamental difficulty arises in a multiperson setting. There is no way of moving from complete and transitive preferences at the individual level to a group level complete and transitive notion of preference that satisfies Arrow's conditions. (K. Arrow, Social Choice and Individual Values (Wiley, 1963)). As a result, we expect difficulties in the multiperson case, using standards or any other formulation of the choice process. But standards cannot even be relied upon in the individual case. 10See J. Demski, "Optimal Performance Measurement," Journal of Accounting Research (Autumn 1972) for a discussion of the relationship between ex ante and ex post information systems.

722 no set of standards (applied to the accounting alternatives per se) exists that will always rank accounting alternatives in relation to consistent individual preferences and beliefs. The major import of the result is to raise a number of questions. We know that standards do not always work. When, then, do they work? Under what types of conditions will various types of standards work; when they fail, how badly do they fail? We know that criteria systems, as in information theory, ASOBAT, or cost-allocation guides cannot be relied upon to provide the desired result in every situation. This does not, however, necessarily imply that they never provide the desired result. Hence, a major question in accounting theory must be conditions under which standards do work.
APPENDIX

The Accounting Review, October 1973
LEMMA: Given -l' and -l" are costless information systems, E( U. ') > E( U. I ") for , I and all choice problems if all i= 1, and only if -q'is as fine as -q".II

Proof: First suppose -q' is as fine as Dropping the i subscript, this implies that
, ',(Y// I ") ==y cyl yl Cd/"y

(Y/

'

Next, some algebraic manipulation of equation [2]establishes the desired result:
E(U I a") A, 1(y" 1 7") max E2 U(p(s, a)) =
'E=-Y V"

aEA

8ES

*?Sy", 1a")
=

Z, A y"EtY (y'f|7') max E U(.) aEA y'c>"

8ES

*4(s I,Y
=
poeY

n")

Z

E y'cy" (y' I ')E(U Iy", d7*) ,a D(y'|I7')E(U I y', n', ay,*)

Proof of the Impossibility Theorem relies on a fineness Lemma. We say that -q is as fine as rq'if every signal from 7 is fully contained in a signal from -i'. Alternatively, we say that Xqis as fine as -q' when is knowledge of a signal from Xq sufficient to construct the corresponding signal from q'. For example, capitalization of human asset values provides an income measurement system that is as fine as a conventional income measurement system; with knowledge of the former measurement one could construct the latter measurement. Similarly, a more timely measurement system is as fine as a less timely system, again because the former measurement can be used to construct the latter. Hence, with iq as fine as -q', we know that -qtells us all that I' tells us, and possibly more. Now consider two costless accounting alternatives, 77'and -q",where by "costless" we mean that p(s, a, q) is strictly independent of I' and I". We now have the following result linking fineness to preference between costless information systems:

<

E ylEY E y'cy"l =E(U

7') 1

? E(Uj-q"), given both systems are costless. E(U 17") for Now suppose E(U') all individuals and any choice problem. proceed by contradiction. Suppose S= {1, 2, 3, 4 } and the partitions induced by a' and a", respectively, are {{ 1,3}, { 2, 4 } } and {{i, 2}, {3, 4} }. Observe that p(I, a)=p(3, a) and p(2, a)=p(4, a) for all aEA implies, for some settings, that
11This Lemma is quite close to Blackwell's Theorem. It is, however, more general in that it does not rely on a payoff adequate partition of the state space. See D. Blackwell and M. Girshick, Theoryof Games and Statistical Decisions (Wiley, 1954) and C. B. McGuire "Comparisons of Information Structures," Chapter 5 in C. McGuire and R. Radner (eds.), Decision and Organization (North-Holland, 1972) for discussion of Blackwell's Theorem. Also see J. Marschak and R. Radner, Economic Theory of Teams (Yale University Press, 1971) for discussion of the Lemma and the fact that it ensures that no measure of the quality of information exists.

Thus, 77'as fine as -q"guarantees E(U

Further suppose t7'is not as fine as 7t". We

Demski: Accounting Standards E(U 1q')>E(Uj1q"). But p(1, a)= p(2, a) and p(3, a) = p(4, a) for all aEA implies, for some settings, that E(U I-q")> E( U|I'). This, however, contradicts our assumption and we must, therefore, have -q' as fine as -q".e We now prove the Impossibility Theorem. Proof: Since the Theorem is a negative result, we need only provide one counter example. Using the Lemma, an entire class is provided by costless accounting alternatives. The Lemma establishes the necessity of I' as fine as -q" for E(Uj7n') > E( Ui II") to hold for all individuals and

723 all action choice problems (given that a' and a" are costless). Hence, in this case, the standards must rank in accordance with fineness. But, in general, this cannot be accomplished because fineness is an incomplete relation; it does not always hold. (See, for example, the two partitions used in proof of the Lemma.) That is, aq' as fine as ai" is necessary and sufficient to 77"), regardensure that E( Us v7') E( Uj I 2 less of the individual's preferences, beliefs, and decision problem. But not all systems can be compared with respect to fineness. Thus, the m(.) function sought for cannot exist. This completes the proof. U