Social Choice and Individual Values

Kenneth Joseph Arrow

• Éditeur: Barakaldo Books
• Année: 2020
• ISBN:
  9781839744426
• Sujet: Psychology
• Sous-sujet: History & Theory in Psychology

Kenneth Arrow's monograph "Social Choice and Individual Values" and a theorem within it created modern social choice theory, a rigorous melding of social ethics and voting theory with an economic flavor. The work culminated in what Arrow called the "General Possibility Theorem, " better known thereafter as Arrow's (impossibility) theorem. The theorem states that, absent restrictions on either individual preferences or neutrality of the constitution to feasible alternatives, there exists no social choice rule that satisfies a set of plausible requirements. The result generalizes the voting paradox, which shows that majority voting may fail to yield a stable outcome.—Print ed.

CHAPTER I — INTRODUCTION

1. THE TYPES OF SOCIAL CHOICE

In a capitalist democracy there are essentially two methods by which social choices can be made: voting, typically used to make “political” decisions, and the market mechanism, typically used to make “economic” decisions. In the emerging democracies with mixed economic systems, Great Britain, France, and Scandinavia, the same two modes of making social choices prevail, though more scope is given to the method of voting and decisions based directly or indirectly on it and less to the rule of the price mechanism. Elsewhere in the world, and even in smaller social units within the democracies, social decisions are sometimes made by single individuals or small groups and sometimes (more and more rarely in this modern world) by a widely encompassing set of traditional rules for making the social choice in any given situation, e.g., a religious code.{3}

The last two methods of social choice, dictatorship and convention, have in their formal structure a certain definiteness absent from voting or the market mechanism. In ideal dictatorship there is but one will involved in choice, in an ideal society ruled by convention there is but the divine will or perhaps, by assumption, a common will of all individuals concerning social decisions, so in either case no conflict of individual wills is involved.{4} The methods of voting and the market, on the other hand, are methods of amalgamating the tastes of many individuals in the making of social choices. The methods of dictatorship and convention are, or can be, rational in the sense that any individual can be rational in his choices. Can such consistency be attributed to collective modes of choice, where the wills of many people are involved?

It should be emphasized here that the present study is concerned only with the formal aspects of the above question. That is, we ask if it is formally possible to construct a procedure for passing from a set of known individual tastes to a pattern of social decision-making, the procedure in question being required to satisfy certain natural conditions. An illustration of the problem is the following well-known “paradox of voting.” Suppose there is a community consisting of three voters, and this community must choose among three alternative modes of social action (e.g., disarmament, cold war, or hot war). It is expected that choices of this type have to be made repeatedly, but sometimes not all of the three alternatives will be available. In analogy with the usual utility analysis of the individual consumer under conditions of constant wants and variable price-income situations, rational behavior on the part of the community would mean that the community orders the three alternatives according to its collective preferences once for all, and then chooses in any given case that alternative among those actually available which stands highest on this list. A natural way of arriving at the collective preference scale would be to say that one alternative is preferred to another if a majority of the community prefer the first alternative to the second, i.e., would choose the first over the second if those were the only two alternatives. Let A, B, and C be the three alternatives, and 1, 2, and 3 the three individuals. Suppose individual 1 prefers A to B and B to C (and therefore A to C), individual 2 prefers B to C and C to A (and therefore B to A), and individual 3 prefers C to A and A to B (and therefore C to B). Then a majority prefer A to B, and a majority prefer B to C. We may therefore say that the community prefers A to B and B to C. If the community is to be regarded as behaving rationally, we are forced to say that A is preferred to C. But in fact a majority of the community prefer C to A.{5} So the method just outlined for passing from individual to collective tastes fails to satisfy the condition of rationality, as we ordinarily understand it. Can we find other methods of aggregating individual tastes which imply rational behavior on the part of the community and which will be satisfactory in other ways?{6}

If we continue the traditional identification of rationality with maximization of some sort (to be discussed at greater length below), then the problem of achieving a social maximum derived from individual desires is precisely the problem which has been central to the field of welfare economics. There is no need to review the history of this subject in detail.{7} There has been controversy as to whether or not the economist qua economist could make statements saying that one social state is better than another. If we admit meaning to interpersonal comparisons of utility, then presumably we could order social states according to the sum of the utilities of individuals under each, and this is the solution of Jeremy Bentham, accepted by Edgeworth and Marshall.{8} Even in this case we have a choice of different mathematical forms of the social utility function in terms of individual utilities; thus, the social utility might be the sum of the individual utilities or their product or the product of their logarithms or the sum of their products taken two at a time. So, as Professor Bergson has pointed out, there are value judgments implicit even at this level.{9} The case is clearly much worse if we deny the possibility of making interpersonal comparisons of utility. It was on the latter grounds that Professor Robbins so strongly attacked the concept that economists could make any policy recommendations,{10} at least without losing their status as economists and passing over into the realm of ethics. On the other hand, Mr. Kaldor and, following him, Professor Hicks have argued that there is a meaningful sense in which we can say that one state is better than another from an economic point of view,{11} even without assuming the reality of interpersonal comparison of utilities. The particular mechanism by which they propose to accomplish the comparison of different social states, the compensation principle, will be examined in more detail in Chapter IV.

The controversy involves a certain confusion between two levels of argument. There can be no doubt that, even if interpersonal comparison is assumed, a value judgment is implied in any given way of making social choices based on individual utilities; so much Bergson has shown clearly. But, given these basic value judgments as to the mode of aggregating individual desires, the economist should investigate those mechanisms for social choice which satisfy the value judgments and should check their consequences to see if still other value judgments might be violated. In particular, he should ask the question whether or not the value judgments are consistent with each other, i.e., do there exist any mechanisms of social choice which will in fact satisfy the value judgments made? For example, in the voting paradox discussed above, if the method of majority choice is regarded as itself a value judgment, then we are forced to the conclusion that the value judgment in question, applied to the particular situation indicated, is self-contradictory.

In the matter of consistency, the question of interpersonal comparison of utilities becomes important. Bergson considers it possible to establish an ordering of social states which is based on indifference maps of individuals, and Samuelson has agreed.{12} On the other hand, Professor Lange, in his discussion of the social welfare function, has assumed the interpersonal measurability of utility,{13} and elsewhere he has insisted on the absolute necessity of measurable utility for normative social judgments.{14} Professor Lerner similarly has assumed the meaningfulness of an interpersonal comparison of intensities of utility in his recent work on welfare economics.{15}

In the following discussion of the consistency of various value judgments as to the mode of social choice, the distinction between voting and the market mechanism will be disregarded, both being regarded as special cases of the more general category of collective social choice. The analogy between economic choice and political choice has been pointed out a number of times. For example, Professor Zassenhaus considered the structure of a planned economy by considering the free market replaced by influence conceived generally as a means of distributing the social product.{16} He argued that, under conditions analogous to free competition, the market for exchanging influence for goods would come to equilibrium in a manner analogous to that of the ordinary market, political influence taking the place of initial distribution of goods. His model, however, is expressed only in very general terms, and it is not easy to see how it would operate in a socialist democracy, for example.

Dr. Howard Bowen has considered voting as the demand for collective consumption.{17} In his treatment he regards distribution of income and costs as given, and other simplifying assumptions are made. Close analogies are found with the ordinary market demand curve.

Knight has also stressed the analogy between voting and the market in that both involve collective choice among a limited range of alternatives.{18} He has also stressed certain differences, particularly that there is likely to be a greater tendency toward inequality under voting than under the market; these differences are, however, largely of a socio-psychological type rather than of the formal type which alone is relevant here.

More recently, there has been a series of papers by Professor Duncan Black, dealing with various aspects of the theory of political choice under certain special assumptions and emphasizing the close similarity between the problems of market and electoral choice.{19} His work will be dealt with in greater detail in Chapter VII, Section 2. There is also a literature on the technical problems of election. The chief relevant point here is that virtually every particular scheme proposed for election from single-member constituencies has been shown to have certain arbitrary features. The problem of choosing by election one among a number of candidates for a single position, such as the Presidency of the United States or membership in a legislative body when each district returns only a single member, is clearly of the same character as choosing one out of a number of alternative social policies; indeed, selection among candidates i...

Table des matières

• Title page
• COWLES COMMISSION FOR RESEARCH IN ECONOMICS
• DEDICATION
• ACKNOWLEDGMENTS
• CHAPTER I - INTRODUCTION
• CHAPTER II - THE NATURE OF PREFERENCE AND CHOICE
• CHAPTER III - THE SOCIAL WELFARE FUNCTION
• CHAPTER IV - THE COMPENSATION PRINCIPLE
• CHAPTER V - THE GENERAL POSSIBILITY THEOREM FOR SOCIAL WELFARE FUNCTIONS
• CHAPTER VI - THE INDIVIDUALISTIC ASSUMPTIONS
• CHAPTER VII - SIMILARITY AS THE BASIS OF SOCIAL WELFARE JUDGMENTS
• REFERENCES