Social choice theory is a theoretical framework for measuring individual interests, values, or welfares as an aggregate towards collective decision. A non-theoretical example of a collective decision is passing a set of laws under a constitution. Social choice theory dates from Condorcet's formulation of the voting paradox. Kenneth Arrow's Social Choice and Individual Values (1951) and the Arrow's impossibility theorem are generally acknowledged as the basis of the modern social choice theory.
Social choice theory blends elements of welfare economics and voting theory. It is methodologically individualistic, in that it aggregates preferences and behaviors of individual members of society. A characteristic approach proceeds from a set of reasonable axioms of social choice to a social welfare function (or constitution). Many earlier results uncover the logical incompatibility of various axioms and, having revealed thus the aggregation problem, suggest reformulation or theoretical triage in dropping some axiom(s).
Social choice theory and public choice theory may overlap but are disjoint if narrowly construed. The JEL classification codes places Social Choice into JEL D71 (with Clubs, Committees, and Associations) whereas most Public Choice subcategories are in JEL D72 (Economic Models of Political Processes: Rent-Seeking, Elections, Legislatures, and Voting Behavior).
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Following Jeremy Bentham, utilitarians have argued that preferences and utility functions of individuals are inter-personally comparable and may therefore be added to arrive at a measure of aggregate utility. Utilitarian ethics call for maximizing this aggregate.
Lionel Robbins questioned whether mental states, and utilities they reflect, can be measured and, a fortiori, interpersonal comparisons of utility as well as the social choice theory on which it is based. Consider for instance the law of diminishing marginal utility, according to which utility of an added quantity of a good decreases with the amount of the good that is already in possession of the individual. It has been used to defend transfers of wealth from the "rich" to the "poor" on the premise that the former do not derive as much utility as the latter from an extra unit of income. In an essay (1935, pp. 138–40), Robbins argued that this notion is beyond positive science; that is, one cannot measure changes in the utility of someone else, nor is it required by positive theory.
Apologists of the interpersonal comparison of utility have argued that Robbins claimed too much. John Harsanyi agrees that full comparability of mental states such as utility is never possible but believes, however, that human beings are able to make some interpersonal comparisons of utility because they share some common backgrounds, cultural experiences, etc. In the example from Amartya Sen (1970, p. 99), it should be possible to say that Emperor Nero's gain from burning Rome was outweighed by the loss incurred by the rest of the Romans. Harsanyi and Sen thus argue that at least partial comparability of utility is possible, and social-choice theory proceeds under that assumption.
Sen proposes, however, that comparability need not be partial. Under Sen's theory of informational broadening, even complete interpersonal comparison of utility would lead to socially suboptimal choices because mental states are malleable. A starving peasant may have a particularly sunny disposition and thereby derive high utility from a small income. This fact should not nullify, however, his claim to compensation or equality in the realm of social choice.
Social decisions should accordingly be based on immalleable factors. Sen proposes interpersonal comparisons based on a wide range of data. His theory is concerned with access to advantage, viewed as an individual's access to goods that satisfy basic needs (e.g., food), freedoms (in the labor market, for instance), and capabilities. We can proceed to make social choices based on real variables, and thereby address actual position, and access to advantage. Most importantly, Sen's method of informational broadening allows social choice theory to escape the objections of Robbins, which looked as though they would permanently harm social choice theory.
Additionally, since the seminal results of Arrow's impossibility theorem and the Gibbard-Satterthwaite theorem, many positive results focusing on the restriction of the domain of preferences of individuals have elucidated such topics as optimal voting. The initial results emphasized the impossibility of satisfactorily providing a social choice function free of dictatorship and inefficiency in the most general settings. Later results have found natural restrictions that can accommodate many desirable properties.
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