Social choice theory

Social choice theory studies voting rules for how individual preferences are aggregated to form a collective preference. It dates from Condorcet's formulation of the voting paradox. Arrow's 1951 book and the theorem in it created the theory in its modern form, which blends and generalizes elements of welfare economics and voting theory. The aggregation is of "individual interests, or judgements, or well-beings, into some notion of social welfare, social judgement, or social choice" (Sen, 1987). A characteristic method proceeds from formulating some set of apparently reasonable axioms of social choice as requirements for a social welfare function (constitution) to capture different aspects of the aggregation problem and to derive implications. The many "impossibility" results of earlier analyses indicate the logical incompatibility of different axioms, which may temper the range of their prescription or suggest reformulation, triage, or abandonment.

A related field is public choice theory. The fields may overlap, but narrowly construed the JEL classification codes place Social Choice under JEL D71 (with Clubs, Committees, and Associations) while most Public Choice articles fall under JEL D72 (Economic Models of Political Processes: Rent-Seeking, Elections, Legislatures, and Voting Behavior).

Interpersonal utility comparison
Following Jeremy Bentham, utilitarians have assumed that individuals attempt to maximize their individual utilities when arriving at individual choices, that such utilities are measurable individually and interpersonally, and that they can be added up for a measure of aggregate utility. Utilitarian ethics calls for maximizing this aggregate.

Lionel Robbins doubted that mental states (including utilities) can be measured. A fortiori he criticized interpersonal comparisons of utility, and the social choice theory on which it was based, for assuming that we could determine the amount of satisfaction other individuals derive from certain situations. For example, the law of diminishing marginal utility states that the more of a good one has, the less utility one receives from an additional unit of the good. Such a principle has been used to defend transfers of wealth from the rich to the poor on the basis that a rich man does not derive as much utility from an extra unit of income as does a poor man. Robbins (1935, pp. 138-40) argued that this notion is beyond positive science. Introspection begs the question, and it is never possible, by testing or observation, to measure changes in utility someone else gets from a change in income, nor is it required by positive theory. From this it is arguable that interpersonal comparisons of utility, and thus social choice theory based on comparing people's utility gains and losses, are a lost cause.

Other theorists have argued that Robbins claimed too much. John Harsanyi for instance agrees that full comparability of mental states such as utility is never possible. He believes, however, that human beings are able to make some interpersonal comparisons of utility. Because human beings share some common backgrounds, cultural experiences, and so on, we should be able to compare welfare in some less controversial cases. To borrow an example from Amartya Sen (1970, p. 99), it should not be difficult to say that Emperor Nero's gain from burning Rome did not outweigh the loss of the rest of the Romans. Thus, Harsanyi and Sen argue we can have partial comparability. Some states are easier to compare than others, and we can proceed with ICU (interpersonal comparisons of utility) and social choice theory based on ICU, as long as we are careful not to claim too much.

Sen, however, proposes pushing beyond partial comparability. Kenneth Arrow's famous impossibility result spelled the second end to social choice theory, by proving the inconsistency of social preferences when held to very minimal standards, such as non-dictatorship and Pareto optimality. Partial comparability does away with some of this result. Sen's theory of informational broadening does away with the rest. Sen believes that IUC, even if it were perfect, would still lead to sub-optimal social choices. The reason for this is simple: mental states are malleable. A starving peasant may have a particularly sunny disposition, and may even find a way to get a great deal of utility from a very small amount of income. However, his high utility value should not nullify his claim to compensation or equality in the realm of social choice.

Instead, social choice decisions should be based on variables that are not subject to such malleability as mental states. Sen proposes interpersonal comparisons based on a wider range of real data. Particularly, Sen is worried about access to advantage, which he measures by a person's access to basic needs-satisfying goods (like food), freedoms (as in a labor market), 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 both the objections of Arrow and Robbins, which looked as though they would cripple social choice theory permanently.