Social choice theory studies how individual preferences are aggregated to form a collective preference. As such it blends elements of welfare economics with voting theory. Arrow's 1951 book and the stunning theorem in it created the theory in its modern form. 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 values 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 values, which may temper the range of their prescription or suggest reformulation, triage, or abandonment. Welfare economics is a branch of economics that uses microeconomic techniques to simultaneously determine the allocational efficiency of a macroeconomy and the income distribution consequences associated with it. ... Voters at the voting booths in the US in 1945 Voting systems are methods (algorithms) for groups of people to select one or more options from many, taking into account the individual preferences of the group members. ... Social Choice and Individual Values is a book written by Kenneth Arrow first published in 1951. ... In voting systems, Arrow’s impossibility theorem, or Arrow’s paradox, demonstrates that no voting system can possibly meet a certain set of reasonable criteria when there are three or more options to choose from. ...

A related field is public choice theory. The fields may overlap, but narrowly construed the Journal of Economic Literature classification codes place Social Choice under JEL D71 (with Clubs, Committees, and Associations) while Public Choice falls under JEL D72 (Economic Models of Political Processes: Rent-Seeking, Elections, Legislatures, and Voting Behavior). Public choice theory is a branch of economics that studies the decision-making behavior of voters, politicians and government officials from the perspective of economic theory, namely game theory and decision theory. ... Articles in economics journals are usually classified according to the system used by the Journal of Economic Literature (JEL). ...

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. Jeremy Bentham (IPA: or ) (February 15, 1748 O.S. (February 26, 1749 N.S.) – June 6, 1832) was an English jurist, philosopher, and legal and social reformer. ... This article or section does not cite its references or sources. ...

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 they receive 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 required it 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. Lionel Charles Robbins, Baron Robbins (1898 - 1984) was a British economist of the 20th century who proposed one of the early contemporary definitions of economics, Economics is a science which studies human behavior as a relationship between ends and scarce means which have alternative uses. ... In economics, utility is a measure of the happiness or satisfaction gained consuming good and services. ... In the humanities and social sciences, the term positive is used in a number of ways. ...

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. John Charles Harsanyi (May 29, 1920 – August 9, 2000) was a Hungarian-American business and economics professor who contributed to the study of game theory in mathematics by developing the analysis of games of incomplete information. ... Amartya Sen Dr. Amartya Kumar Sen CH (Hon) (Bengali: Ômorto Kumar Shen) (born 3 November 1933 in Santiniketan, India), is an economist and a winner of the Bank of Sweden Prize in Economic Sciences (sometimes referred to informally as the Nobel Prize for Economics) in 1998, for his work on...

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 ICU, 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. Kenneth Arrow Kenneth Joseph Arrow (born August 23, 1921) is an American economist, winner of the Bank of Sweden Prize in Economic Sciences in 1972. ... In voting systems, Arrow’s impossibility theorem, or Arrow’s paradox, demonstrates that no voting system can possibly meet a certain set of reasonable criteria when there are three or more options to choose from. ... Pareto efficiency, or Pareto optimality, is a central concept in game theory with broad applications in economics, engineering and the social sciences. ...

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) and freedoms (like a labor market). 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. Labour economics seeks to understand the functioning of the market for labour. ...

See also

• Compensation principle
• Social welfare function
• Voting system

The compensation principle in welfare economics refers to a decision rule used to select between pairs of alternative feasible social states. ... A social welfare function, in welfare economics, is a function which gives a measure of the material welfare of society, given a number of economic variables as inputs. ... A voting system is a means of choosing between a number of options, based on the input of a number of voters. ...

References

• Kenneth J. Arrow, 1951, 2nd ed., 1963, Social Choice and Individual Values ISBN 0-300-01364-7
• _____, 1972, Link to text of Nobel lecture with Section 8 on the theory and background
• _____, 1983, Collected Papers, v. 1, Social Choice and Justice ISBN 0-674-13760-4
• Kenneth J. Arrow, Amartya K. Sen, and Kotaro Suzumura, ed., 1997, Social Choice Re-Examined, 2 vol. ISBN 0-312-12741-3 & ISBN 0-312-12739-1
• _____, ed., 2002, Handbook of Social Choice and Welfare, 2 vol.
• John C. Harsanyi, 1987, “interpersonal utility comparisons," The New Palgrave: A Dictionary of Economics, v. 2, 955-58
• Lionel Robbins, 1935, 2nd ed.. An Essay on the Nature and Significance of Economic Science, ch. VI
• ____, 1938, "Interpersonal Comparisons of Utility: A Comment," Economic Journal, 43(4), 635-41
• Amartya K. Sen, 1970 [1984], Collective Choice and Social Welfare ISBN 0-444-85127-5
• _____, 1987, “Social choice," The New Palgrave: A Dictionary of Economics, v. 4, pp. 382-93
• _____, 1998, "The Possibility of Social Choice," Nobel lecture
• Kotaro Suzumura, 1983, Rational Choice, Collective Decisions, and Social Welfare ISBN 0-521-23862-5