Social choice theory
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Social choice theory or social choice is a theoretical framework for analysis of combining individual preferences, interests, or welfares to reach a collective decision or social welfare in some sense. A non-theoretical example of a collective decision is enacting a law or 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 Arrow's impossibility theorem in it are generally acknowledged as the basis of the modern social choice theory.
Social choice blends elements of welfare economics and voting theory. It is methodologically individualistic, in that it aggregates preferences and behaviors of individual members of society. Using elements of formal logic for generality, analysis proceeds from a set of seemingly reasonable axioms of social choice to form a social welfare function (or constitution). Results uncovered the logical incompatibility of various axioms, as in Arrow's theorem, revealing an aggregation problem and suggesting reformulation or theoretical triage in dropping some axiom(s).
Later work also considers approaches to compensations and fairness, liberty and rights, axiomatic domain restrictions on preferences of agents, variable populations, strategy-proofing of social-choice mechanisms, natural resources, capabilities and functionings, and welfare, justice, and poverty.
Social choice and public choice theory may overlap but are disjoint if narrowly construed. The Journal of Economic Literature classification codes place Social Choice under Microeconomics at 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).
Interpersonal utility comparison 
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.
- Amartya Sen, 2008. "social choice,". The New Palgrave Dictionary of Economics, 2nd Edition, Abstract & TOC.
- For example, in Kenneth J. Arrow, 1951, Social Choice and Individual Values, ch. II, section 2, A Notation for Preferences and Choice, and ch. III, "The Social Welfare Function".
- Walter Bossert and John A. Weymark, 2008. "social choice (new developments)," The New Palgrave Dictionary of Economics, 2nd Edition, Abstract & TOC.
- Basu Kaushik and Luis F. Lòpez-Calva, 2011. "Functionings and Capabilities," Handbook of Social Choice and Welfare, v. 2, pp. 153-187. Abstract.
- Claude d'Aspremont and Louis Gevers, 2002. "Social Welfare Functionals and Interpersonal Comparability," Handbook of Social Choice and Welfare, v. 1, ch. 10, pp. 459–541. Abstract.
- • Amartya Sen 2008. "justice," The New Palgrave Dictionary of Economics, 2nd Edition. Abstract & TOC.
• Bertil Tungodden, 2008. "justice (new perspectives)," The New Palgrave Dictionary of Economics, 2nd Edition. Abstract.
• Louis Kaplow, 2008. "Pareto principle and competing principles," The New Palgrave Dictionary of Economics, 2nd Edition. Abstract.
• Amartya K. Sen, 1970 . Collective Choice and Social Welfare (description):
ch. 9, "Equity and Justice," pp. 131-51.
ch. 9*, "Impersonality and Collective Quasi-Orderings," pp. 152-160.
• Kenneth J. Arrow, 1983. Collected Papers, v. 1, Social Choice and Justice. Description, contents, and chapter-preview links.
• Charles Blackorby, Walter Bossert, and David Donaldson, 2002. "Utilitarianism and the Theory of Justice, Handbook of Social Choice and Welfare, v. 1, ch. 11, pp. 543–596. Abstract.
- Bhaskar Dutta, 2002. Inequality, Poverty and Welfare, Handbook of Social Choice and Welfare, ch. 12, pp. 597–633. Abstract.
See also 
|Part of a series on|
- Compensation principle
- Extended sympathy
- Justice (economics)
- Liberal paradox
- The Magical Number 7 ± 2
- Mechanism design
- Nakamura number
- Rule according to higher law
- Relative utilitarianism
- Voting system
- 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 0-312-12739-1 & ISBN 0-312-12741-3
- _____, ed., 2002, Handbook of Social Choice and Welfare, v. 1. Chapter-preview links.
- _____, ed., 2011, Handbook of Social Choice and Welfare, v. 2. Chapter-preview links.
- Walter Bossert and John A. Weymark, 2008. "social choice (new developments)," The New Palgrave Dictionary of Economics, 2nd Edition, Abstract.
- John S. Dryzek and Christian List, 2003. "Social Choice Theory and Deliberative Democracy: A Reconciliation," British Journal of Political Science, 33(1), pp. 1-28. 2002 PDF link.
- Allan M. Feldman and Roberto Serrano, 2006. Welfare Economics and Social Choice Theory, 2nd ed. ISBN 0-387-29367-1, ISBN 978-0-387-29367-7 Arrow-serachable chapter previews.
- Gaertner, Wulf (2006). A primer in social choice theory. Oxford: Oxford University Press. ISBN 0-19-929751-7.
- John C. Harsanyi, 1987, “interpersonal utility comparisons," The New Palgrave: A Dictionary of Economics, v. 2, pp. 955–58.
- Moulin, Herve (1988). Axioms of cooperative decision making. Cambridge: Cambridge University Press. ISBN 0-521-42458-5.
- Nitzan, Shmuel (2010). Collective Preference and Choice. Cambridge, UK: Cambridge University Press. ISBN 0-521-72213-6.
- 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 , Collective Choice and Social Welfare. ISBN 0-444-85127-5 Description.
- _____, 1998, "The Possibility of Social Choice," Nobel lecture.
- _____, 1987, “social choice," The New Palgrave: A Dictionary of Economics, v. 4, pp. 382–93.
- _____, 2008. “social choice,". The New Palgrave Dictionary of Economics, 2nd Edition, Abstract.
- Shoham, Yoav; Leyton-Brown, Kevin (2009). Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations. New York: Cambridge University Press. ISBN 978-0-521-89943-7.. A comprehensive reference from a computational perspective; see Chapter 9. Downloadable free online.
- Kotaro Suzumura, 1983, Rational Choice, Collective Decisions, and Social Welfare. ISBN 0-521-23862-5
- Taylor, Alan D. (2005). Social choice and the mathematics of manipulation. New York: Cambridge University Press. ISBN 0-521-00883-2.