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Social choice theory

Social choice theory or social choice is a branch of welfare economics that studies the processes of collective decision-making.[1] Social choice incorporates insights from economics, mathematics, and game theory to find the best ways to combine individual opinions, preferences, or beliefs into a single coherent measure of the quality of different outcomes, called a social welfare function.[2][3] Social choice theory includes the closely-related field of voting theory,[4][5][6] and is strongly tied to the field of mechanism design, which can be thought of as the combination of social choice with game theory.

Whereas decision theory is concerned with individuals making choices based on their preferences, social choice theory is concerned with groups making decisions, based on the preferences of individuals. Real-world examples include enacting laws under a constitution or voting, where individual preferences over candidates are collected to elect a person that best represents the group's preferences.[4]

History[edit]

The earliest work on social choice theory comes from the writings of the Marquis de Condorcet, who formulated several key results including his jury theorem and his example showing the impossibility of majority rule. His work was prefigured by Ramon Llull's 1299 manuscript Ars Electionis (The Art of Elections), which discussed many of the same concepts, but was lost in the Late Middle Ages and only rediscovered in the early 21st century.[7]


Kenneth Arrow's book Social Choice and Individual Values is often recognized as inaugurating modern social choice theory.[1] Later work also considers approaches to compensation, fair division, variable populations, strategy-proofing of social-choice mechanisms,[8] natural resources,[1] capabilities and functionings approaches,[9] and measures of welfare.[10][11][12]

Empirical research[edit]

Since Arrow, social choice theory has been characterized by being predominantly mathematical and theoretical, but some research has aimed at estimating the frequency of various voting paradoxes, such as the Condorcet paradox.[15][16] A summary of 37 individual studies, covering a total of 265 real-world elections, large and small, found 25 instances of a Condorcet paradox for a total likelihood of 9.4%.[16]: 325  While examples of the paradox seem to occur often in small settings like parliaments, very few examples have been found in larger groups (electorates), although some have been identified.[17] However, the frequency of such paradoxes depends heavily on the number of options and other factors.

– sometimes called the max-sum rule or Benthamite welfare – aims to maximize the sum of utilities.

Utilitarian rule

– sometimes called the max-min rule or Rawlsian welfare – aims to maximize the smallest utility.

Egalitarian rule

Let be a set of possible 'states of the world' or 'alternatives'. Society wishes to choose a single state from . For example, in a single-winner election, may represent the set of candidates; in a resource allocation setting, may represent all possible allocations.


Let be a finite set, representing a collection of individuals. For each , let be a utility function, describing the amount of happiness an individual i derives from each possible state.


A social choice rule is a mechanism which uses the data to select some element(s) from which are 'best' for society. The question of what 'best' means is a common question in social choice theory. The following rules are most common:

(1951, 2nd ed., 1963). Social Choice and Individual Values, New York: Wiley. ISBN 0-300-01364-7

Arrow, Kenneth J.

_____, (1972). "General Economic Equilibrium: Purpose, Analytic Techniques, Collective Choice", Nobel Prize Lecture, , with Section 8 on the theory and background.

Link to text

_____, (1983). Collected Papers, v. 1, Social Choice and Justice, Oxford: Blackwell  0-674-13760-4

ISBN

Arrow, Kenneth J., Amartya K. Sen, and Kotaro Suzumura, eds. (1997). Social Choice Re-Examined, 2 vol., London: Palgrave Macmillan  0-312-12739-1 & ISBN 0-312-12741-3

ISBN

_____, eds. (2002). Handbook of Social Choice and Welfare, v. 1. Chapter-preview .

links

_____, ed. (2011). Handbook of Social Choice and Welfare, v. 2, Amsterdam: Elsevier. Chapter-preview .

links

Bossert, Walter and John A. Weymark (2008). "Social Choice (New Developments)," , 2nd Edition, London: Palgrave Macmillan Abstract.

The New Palgrave Dictionary of Economics

and Christian List (2003). "Social Choice Theory and Deliberative Democracy: A Reconciliation," British Journal of Political Science, 33(1), pp. 1–28, https://www.jstor.org/discover/10.2307/4092266?uid=3739936&uid=2&uid=4&uid=3739256&sid=21102056001967, 2002 PDF link.

Dryzek, John S.

Feldman, Allan M. and Roberto Serrano (2006). Welfare Economics and Social Choice Theory, 2nd ed., New York: Springer  0-387-29367-1, ISBN 978-0-387-29367-7 Arrow-searchable chapter previews.

ISBN

(1996). Théories économiques de la justice, Paris: Economica.

Fleurbaey, Marc

(2006). A primer in social choice theory. Oxford: Oxford University Press. ISBN 978-0-19-929751-1.

Gaertner, Wulf

(1987). "Interpersonal Utility Comparisons," The New Palgrave: A Dictionary of Economics, v. 2, London: Palgrave, pp. 955–58.

Harsanyi, John C.

(1988). Axioms of cooperative decision making. Cambridge: Cambridge University Press. ISBN 978-0-521-42458-5.

Moulin, Herve

(June 2013). "Fundamentals of social choice theory". Quarterly Journal of Political Science. 8 (3): 305–337. CiteSeerX 10.1.1.297.6781. doi:10.1561/100.00013006.

Myerson, Roger B.

(2010). Collective Preference and Choice. Cambridge, UK: Cambridge University Press. ISBN 978-0-521-72213-1.

Nitzan, Shmuel

(1935). An Essay on the Nature and Significance of Economic Science, 2nd ed., London: Macmillan, ch. VI

Robbins, Lionel

____, (1938). "Interpersonal Comparisons of Utility: A Comment," Economic Journal, 43(4), 635–41.

(1970 [1984]). Collective Choice and Social Welfare, New York: Elsevier ISBN 0-444-85127-5 Description.

Sen, Amartya K.

_____, (1998). "The Possibility of Social Choice", Nobel Prize Lecture .

[1]

_____, (1987). "Social Choice," The New Palgrave: A Dictionary of Economics, v. 4, London: Palgrave, pp. 382–93.

_____, (2008). "Social Choice,". The New Palgrave Dictionary of Economics, 2nd Edition, London: Palgrave

Abstract.

Shoham, Yoav; Leyton-Brown, Kevin (2009). . New York: Cambridge University Press. ISBN 978-0-521-89943-7.. A comprehensive reference from a computational perspective; see Chapter 9. Downloadable free online.

Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations

(1983). Rational Choice, Collective Decisions, and Social Welfare, Cambridge: Cambridge University Press ISBN 0-521-23862-5

Suzumura, Kotaro

(2005). Social choice and the mathematics of manipulation. New York: Cambridge University Press. ISBN 978-0-521-00883-9.

Taylor, Alan D.

List, Christian. . In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy.

"Social Choice Theory"

Archived 2017-12-23 at the Wayback Machine

Social Choice Bibliography by J. S. Kelly

a wiki covering many subjects of social choice and voting theory

Electowiki