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Social choice theory

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Social choice theory or social choice is a theoretical framework for analysis of combining individual opinions, 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. In addition to Arrow's theorem and the voting paradox, the Gibbard–Satterthwaite theorem, the Condorcet jury theorem, the median voter theorem, and May's theorem are among the more well known results from 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).

Contents

Social choice theory is the study of theoretical and practical methods to aggregate or combine individual preferences into a collective social welfare function. The field generally assumes that individuals have preferences, and it follows that they can be modeled using utility functions. But much of the research in the field assumes that those utility functions are internal to humans, lack a meaningful unit of measure and cannot be compared across different individuals Whether this type of interpersonal utility comparison is possible or not significantly alters the available mathematical structures for social welfare functions and social choice theory.

In one perspective, following Jeremy Bentham, utilitarians have argued that preferences and utility functions of individuals are interpersonally comparable and may therefore be added together to arrive at a measure of aggregate utility. Utilitarian ethics call for maximizing this aggregate.

In contrast many twentieth century economists, following Lionel Robbins, questioned whether mental states, and the 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. Robbins (1935, pp. 138–40) argues 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 of interpersonal utility 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 utility 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. 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.[citation needed]

Since Arrow social choice analysis has primarily been characterized by being extremely theoretical and formal in character. However, since ca. 1960 attention began to be paid to empirical applications of social choice theoretical insights, first and foremost by American political scientist William H. Riker.

The vast majority of such studies have been focused on finding empirical examples of the Condorcet paradox.

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%: 325 (and this may be a high estimate, since cases of the paradox are more likely to be reported on than cases without). On the other hand, the empirical identification of a Condorcet paradox presupposes extensive data on the decision-makers' preferences over all alternatives—something that is only very rarely available.

While examples of the paradox seem to occur occasionally in small settings (e.g., parliaments) very few examples have been found in larger groups (e.g. electorates), although some have been identified.

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

Let I {\displaystyle I} be a finite set, representing a collection of individuals. For each i I {\displaystyle i\in I} , let u i : X R {\displaystyle u_{i}:X\longrightarrow \mathbb {R} } 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 ( u i ) i I {\displaystyle (u_{i})_{i\in I}} to select some element(s) from X {\displaystyle X} which are `best' for society. The question of what 'best' means is the basic question of social choice theory. The following rules are most common:

  • The utilitarian rule - also called the max-sum rule - aims to maximize the sum of utilities, thus maximizing the efficiency.
  • The egalitarian rule - also called the max-min rule - aims to maximize the smallest utility, thus maximizing the fairness.
  • The proportional-fair rule - sometimes called the max-product rule - aims to balance between the previous two rules, attaining a balance between efficiency and fairness.
  1. Amartya Sen (2008). "Social Choice,". The New Palgrave Dictionary of Economics, 2nd Edition, Abstract & TOC.
  2. For example, in Kenneth J. Arrow (1951). Social Choice and Individual Values, New York: Wiley, ch. II, section 2, A Notation for Preferences and Choice, and ch. III, "The Social Welfare Function".
  3. Walter Bossert and John A. Weymark (2008). "Social Choice (New Developments)," The New Palgrave Dictionary of Economics, 2nd Edition, Abstract & TOC.
  4. Kaushik, Basu; Lòpez-Calva, Luis F. (2011). Functionings and Capabilities. Handbook of Social Choice and Welfare. 2. pp. 153–187. doi:10.1016/S0169-7218(10)00016-X. ISBN 9780444508942.
  5. d'Aspremont, Claude; Gevers, Louis (2002). Chapter 10 Social welfare functionals and interpersonal comparability. Handbook of Social Choice and Welfare. 1. pp. 459–541. doi:10.1016/S1574-0110(02)80014-5. ISBN 9780444829146.
  6. Amartya Sen ([1987] 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 (1979 [1984]). Collective Choice and Social Welfare, New York: Elsevier, (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, Cambridge, MA: Belknap Press, Description, contents, and chapter-preview links.
    Charles Blackorby, Walter Bossert, and David Donaldson, 2002. "Utilitarianism and the Theory of Justice", in Handbook of Social Choice and Welfare, edited by Kenneth J. Arrow, Amartya K. Sen, and Kotaro Suzumura, v. 1, ch. 11, pp. 543–596. Abstract.
  7. Dutta, Bhaskar (2002). Chapter 12 Inequality, poverty and welfare. Handbook of Social Choice and Welfare. 1. pp. 597–633. doi:10.1016/S1574-0110(02)80016-9. ISBN 9780444829146.
  8. Lionel Robbins (1932, 1935, 2nd ed.). An Essay on the Nature and Significance of Economic Science, London: Macmillan. Links for 1932 HTML and 1935 facsimile.
  9. Kurrild-Klitgaard, Peter (2014). "Empirical social choice: An introduction". Public Choice. 158 (3–4): 297–310. doi:10.1007/s11127-014-0164-4. ISSN 0048-5829. S2CID 148982833.
  10. Van Deemen, Adrian (2014). "On the empirical relevance of Condorcet's paradox". Public Choice. 158 (3–4): 311–330. doi:10.1007/s11127-013-0133-3. ISSN 0048-5829. S2CID 154862595.
  11. Kurrild-Klitgaard, Peter (2014). "An empirical example of the Condorcet paradox of voting in a large electorate". Public Choice. 107: 135–145. doi:10.1023/A:1010304729545. ISSN 0048-5829. S2CID 152300013.

Social choice theory
Social choice theory Language Watch Edit This article has an unclear citation style The references used may be made clearer with a different or consistent style of citation and footnoting April 2021 Learn how and when to remove this template message Social choice theory or social choice is a theoretical framework for analysis of combining individual opinions preferences interests or welfares to reach a collective decision or social welfare in some sense 1 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 1 In addition to Arrow s theorem and the voting paradox the Gibbard Satterthwaite theorem the Condorcet jury theorem the median voter theorem and May s theorem are among the more well known results from 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 2 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 1 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 1 3 capabilities and functionings 4 and welfare 5 justice 6 and poverty 7 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 Contents 1 Interpersonal utility comparison 2 Empirical social choice studies 3 Social choice rules 4 See also 5 Notes 6 References 7 External linksInterpersonal utility comparison EditSocial choice theory is the study of theoretical and practical methods to aggregate or combine individual preferences into a collective social welfare function The field generally assumes that individuals have preferences and it follows that they can be modeled using utility functions But much of the research in the field assumes that those utility functions are internal to humans lack a meaningful unit of measure and cannot be compared across different individuals 8 Whether this type of interpersonal utility comparison is possible or not significantly alters the available mathematical structures for social welfare functions and social choice theory In one perspective following Jeremy Bentham utilitarians have argued that preferences and utility functions of individuals are interpersonally comparable and may therefore be added together to arrive at a measure of aggregate utility Utilitarian ethics call for maximizing this aggregate In contrast many twentieth century economists following Lionel Robbins questioned whether mental states and the 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 Robbins 1935 pp 138 40 argues 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 of interpersonal utility 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 utility 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 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 citation needed Empirical social choice studies EditSince Arrow social choice analysis has primarily been characterized by being extremely theoretical and formal in character However since ca 1960 attention began to be paid to empirical applications of social choice theoretical insights first and foremost by American political scientist William H Riker The vast majority of such studies have been focused on finding empirical examples of the Condorcet paradox 9 10 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 10 325 and this may be a high estimate since cases of the paradox are more likely to be reported on than cases without On the other hand the empirical identification of a Condorcet paradox presupposes extensive data on the decision makers preferences over all alternatives something that is only very rarely available While examples of the paradox seem to occur occasionally in small settings e g parliaments very few examples have been found in larger groups e g electorates although some have been identified 11 Social choice rules EditLet X displaystyle X be a set of possible states of the world or alternatives Society wishes to choose a single state from X displaystyle X For example in a single winner election X displaystyle X may represent the set of candidates in a resource allocation setting X displaystyle X may represent all possible allocations Let I displaystyle I be a finite set representing a collection of individuals For each i I displaystyle i in I let u i X R displaystyle u i X longrightarrow mathbb R 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 u i i I displaystyle u i i in I to select some element s from X displaystyle X which are best for society The question of what best means is the basic question of social choice theory The following rules are most common The utilitarian rule also called the max sum rule aims to maximize the sum of utilities thus maximizing the efficiency The egalitarian rule also called the max min rule aims to maximize the smallest utility thus maximizing the fairness The proportional fair rule sometimes called the max product rule aims to balance between the previous two rules attaining a balance between efficiency and fairness See also EditCompensation principle Computational social choice Condorcet paradox Emotional choice theory Extended sympathy Game theory Group decision making Justice economics Liberal paradox Mechanism design Nakamura number Rational choice theory Rule according to higher law Voting systemNotes Edit a b c d Amartya Sen 2008 Social Choice The New Palgrave Dictionary of Economics 2nd Edition Abstract amp TOC For example in Kenneth J Arrow 1951 Social Choice and Individual Values New York Wiley 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 amp TOC Kaushik Basu Lopez Calva Luis F 2011 Functionings and Capabilities Handbook of Social Choice and Welfare 2 pp 153 187 doi 10 1016 S0169 7218 10 00016 X ISBN 9780444508942 d Aspremont Claude Gevers Louis 2002 Chapter 10 Social welfare functionals and interpersonal comparability Handbook of Social Choice and Welfare 1 pp 459 541 doi 10 1016 S1574 0110 02 80014 5 ISBN 9780444829146 Amartya Sen 1987 2008 Justice The New Palgrave Dictionary of Economics 2nd Edition Abstract amp 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 1979 1984 Collective Choice and Social Welfare New York Elsevier 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 Cambridge MA Belknap Press Description contents and chapter preview links Charles Blackorby Walter Bossert and David Donaldson 2002 Utilitarianism and the Theory of Justice in Handbook of Social Choice and Welfare edited by Kenneth J Arrow Amartya K Sen and Kotaro Suzumura v 1 ch 11 pp 543 596 Abstract Dutta Bhaskar 2002 Chapter 12 Inequality poverty and welfare Handbook of Social Choice and Welfare 1 pp 597 633 doi 10 1016 S1574 0110 02 80016 9 ISBN 9780444829146 Lionel Robbins 1932 1935 2nd ed An Essay on the Nature and Significance of Economic Science London Macmillan Links for 1932 HTML and 1935 facsimile Kurrild Klitgaard Peter 2014 Empirical social choice An introduction Public Choice 158 3 4 297 310 doi 10 1007 s11127 014 0164 4 ISSN 0048 5829 S2CID 148982833 a b Van Deemen Adrian 2014 On the empirical relevance of Condorcet s paradox Public Choice 158 3 4 311 330 doi 10 1007 s11127 013 0133 3 ISSN 0048 5829 S2CID 154862595 Kurrild Klitgaard Peter 2014 An empirical example of the Condorcet paradox of voting in a large electorate Public Choice 107 135 145 doi 10 1023 A 1010304729545 ISSN 0048 5829 S2CID 152300013 References EditArrow Kenneth J 1951 2nd ed 1963 Social Choice and Individual Values New York Wiley ISBN 0 300 01364 7 1972 General Economic Equilibrium Purpose Analytic Techniques Collective Choice Nobel Prize Lecture Link to text with Section 8 on the theory and background 1983 Collected Papers v 1 Social Choice and Justice Oxford Blackwell ISBN 0 674 13760 4 Arrow Kenneth J Amartya K Sen and Kotaro Suzumura eds 1997 Social Choice Re Examined 2 vol London Palgrave Macmillan ISBN 0 312 12739 1 amp ISBN 0 312 12741 3 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 The New Palgrave Dictionary of Economics 2nd Edition London Palgrave Macmillan Abstract Dryzek John S 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 amp uid 2 amp uid 4 amp uid 3739256 amp sid 21102056001967 2002 PDF link Feldman Allan M and Roberto Serrano 2006 Welfare Economics and Social Choice Theory 2nd ed New York Springer ISBN 0 387 29367 1 ISBN 978 0 387 29367 7 Arrow searchable chapter previews Fleurbaey Marc 1996 Theories economiques de la justice Paris Economica Gaertner Wulf 2006 A primer in social choice theory Oxford Oxford University Press ISBN 978 0 19 929751 1 Harsanyi John C 1987 Interpersonal Utility Comparisons The New Palgrave A Dictionary of Economics v 2 London Palgrave pp 955 58 Moulin Herve 1988 Axioms of cooperative decision making Cambridge Cambridge University Press ISBN 978 0 521 42458 5 Myerson Roger B 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 Nitzan Shmuel 2010 Collective Preference and Choice Cambridge UK Cambridge University Press ISBN 978 0 521 72213 1 Robbins Lionel 1935 An Essay on the Nature and Significance of Economic Science 2nd ed London Macmillan ch VI 1938 Interpersonal Comparisons of Utility A Comment Economic Journal 43 4 635 41 Sen Amartya K 1970 1984 Collective Choice and Social Welfare New York Elsevier ISBN 0 444 85127 5 Description 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 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 Suzumura Kotaro 1983 Rational Choice Collective Decisions and Social Welfare Cambridge Cambridge University Press ISBN 0 521 23862 5 Taylor Alan D 2005 Social choice and the mathematics of manipulation New York Cambridge University Press ISBN 978 0 521 00883 9 External links EditList Christian Social Choice Theory In Zalta Edward N ed Stanford Encyclopedia of Philosophy Social Choice Bibliography by J S Kelly Electowiki a wiki covering many subjects of social choice and voting theory Retrieved from https en wikipedia org w index php title Social choice theory amp oldid 1047604118, wikipedia, wiki, book,

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