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. [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).

Interpersonal utility comparison

Social choice theory depends upon the ability to aggregate, or sum up, individual preferences into a combined social welfare function. Individual preference can be modeled in terms of an economic utility function. The ability to sum utility functions of different individuals depends on the utility functions being comparable to each other; informally, individuals' preferences must be measured with the same yardstick. Then the ability to create a social welfare function depends crucially on the ability to compare utility functions. This is called interpersonal utility comparison.

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.

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

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. [8] [9]

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% [9] :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. [10]

See also


  1. 1 2 3 4 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, 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, 1970 [1984]. 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.
  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. 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.
  9. 1 2 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.
  10. 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.

Related Research Articles

Rational choice theory, also known as choice theory or rational action theory, is a framework for understanding and often formally modeling social and economic behavior. The basic premise of rational choice theory is that aggregate social behavior results from the behavior of individual actors, each of whom is making their individual decisions. The theory also focuses on the determinants of the individual choices. Rational choice theory then assumes that an individual has preferences among the available choice alternatives that allow them to state which option they prefer. These preferences are assumed to be complete and transitive. The rational agent is assumed to take account of available information, probabilities of events, and potential costs and benefits in determining preferences, and to act consistently in choosing the self-determined best choice of action. In simpler terms, this theory dictates that every person, even when carrying out the most mundane of tasks, perform their own personal cost and benefit analysis in order to determine whether the action is worth pursuing for the best possible outcome. And following this, a person will choose the optimum venture in every case. This could culminate in a student deciding on whether to attend a lecture or stay in bed, a shopper deciding to provide their own bag to avoid the five pence charge or even a voter deciding which candidate or party based on who will fulfill their needs the best on issues that have an impact on themselves especially.

The Condorcet paradox in social choice theory is a situation noted by the Marquis de Condorcet in the late 18th century, in which collective preferences can be cyclic, even if the preferences of individual voters are not cyclic. This is paradoxical, because it means that majority wishes can be in conflict with each other: Majorities prefer, for example, candidate A over B, B over C, and yet C over A. When this occurs, it is because the conflicting majorities are each made up of different groups of individuals.

Kenneth Arrow American economist

Kenneth Joseph Arrow was an American economist, mathematician, writer, and political theorist. He was the joint winner of the Nobel Memorial Prize in Economic Sciences with John Hicks in 1972.

Amartya Sen Indian economist and philosopher

Amartya Kumar Sen is an Indian economist, who since 1972 has taught and worked in the United Kingdom and the United States. Sen has made contributions to welfare economics, social choice theory, economic and social justice, economic theories of famines, decision theory, development economics, public health, and measures of well-being of countries.

In social choice theory, Arrow's impossibility theorem, the general possibility theorem or Arrow's paradox is an impossibility theorem stating that when voters have three or more distinct alternatives (options), no ranked voting electoral system can convert the ranked preferences of individuals into a community-wide ranking while also meeting a specified set of criteria: unrestricted domain, non-dictatorship, Pareto efficiency, and independence of irrelevant alternatives. The theorem is often cited in discussions of voting theory as it is further interpreted by the Gibbard–Satterthwaite theorem. The theorem is named after economist and Nobel laureate Kenneth Arrow, who demonstrated the theorem in his doctoral thesis and popularized it in his 1951 book Social Choice and Individual Values. The original paper was titled "A Difficulty in the Concept of Social Welfare".

In welfare economics, a social welfare function is a function that ranks social states as less desirable, more desirable, or indifferent for every possible pair of social states. Inputs of the function include any variables considered to affect the economic welfare of a society. In using welfare measures of persons in the society as inputs, the social welfare function is individualistic in form. One use of a social welfare function is to represent prospective patterns of collective choice as to alternative social states. The social welfare function provides the government with a simple guideline for achieving the optimal distribution of income.

In philosophical ethics, welfarism is a form of consequentialism. Like all forms of consequentialism, welfarism is based on the premise that actions, policies, and/or rules should be evaluated on the basis of their consequences. Welfarism is the view that the morally significant consequences are impacts on human welfare. There are many different understandings of human welfare, but the term "welfarism" is usually associated with the economic conception of welfare. Economists usually think of individual welfare in terms of utility functions, a perspective in which social welfare can be conceived as an aggregation of individual utilities or utility functions.

In philosophy, economics, and political science, the common good refers to either what is shared and beneficial for all or most members of a given community, or alternatively, what is achieved by citizenship, collective action, and active participation in the realm of politics and public service. The concept of the common good differs significantly among philosophical doctrines. Early conceptions of the common good were set out by Ancient Greek philosophers, including Aristotle and Plato. One understanding of the common good rooted in Aristotle's philosophy remains in common usage today, referring to what one contemporary scholar calls the "good proper to, and attainable only by, the community, yet individually shared by its members."

Welfare economics is a branch of economics that uses microeconomic techniques to evaluate well-being (welfare) at the aggregate (economy-wide) level.

Normative economics is a part of economics that is objective fairness or what the outcome of the economy or goals of public policy ought to be.

Liberal paradox Logical paradox in economic theory

The liberal paradox, also Sen paradox or Sen's paradox, is a logical paradox proposed by Amartya Sen which purports to show that no social system can simultaneously

  1. be committed to a minimal sense of freedom,
  2. always result in a type of economic efficiency known as Pareto efficiency, and
  3. be capable of functioning in any society whatsoever.

Philosophy and economics, also philosophy of economics, studies topics such as rational choice, the appraisal of economic outcomes, institutions and processes, and the ontology of economic phenomena and the possibilities of acquiring knowledge of them.

<i>Social Choice and Individual Values</i> book by Kenneth Arrow

Kenneth Arrow's monograph Social Choice and Individual Values and a theorem within it created modern social choice theory, a rigorous melding of social ethics and voting theory with an economic flavor. Somewhat formally, the "social choice" in the title refers to Arrow's representation of how social values from the set of individual orderings would be implemented under the constitution. Less formally, each social choice corresponds to the feasible set of laws passed by a "vote" under the constitution even if not every individual voted in favor of all the laws.

Quasitransitive relation type of binary relation

The mathematical notion of quasitransitivity is a weakened version of transitivity that is used in social choice theory and microeconomics. Informally, a relation is quasitransitive if it is symmetric for some values and transitive elsewhere. The concept was introduced by Sen (1969) to study the consequences of Arrow's theorem.

Extended sympathy in welfare economics refers to interpersonal value judgments of the form that social state x for person A is ranked better than, worse than, or as good as social state y for person B. Here any characteristics that define each person are distinguished from the rest of the social state and put on a par with conventional measures of wealth insofar as they affect an extended sympathy judgment.

An aggregate in economics is a summary measure. The aggregation problem is the difficult problem of finding a valid way to treat an empirical or theoretical aggregate as if it reacted like a less-aggregated measure, say, about behavior of an individual agent as described in general microeconomic theory. Examples of aggregates in micro- and macroeconomics relative to less aggregated counterparts are:

Justice in economics is a subcategory of welfare economics with models frequently representing the ethical-social requirements of a given theory, whether "in the large", as of a just social order, or "in the small", as in the equity of "how institutions distribute specific benefits and burdens". That theory may or may not elicit acceptance. In the Journal of Economic Literature classification codes 'justice' is scrolled to at JEL: D63, wedged on the same line between 'Equity' and 'Inequality' along with 'Other Normative Criteria and Measurement'. Categories above and below the line are Externalities and Altruism.

Public economics is the study of government policy through the lens of economic efficiency and equity. Public economics builds on the theory of welfare economics and is ultimately used as a tool to improve social welfare.

Kevin W. S. Roberts British economist

Kevin W.S. RobertsFBA is the Sir John Hicks professor of economics at Nuffield College, University of Oxford.

Prasanta Kumar Pattanaik, is emeritus professor at the Department of Economics at the University of California. He is a Fellow of the Econometric Society.