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.

A theory is a contemplative and rational type of abstract or generalizing thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking often is associated with such processes like observational study, research. Theories may either be scientific or other than scientific. Depending on the context, the results might, for example, include generalized explanations of how nature works. The word has its roots in ancient Greek, but in modern use it has taken on several related meanings.

Constitution Set of fundamental principles or established precedents according to which a state or other organization is governed

A constitution is an aggregate of fundamental principles or established precedents that constitute the legal basis of a polity, organisation or other type of entity, and commonly determine how that entity is to be governed.

Marquis de Condorcet French philosopher, mathematician, and political scientist

Marie Jean Antoine Nicolas de Caritat, Marquis of Condorcet, known as Nicolas de Condorcet, was a French philosopher and mathematician. His ideas, including support for a liberal economy, free and equal public instruction, constitutional government, and equal rights for women and people of all races, have been said to embody the ideals of the Age of Enlightenment and Enlightenment rationalism. He died in prison after a period of flight from French Revolutionary authorities.

Contents

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]

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

In the social sciences, methodological individualism is the principle that subjective individual motivation explains social phenomena, rather than class or group dynamics which are illusory or artificial and therefore cannot truly explain market or social phenomena. Methodological individualism is often contrasted with methodological holism.

An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Greek axíōma (ἀξίωμα) 'that which is thought worthy or fit' or 'that which commends itself as evident.'

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]

In welfare economics, the compensation principle refers to a decision rule used to select between pairs of alternative feasible social states. One of these states is the hypothetical point of departure. According to the compensation principle, if the prospective gainers could compensate (any) prospective losers and leave no one worse off, the alternate state is to be selected. An example of a compensation principle is the Pareto criterion in which a change in states entails that such compensation is not merely feasible but required. Two variants are:

Fair division is the problem of dividing a set of resources among several people who have an entitlement to them, such that each person receives his/her due share. This problem arises in various real-world settings, such as: division of inheritance, partnership dissolutions, divorce settlements, electronic frequency allocation, airport traffic management, and exploitation of Earth Observation Satellites. This is an active research area in Mathematics, Economics, Game theory, Dispute resolution, and more. The central tenet of fair division is that such a division should be performed by the players themselves, maybe using a mediator but certainly not an arbiter as only the players really know how they value the goods.

Domain of a function mathematical concept

In mathematics, the domain of definition of a function is the set of "input" or argument values for which the function is defined. That is, the function provides an "output" or value for each member of the domain. Conversely, the set of values the function takes on as output is termed the image of the function, which is sometimes also referred to as the range of the function.

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).

Public choice, or public choice theory, is "the use of economic tools to deal with traditional problems of political science". Its content includes the study of political behavior. In political science, it is the subset of positive political theory that studies self-interested agents and their interactions, which can be represented in a number of ways – using standard constrained utility maximization, game theory, or decision theory.

Articles in economics journals are usually classified according to the JEL classification codes, a system originated by the Journal of Economic Literature. The JEL is published quarterly by the American Economic Association (AEA) and contains survey articles and information on recently published books and dissertations. The AEA maintains EconLit, a searchable data base of citations for articles, books, reviews, dissertations, and working papers classified by JEL codes for the years from 1969. A recent addition to EconLit is indexing of economics-journal articles from 1886 to 1968 parallel to the print series Index of Economic Articles.

Microeconomics is a branch of economics that studies the behaviour of individuals and firms in making decisions regarding the allocation of scarce resources and the interactions among these individuals and firms.

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.

Jeremy Bentham British philosopher, jurist, and social reformer

Jeremy Bentham was an English philosopher, jurist, and social reformer regarded as the founder of modern utilitarianism.

Utilitarianism is a family of consequentialist ethical theories that promotes actions that maximize happiness and well-being for the majority of a population. Although different varieties of utilitarianism admit different characterizations, the basic idea behind all of them is to in some sense maximize utility, which is often defined in terms of well-being or related concepts. For instance, Jeremy Bentham, the founder of utilitarianism, described utility as

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 ]

See also

Notes

  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.

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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 and philosopher, who since 1972 has taught and worked in India, 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, and indices of the measure of well-being of citizens of developing 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.

Normative economics is a part of economics that expresses value or normative judgments about economic fairness or what the outcome of the economy or goals of public policy ought to be.

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.

Lexicographic preferences or lexicographic orderings describe comparative preferences where an economic agent prefers any amount of one good (X) to any amount of another (Y). Specifically, if offered several bundles of goods, the agent will choose the bundle that offers the most X, no matter how much Y there is. Only when there is a tie between bundles with regard to the number of units of X will the agent start comparing the number of units of Y across bundles. Lexicographic preferences extend utility theory analogously to the way that nonstandard infinitesimals extend the real numbers. With lexicographic preferences, the utility of certain goods is infinitesimal in comparison to others.

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<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

Quasitransitivity is a weakened version of transitivity that is used in social choice theory or 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.

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.

Yew-Kwang Ng is a professor of economics at Nanyang Technological University. He has published in a variety of academic disciplines, and is best known for his work in welfare economics.

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.

Kotaro Suzumura Japanese economist

Kotaro Suzumura is a Japanese economist and professor emeritus of Hitotsubashi University. He graduated from Hitotsubashi University in 1966. His research interests have included social choice theory and welfare economics. He was also a Fellow of the Econometric Society.

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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, a research associate for the Oxford Poverty & Human Development Initiative (OPHI), and a fellow of the Human Development and Capability Association.

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