Social choice theory
Encyclopedia
Social choice theory is a theoretical
framework for measuring individual interests, values, or welfares as an aggregate towards collective decision. A non-theoretical example of a collective decision is passing a 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 the Arrow's impossibility theorem
are generally acknowledged as the basis of the modern social choice theory.
Social choice theory blends elements of welfare economics
and voting theory. It is methodologically individualistic
, in that it aggregates preferences and behaviors of individual members of society. A characteristic approach proceeds from a set of reasonable axioms of social choice to a social welfare function
(or constitution). Many earlier results uncover the logical incompatibility of various axioms and, having revealed thus the aggregation problem
, suggest reformulation or theoretical triage
in dropping some axiom(s).
Social choice theory and public choice theory
may overlap but are disjoint if narrowly construed. The JEL classification codes places Social Choice into 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).
, 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 (ICU)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 ICU 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.
Theory
The English word theory was derived from a technical term in Ancient Greek philosophy. The word theoria, , meant "a looking at, viewing, beholding", and referring to contemplation or speculation, as opposed to action...
framework for measuring individual interests, values, or welfares as an aggregate towards collective decision. A non-theoretical example of a collective decision is passing a set of laws under a constitution. Social choice theory dates from Condorcet
Marquis de Condorcet
Marie Jean Antoine Nicolas de Caritat, marquis de Condorcet , known as Nicolas de Condorcet, was a French philosopher, mathematician, and early political scientist whose Condorcet method in voting tally selects the candidate who would beat each of the other candidates in a run-off election...
's formulation of the voting paradox
Voting paradox
The voting paradox 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. This is paradoxical, because it means that majority wishes can be in conflict with each other...
. Kenneth Arrow
Kenneth Arrow
Kenneth Joseph Arrow is an American economist and joint winner of the Nobel Memorial Prize in Economics with John Hicks in 1972. To date, he is the youngest person to have received this award, at 51....
's Social Choice and Individual Values
Social Choice and Individual Values
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...
(1951) and the Arrow's impossibility theorem
Arrow's impossibility theorem
In social choice theory, Arrow’s impossibility theorem, the General Possibility Theorem, or Arrow’s paradox, states that, when voters have three or more distinct alternatives , no voting system can convert the ranked preferences of individuals into a community-wide ranking while also meeting a...
are generally acknowledged as the basis of the modern social choice theory.
Social choice theory blends elements of welfare economics
Welfare economics
Welfare economics is a branch of economics that uses microeconomic techniques to evaluate economic well-being, especially relative to competitive general equilibrium within an economy as to economic efficiency and the resulting income distribution associated with it...
and voting theory. It is methodologically individualistic
Methodological individualism
Methodological individualism is the theory that social phenomena can only be accurately explained by showing how they result from the intentional states that motivate the individual actors. The idea has been used to criticize historicism, structural functionalism, and the roles of social class,...
, in that it aggregates preferences and behaviors of individual members of society. A characteristic approach proceeds from a set of reasonable axioms of social choice to a social welfare function
Social welfare function
In economics, a social welfare function is a real-valued function that ranks conceivable social states from lowest to highest. Inputs of the function include any variables considered to affect the economic welfare of a society...
(or constitution). Many earlier results uncover the logical incompatibility of various axioms and, having revealed thus the aggregation problem
Aggregation problem
An aggregate in economics is a summary measure describing a market or economy. The aggregation problem refers to the difficulty of treating 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...
, suggest reformulation or theoretical triage
Triage
Triage or ) is the process of determining the priority of patients' treatments based on the severity of their condition. This rations patient treatment efficiently when resources are insufficient for all to be treated immediately. The term comes from the French verb trier, meaning to separate,...
in dropping some axiom(s).
Social choice theory and public choice theory
Public choice theory
In economics, public choice theory is the use of modern economic tools to study problems that traditionally are in the province of political science...
may overlap but are disjoint if narrowly construed. The JEL classification codes places Social Choice into 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 BenthamJeremy Bentham
Jeremy Bentham was an English jurist, philosopher, and legal and social reformer. He became a leading theorist in Anglo-American philosophy of law, and a political radical whose ideas influenced the development of welfarism...
, utilitarians
Utilitarianism
Utilitarianism is an ethical theory holding that the proper course of action is the one that maximizes the overall "happiness", by whatever means necessary. It is thus a form of consequentialism, meaning that the moral worth of an action is determined only by its resulting outcome, and that one can...
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
Lionel Robbins
Lionel Charles Robbins, Baron Robbins, FBA was a British economist and head of the economics department at the London School of Economics...
questioned whether mental states, and utilities they reflect, can be measured and, a fortiori, interpersonal comparisons of utility
Utility
In economics, utility is a measure of customer satisfaction, referring to the total satisfaction received by a consumer from consuming a good or service....
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
An Essay on the Nature and Significance of Economic Science
Lionel Robbins' Essay sought to define more precisely economics as a science and to derive substantive implications. Analysis is relative to "accepted solutions of particular problems" based on best modern practice as referenced, especially including the works of Philip Wicksteed, Ludwig von...
, pp. 138–40), Robbins argued that this notion is beyond positive science
Positive science
In the humanities and social sciences, the term positive is used in at least two ways.The most common usage refers to analysis or theories which only attempt to describe how things 'are', as opposed to how they 'should' be. Positive means also 'value free'. In this sense, the opposite of positive...
; 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 (ICU)have argued that Robbins claimed too much. John Harsanyi
John Harsanyi
John Charles Harsanyi was a Hungarian-Australian-American economist and Nobel Memorial Prize in Economic Sciences winner....
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
Amartya Sen
Amartya Sen, CH is an Indian economist who was awarded the 1998 Nobel Prize in Economic Sciences for his contributions to welfare economics and social choice theory, and for his interest in the problems of society's poorest members...
(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 ICU 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
Capability approach
The capability approach was initially conceived in the 1980s as an approach to welfare economics....
. 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.
See also
- Arrow's impossibility theoremArrow's impossibility theoremIn social choice theory, Arrow’s impossibility theorem, the General Possibility Theorem, or Arrow’s paradox, states that, when voters have three or more distinct alternatives , no voting system can convert the ranked preferences of individuals into a community-wide ranking while also meeting a...
- Capability approachCapability approachThe capability approach was initially conceived in the 1980s as an approach to welfare economics....
- Compensation principleCompensation principleIn 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...
- Extended sympathyExtended sympathyExtended 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...
- Gibbard–Satterthwaite theorem
- Justice (economics)Justice (economics)Justice in economics is a subcategory of welfare economics with models frequently representing the ethical-social requirements of a given theory. That theory may or may not elicit acceptance...
- Liberal paradoxLiberal paradoxThe liberal paradox is a logical paradox advanced by Amartya Sen, building on the work of Kenneth Arrow and his impossibility theorem, which showed that within a system of menu-independent social choice, it is impossible to have both a commitment to "Minimal Liberty", which was defined as the...
- Mechanism designMechanism designMechanism design is a field in game theory studying solution concepts for a class of private information games...
- Nakamura numberNakamura numberIn cooperative game theory and social choice theory, the Nakamura number measures the degree of rationalityof preference aggregation rules , such as voting rules....
- Rule according to higher lawRule according to higher lawThe rule according to a higher law means that no written law may be enforced by the government unless it conforms with certain unwritten, universal principles of fairness, morality, and justice...
- Relative Utilitarianism
- Voting systemVoting systemA voting system or electoral system is a method by which voters make a choice between options, often in an election or on a policy referendum....