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Score voting or range voting is an electoral system for single-seat elections, in which voters give each candidate a score, the scores are added, and the candidate with the highest total is elected. It has been described by various other names including evaluative voting, utilitarian voting, interval measure voting, the point system, ratings summation, 0-99 voting, average voting and utilityvoting. It is a type of cardinal voting electoral system, and aims to implement the utilitarian social choice rule.
Arrow's impossibility theorem, the general possibility theorem or Arrow's paradox is an impossibility theorem in social choice theory that states 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 the 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.
The independence of irrelevant alternatives (IIA), also known as binary independence or the independence axiom, is an axiom of decision theory and various social sciences. The term is used in different connotation in several contexts. Although it always attempts to provide an account of rational individual behavior or aggregation of individual preferences, the exact formulation differs widely in both language and exact content.
In social choice theory, the Gibbard–Satterthwaite theorem is a result published independently by philosopher Allan Gibbard in 1973 and economist Mark Satterthwaite in 1975. It deals with deterministic ordinal electoral systems that choose a single winner. It states that for every voting rule, one of the following three things must hold:
- The rule is dictatorial, i.e. there exists a distinguished voter who can choose the winner; or
- The rule limits the possible outcomes to two alternatives only; or
- The rule is susceptible to tactical voting: in certain conditions, a voter's sincere ballot may not best defend their opinion.
Welfare economics is a field of economics that applies microeconomic techniques to evaluate the overall well-being (welfare) of a society. This evaluation is typically done at the economy-wide level, and attempts to assess the distribution of resources and opportunities among members of society.
Strategic nomination refers to the entry of a candidate into an election with the intention of changing the ranking of other candidates. The name is an echo of ‘tactical voting’ and is intended to imply that it is the candidates rather than the voters who are seeking to manipulate the result in a manner unfaithful to voters’ true preferences.
In social choice theory, May's theorem states that simple majority voting is the only anonymous, neutral, and positively responsive social choice function between two alternatives. Further, this procedure is resolute when there are an odd number of voters and ties (indecision) are not allowed. Kenneth May first published this theorem in 1952.
The liberal paradox, also Sen paradox or Sen's paradox, is a logical paradox proposed by Amartya Sen which shows that no means of aggregating individual preferences into a single, social choice, can simultaneously fulfill the following, seemingly mild conditions:
- The unrestrictedness condition, or U: every possible ranking of each individual's preferences and all outcomes of every possible voting rule will be considered equally,
- The Pareto condition, or P: if everybody individually likes some choice better at the same time, the society in its voting rule as a whole likes it better as well, and
- Liberalism, or L : all individuals in a society must have at least one possibility of choosing differently, so that the social choice under a given voting rule changes as well. That is, as an individual liberal, anyone can exert their freedom of choice at least in some decision with tangible results.
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. Whereas choice theory is concerned with individuals making choices based on their preferences, social choice theory is concerned with how to translate the preferences of individuals into the preferences of a group. A non-theoretical example of a collective decision is enacting a law or set of laws under a constitution. Another example is voting, where individual preferences over candidates are collected to elect a person that best represents the group's preferences.
Positional voting is a ranked voting electoral system in which the options or candidates receive points based on their rank position on each ballot and the one with the most points overall wins. The lower-ranked preference in any adjacent pair is generally of less value than the higher-ranked one. Although it may sometimes be weighted the same, it is never worth more. A valid progression of points or weightings may be chosen at will or it may form a mathematical sequence such as an arithmetic progression, a geometric one or a harmonic one. The set of weightings employed in an election heavily influences the rank ordering of the candidates. The steeper the initial decline in preference values with descending rank, the more polarised and less consensual the positional voting system becomes.
Allan Fletcher Gibbard is the Richard B. Brandt Distinguished University Professor of Philosophy Emeritus at the University of Michigan, Ann Arbor. Gibbard has made major contributions to contemporary ethical theory, in particular metaethics, where he has developed a contemporary version of non-cognitivism. He has also published articles in the philosophy of language, metaphysics, and social choice theory.
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.
The Duggan–Schwartz theorem is a result about voting systems designed to choose a nonempty set of winners from the preferences of certain individuals, where each individual ranks all candidates in order of preference. It states that for three or more candidates, at least one of the following must hold:
- The system is not anonymous.
- The system is imposed.
- Every voter's top preference is in the set of winners.
- The system can be manipulated by either an optimistic voter, one who can cast a ballot that would elect some candidate to a higher rank than all of those candidates who would have been elected if that voter had voted honestly; or by a pessimistic voter, one who can cast a ballot that would exclude some candidate to a lower rank than all of those candidates who were elected due that voter voting strategically.
In social choice theory, a dictatorship mechanism is a rule by which, among all possible alternatives, the results of voting mirror a single pre-determined person's preferences, without consideration of the other voters. Dictatorship by itself is not considered a good mechanism in practice, but it is theoretically important: by Arrow's impossibility theorem, when there are at least three alternatives, dictatorship is the only ranked voting electoral system that satisfies unrestricted domain, Pareto efficiency, and independence of irrelevant alternatives. Similarly, by Gibbard's theorem, when there are at least three alternatives, dictatorship is the only strategyproof rule.
Intensity of preference, also known as intensity preference, is a term popularized by the work of the economist Kenneth Arrow, who was a co-recipient of the 1972 Nobel Memorial Prize in Economics. This term is used in reference to models for aggregating ordinal rankings.
The term ranked voting, also known as preferential voting or ranked choice voting refers to any voting system in which voters rank their candidates or options—in a sequence of first, second, third, and so on—on their respective ballots. Ranked voting systems differ on the basis of how the ballots are marked, how the preferences are tabulated and counted, how many seats are filled, and whether voters are allowed to rank candidates equally. An electoral system that uses ranked voting uses one of the many available counting methods to select the winning candidate or candidates. There is also variation among ranked voting electoral systems in that in some ranked voting systems, officials require voters to rank a set number of candidates, sometimes all of them; in others, citizens may rank as many candidates as they see fit.
Arunava Sen is a professor of economics at the Indian Statistical Institute. He works on Game Theory, Social Choice Theory, Mechanism Design, Voting and Auctions.
Maximal lotteries refers to a probabilistic voting system first considered by the French mathematician and social scientist Germain Kreweras in 1965. The method uses preferential ballots and returns so-called maximal lotteries, i.e., probability distributions over the alternatives that are weakly preferred to any other probability distribution. Maximal lotteries satisfy the Condorcet criterion, the Smith criterion, reversal symmetry, polynomial runtime, and probabilistic versions of reinforcement, participation, and independence of clones.
Computational social choice is a field at the intersection of social choice theory, theoretical computer science, and the analysis of multi-agent systems. It consists of the analysis of problems arising from the aggregation of preferences of a group of agents from a computational perspective. In particular, computational social choice is concerned with the efficient computation of outcomes of voting rules, with the computational complexity of various forms of manipulation, and issues arising from the problem of representing and eliciting preferences in combinatorial settings.
References
- Arrow, K.J. (August 1950), "A Difficulty in the Concept of Social Welfare" (PDF), Journal of Political Economy , 58 (4): 328–346, doi:10.1086/256963, S2CID 13923619 .
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