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Social choice theory is a branch of welfare economics that extends the theory of rational choice to collective decision-making. [1] Social choice studies the behavior of different mathematical procedures ( social welfare functions ) used to combine individual preferences into a coherent whole.
In social choice theory, Condorcet's voting paradox is a fundamental discovery by the Marquis de Condorcet that majority rule is inherently self-contradictory.The result implies that it is logically impossible for any voting system to guarantee that a winner will have support from a majority of voters: for example there can be rock-paper-scissors scenario where a majority of voters will prefer ...
In social choice theory, unrestricted domain, or universality, is a property of social welfare functions in which all preferences of all voters (but no other considerations) are allowed. Intuitively, unrestricted domain is a common requirement for social choice functions, and is a condition for Arrow's impossibility theorem.
Arrow's theorem assumes as background that any non-degenerate social choice rule will satisfy: [15]. Unrestricted domain — the social choice function is a total function over the domain of all possible orderings of outcomes, not just a partial function.
In social choice theory, May's theorem, also called the general possibility theorem, [1] says that majority vote is the unique ranked social choice function between two candidates that satisfies the following criteria: Anonymity – each voter is treated identically, Neutrality – each candidate is treated identically,
The McKelvey–Schofield chaos theorem is a result in social choice theory. It states that if preferences are defined over a multidimensional policy space, then choosing policies using majority rule is unstable.
The Gibbard–Satterthwaite theorem is a theorem in social choice theory.It was first conjectured by the philosopher Michael Dummett and the mathematician Robin Farquharson in 1961 [1] and then proved independently by the philosopher Allan Gibbard in 1973 [2] and economist Mark Satterthwaite in 1975. [3]
(Intuitively, the social choice function represents a societal principle for choosing one or more social outcomes based on individuals' preferences. By representing the social choice process as a function on Rel(X) N , we are tacitly assuming that the social choice function is defined for any possible configuration of preference relations; this ...
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related to: social choice theory math examples for high schoolPrices are reasonable and worth every penny - Wendi Kitsteiner