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Because of this example, some authors credit Condorcet with having given an intuitive argument that presents the core of Arrow's theorem. [20] However, Arrow's theorem is substantially more general; it applies to methods of making decisions other than one-man-one-vote elections, such as markets or weighted voting, based on ranked ballots.
The work culminated in what Arrow called the "General Possibility Theorem," better known thereafter as Arrow's (impossibility) theorem. The theorem states that, absent restrictions on either individual preferences or neutrality of the constitution to feasible alternatives, there exists no social choice rule that satisfies a set of plausible ...
Arrow's impossibility theorem shows that no reasonable (non-random, non-dictatorial) ranked voting system can satisfy IIA. However, Arrow's theorem does not apply to rated voting methods. These can pass IIA under certain assumptions, but fail it if they are not met. Methods that unconditionally pass IIA include sortition and random dictatorship.
Unrestricted domain is one of the conditions for Arrow's impossibility theorem. Under that theorem, it is impossible to have a social choice function that satisfies unrestricted domain, Pareto efficiency, independence of irrelevant alternatives, and non-dictatorship. However, the conditions of the theorem can be satisfied if unrestricted domain ...
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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.
Gibbard's theorem can be proven using Arrow's impossibility theorem. Gibbard's theorem is itself generalized by Gibbard's 1978 theorem [ 11 ] and Hylland's theorem , which extend these results to non-deterministic processes, i.e. where the outcome may not only depend on the agents' actions but may also involve an element of chance.
Non-dictatorship is one of the necessary conditions in Arrow's impossibility theorem. [1] In Social Choice and Individual Values , Kenneth Arrow defines non-dictatorship as: There is no voter i {\displaystyle i} in { 1 , ..., n } such that, for every set of orderings in the domain of the constitution, and every pair of social states x and y , x ...