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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.
It is closely tied to many of the most important theorems in these fields, including Arrow's impossibility theorem, the Balinski–Young theorem, and the money pump arguments. In behavioral economics, failures of IIA (caused by irrationality) are called menu effects or menu dependence. [3]
Arrow's Theorem [2]: The constitution is impossible, that is, the 4 conditions of a constitution imply a contradiction. Each voter has an ordering (by attribution). Yet a set of orderings used as an argument of the voting rule does not carry over to a social ordering, with a corresponding loss of social adaptivity and constitutional generality ...
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 ...
Arrow's impossibility theorem states that for three and more candidates, the only unanimous voting rule for which there is always a Condorcet winner is a dictatorship. The usual proof of Arrow's theorem is combinatorial. Kalai [13] gave an alternative proof of this result in the case of three candidates using Fourier analysis.
Arrow's impossibility theorem is a key result on social welfare functions, showing an important difference between social and consumer choice: whereas it is possible to construct a rational (non-self-contradictory) decision procedure for consumers based only on ordinal preferences, it is impossible to do the same in the social choice setting ...
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