Arrow's impossibility theorem

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The theorem provides a proof that no perfect process exists for aggregating individual rankings of alternatives into a collective (or social) ranking. An example of an aggregation process is majority voting but the Condorcet paradox shows how this can fail to produce a useful outcome. A perfect process is defined as one that satisfies a set of desirable axioms. The basis of Arrow's theorem is a set of axioms that a collective ranking must satisfy. One of several equivalent ways of expressing these axioms is the following. Independence of irrelevant alternatives: adding a new option should not affect the initial ranking of the old options, so the collective ranking over the old options should remain unchanged. Non‐dictatorship: the collective ranking should not be determined by the preferences of a single individual. Pareto criterion: if every individual agrees on the ranking of the options, so should society. Hence, the collective ranking should coincide with the common individual ranking. Unrestricted domain: the collective choice method should accommodate any possible individual ranking of options. Transitivity: if option A is preferred to option B and B to C in the social ranking then C cannot be preferred to A. The theorem proves that there is no aggregation process that simultaneously satisfies these five axioms. See also collective choice; interpersonal comparisons; voting.

Subjects: Psychology — Economics.

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