## Quick Reference

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.