Approval Voting and Arrow's Impossibility Theorem


Social Choice and Welfare

mars 2015, vol. 44, n°3, pp.519-532

Départements : Economie et Sciences de la décision, GREGHEC (CNRS)

Approval voting has attracted considerable attention in voting theory, but ithasrarelybeeninvestigatedinanArrovianframeworkofcollectivepreference(”socialwelfare”) functions and never been connected with Arrow’s impossibility theorem.The article explores these two directions. Assuming that voters have dichotomouspreferences, it first characterizes approval voting in terms of its collective preferenceproperties and then shows that these properties become incompatible if the collectivepreference is also taken to be dichotomous. As approval voting and majority votinghappen to share the same collective preference function on the dichotomous domain,the positive result also bears on majority voting, and is seen to extend May’s andInada’s early findings on this rule. The negative result is a novel and perhaps surprisingversion of Arrow’s impossibility theorem, because the axiomatic inconsistency herestems from the collective preference range, not the individual preference domain