Approval voting and Arrow’s impossibility theorem

Approval voting has attracted considerable attention in voting theory, but it has rarely been investigated in an Arrovian framework of collective preference (”social welfare”) functions and never been connected with Arrow’s impossibility theorem. The article explores these two directions. Assuming that voters have dichotomous preferences, it first characterizes approval voting in terms of its collective preference properties and then shows that these properties become incompatible if the collective preference is also taken to be dichotomous. As approval voting and majority voting happen 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 and Inada’s early findings on this rule. The negative result is a novel and perhaps surprising version of Arrow’s impossibility theorem, because the axiomatic inconsistency here stems from the collective preference range, not the individual preference domain.