Approval voting reconsidered

Abstract

The merit of approval voting has been widely discussed in the past 25 years. The distinct property of this rule is the extent of flexibility it allows; any voter can approve as many alternatives/candidates as he wishes. Nevertheless, this advantage is the very reason for two drawbacks of approval voting: its extreme vulnerability to majority decisiveness (Theorem 1) and its extreme vulnerability to erosion of the majority principle (Theorem 2). On the one hand, under some feasible voting strategies any majority of more than 1/2 of the voters can guarantee the selection of its most favorable candidate, regardless of the preferences of the other voters. On the other hand, under alternative voting strategies even the largest majority cannot impose its common most preferred candidate. A simultaneous resolution of the two problems is possible by restricted approval voting (RAV), a voting rule that allows partial voter flexibility by restricting the minimal and maximal number of candidates that can be approved. Our main result (Theorem 3) clarifies how the foregone flexibility in voters’ sovereignty mitigates the above mentioned drawbacks under sincere and insincere coordinated voting. Our findings suggest a new possible justification of a particular voting rule which is based on the significance assigned to three considerations: the advantages of voters’ flexibility, immunity to majority decisiveness and immunity to erosion of the majority principle. Such justification can provide a possible explanation to the prevalent use of some special cases of RAV, notably, of the plurality rule and of approval voting. Copyright Springer-Verlag Berlin/Heidelberg 2005