Sincere Voting with Cardinal Preferences: Approval Voting

Abstract

We discuss sincere voting when voters have cardinal preferences over alternatives. We interpret sincerity as opposed to strategic voting, and thus define sincerity as the optimal behaviour when conditions to vote strategically vanish. When voting mechanisms allow for only one message type we show that this optimal behaviour coincides with an intuitive and common definition of sincerity. For voting mechanisms allowing for multiple message types, such as approval voting (AV), there exists no conclusive definition of sincerity in the literature. We show that for AV, voters' optimal strategy tends to one of the existent definitions of sincerity, consisting in voting for those alternatives that yield more than the average of cardinal utilities. ; Financial support from Ministerio de Ciencia y Tecnología through grants BEC 2005-00836, SEJ2005-01481/ECON and FEDER, Generalitat de Catalunya through grant 2005SGR00454 and Barcelona Economics-XREA is gratefully acknowledged.