To vote or not to vote: What is the quota?

The observatton of a new type of perverse behavior of votmg rules-Brams and Ftshburn’s “no-show paradox”--led Mouhn to Introduce the Parttctpatton Axtom (PA) It requires that an elector’s failure to vote should never result m the election of a candtdate whom he/she prefers to the one elected tf he/she votes sincerely The present paper examines PA in the context of Condorcet-type conditions For a given quota q, 3 5 qs 1, the q-Core Condition (qCC) requires that whenever there exists a candidate such that no other candidate 1s preferred to him/her by a fraction of q or more of the voters, the elected candidate should have this property It 1s shown here that PA and qCC are consistent rff qz (m 1)/m or tn 5 3, where m IS the number of candidates. This essentially confirms a conjecture of Mouhn and extends hts original result for q = j