CONSTANT SCORING RULES, CONDORCET CRITERIA AND SINGLE-PEAKED PREFERENCES

A constant scoring rule asks each individual to vote for a given (and constant) number of alternatives and the alternative with the most vot es is elected. A sequential constant scoring rule applies this princip le in a process of sequential elimination. Constant scoring rules as w ell as sequential constant scoring rules fail to satisfy Condorcet cri teria when individual preferences are unrestricted. The purpose of thi s paper is to show that, if we assume that preferences are single-peak ed, then some constant scoring rules satisfy the Condorcet loser crite rion and some sequential constant scoring rules satisfy the Condorcet winner criterion. The results we provide make possible the identificat ion of these rules.