Abstract
A constant scoring rule asks each individual to vote for a given (and constant) number of alternatives and the alternative with the most votes is elected. A sequential constant scoring rule applies this principle in a process of sequential elimination. Constant scoring rules as well as sequential constant scoring rules fail to satisfy Condorcet criteria when individual preferences are unrestricted. The purpose of this paper is to show that, if we assume that preferences are single-peaked, then some constant scoring rules satisfy the Condorcet loser criterion and some sequential constant scoring rules satisfy the Condorcet winner criterion. The results we provide make possible the identification of these rules.
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