A Model of k-Winners

The concept of the Condorcet winner has become central to most electoral models in the political economy literature. A Condorcet winner is the alternative preferred by a plurality in every pairwise competition; the notion of a k-winner generalizes that of a Condorcet winner. The k-winner is the unique alternative top-ranked by the plurality in every competition comprising exactly k alternatives (including itself). This study uses a spatial voting setting to characterize this theoretical concept, showing that if a k-winner exists for some k>2, then the same alternative must be the k′-winner for every k′>k. We derive additional results, including sufficient and necessary conditions for the existence of a k-winner for some k>2.