Hybrid choice systems in small-n elections with sophisticated electorates

Abstract Faced with the classic paradoxes of voting, system designers have sometimes offered hybrid systems. The paper reviews Condorcet–Borda hybrids proposed by Daunou, Dodgson, Nanson, and Kemeny; and Borda-Balinski hybrids in use in at least one scientific academy. The justification of the hybrids is practical rather than theoretical, as they cannot escape the known features of their parent systems. In particular, as Condorcet showed in 1788, all Borda systems violate independence of irrelevant alternatives (in some formulation).