I establish conditions for existence of pure strategy equilibria in K-candidate Downsian electoral competition (K ≥ 2) with valence when the voting rule is monotonic, generalizing results by Ansolabehere and Snyder (2000) and Martin et al. (2021). The conditions are sufficient when K ≥ 2 and...

When is a finite number of binary voting choices consistent with the hypothesis that the voter has preferences that admit a (quasi)concave utility representation? I derive necessary and sufficient conditions and a tractable algorithm to verify their validity. I show that the hypothesis that the...