Axioms for Euclidean preferences with a valence dimension

Recent works on political competition incorporate a valence dimension to the standard spatial model. The goal of this paper is to axiomatize rankings of candidates by voters that are consistent with Euclidean preferences on the policy space and an additive valence dimension. Specifically, we consider the case where only the ideal point in the policy space and the ranking over candidates are known for each voter. We characterize the case where there are policies x1,…,xm for m candidates and numbers v1,…,vm representing valence scores, such that a voter with an ideal policy y ranks the candidates according to vi−‖xi−y‖2.