In settings where the policy space is single dimensional, non-single peaked preferences by some implies there is no Condorcet winner.

Question

Quizplus · Accepted Answer

In single-dimensional policy spaces, even if some individuals have non-single-peaked preferences, a Condorcet winner can still exist if a majority of voters have preferences that align in a way that one option is preferred over all others in pairwise comparisons. Non-single-peaked preferences complicate the identification of a Condorcet winner but do not make it impossible.

In Settings Where the Policy Space Is Single Dimensional, Non-Single