Single-peaked preferences over multidimensional binary alternatives

Single-peaked preferences are important throughout social choice theory. In this article, we consider single-peaked preferences over multidimensional binary alternative spaces-that is, alternative spaces of the form {0,1}n for some integer n≥2. We show that preferences that are single-peaked with respect to a normalized separable base order are nonseparable except in the most trivial cases. We establish that two distinct base orders can induce the same single-peaked preference order if any only if they differ by a transposition of their two central elements. We then use this result to enumerate single-peaked binary preference orders over a separable base order.