Single-peaked consistency and its complexity

A common way of dealing with the paradoxes of preference aggregation consists in restricting the domain of admissible preferences. The most well-known such restriction is single-peakedness. In this paper we focus on the problem of determining whether a given profile is single-peaked with respect to some axis, and on the computation of such an axis. This problem has already been considered in [2]; we give here a more efficient algorithm and address some related issues, such as the number of orders that may be compatible with a given profile, or the communication complexity of preference aggregation under the single-peakedness assumption.