Single-peakedness and semantic dimensions of preferences

Among the possible solutions to the paradoxes of collective preferences, single-peakedness is significant because it has been associated to a suggestive conceptual interpretation: a single-peaked preference profile entails that, although individuals may disagree on which option is the best, they conceptualize the choice along a shared unique dimension, i.e. they agree on the rationale of the collective decision. In this article, we discuss the relationship between the structural property of single-peakedness and its suggested interpretation as uni-dimensionality of a social choice. In particular, we offer a formalization of the relationship between single-peakedness and its conceptual counterpart, we discuss their logical relations, and we question whether single-peakedness provides a rationale for collective choices.