The Single-Peaked Domain Revisited: A Simple Global Characterization
It is proved that, among all restricted preference domains that guarantee consistency (i.e. transitivity) of pairwise majority voting, the single-peaked domain is the only minimally rich and connected domain that contains two completely reversed strict preference orders.This result has a number of corollaries, among other things it implies that a single-crossing (‘order-restricted’) domain can be minimally rich only if it is a subdomain of a single-peaked domain.