The single-peaked domain revisited: A simple global characterization - Clemens Puppe (Karlsruher Institut für Technologie (KIT), Institut für Volkswirtschaftslehre (ECON), 2016)
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. It is argued that this result explains the predominant role of single-peakedness as a domain restriction in models of political economy and elsewhere. The main result has a number of corollaries, among them a dual characterization of the single-dipped do- main; it also implies that a single-crossing ('order-restricted') domain can be minimally rich only if it is a subdomain of a single-peaked domain. The conclusions are robust as the results apply both to domains of strict and of weak preference orders, respectively.
urn:nbn:de:swb:90-620151
Keywords: D71; C72; 330; social choice; restricted domains; Condorcet domains; single-peakedness; single-dippedness; majority voting; single-crossing property