A taxonomy of non-dictatorial domains - CHATTERJI, Shurojit (Institutional Knowledge at Singapore Management University, 2020)
We provide an exhaustive classiﬁcation of all preference domains that allow the design of unanimous social choice functions (henceforth, rules) that are non-dictatorial and strategy-proof. This taxonomy is based on a richness assumption and employs a simple property of two-voter rules called invariance. The preference domains that form the classiﬁcation are semi-single-peaked domains (introduced by Chatterji et al. (2013)) and semi-hybrid domains (introduced here) which are two appropriate weakenings of the single-peaked domains, and which, more importantly, are shown to allow strategy-proof rules to depend on non-peak information of voters’ preferences. As a reﬁnement of the classiﬁcation, single-peaked domains and hybrid domains emerge as the only preference domains that force strategy-proof rules to be determined completely by the peaks of voters’ preferences. We also provide characterization results for strategy-proof rules on these domains.