Solidarity for public goods under single-peaked preferences: characterizing target set correspondences

Abstract

We consider the problem of choosing a set of locations of a public good on the real line R. Similarly to Klaus and Storcken (2002), we ordinally extend the agents' preferences over compact subsets of R, and extend the results of Ching and Thomson (1996), Vohra (1999 to choice correspondences. Specifically, we show that efficiency and either population-monotonicity or one-sided replacement-dominance characterize the class of target set correspondences on the domains of single-peaked preferences and symmetric single-peaked preferences.

On strategy-proofness and single-peakedness: median-voting over intervals

“…The next characterization of efficient sets follows from Klaus and Protopapas (2020) and it coincides with the well-known characterization of (Pareto) efficient points for choice functions. Note that the original result is a little more complicated since it holds for all compact sets.…”

“…Klaus and Storcken (2002) also use the best-worst extension of preferences to sets we use here. In a predecessor paper, Klaus and Protopapas (2020), for the same model as in this paper, considered so-called solidarity properties and show that efficiency and replacement-dominance 10 characterize the class of target point functions while efficiency and population-monotonicity 11 characterize the larger class of target set correspondences.…”

“…Although this correspondence seems to choose the two left-most peaks, when two or more agents share the minimum peak, it only chooses the minimum peak. Furthermore, in Klaus and Protopapas (2020) the same properties as in Miyagawa (2001) (namely, efficiency and replacementdominance) are considered, for (almost) the same setting as in this paper. There, it is shown that each correspondence satisfying said properties is essentially a function, reconfirming a characterization of Vohra (1999) for target-point functions.…”