Single-peaked domains with designer uncertainty

TL;DR

This paper explores how to implement social choice rules in single-peaked domains when the designer faces uncertainty about the underlying preferences, proposing a new solution concept and characterizing robust median rules.

Contribution

It introduces implementation in mixed information equilibria and characterizes which median rules are robust to designer uncertainty in single-peaked domains.

Findings

Necessary and sufficient conditions for social rule implementability.

Identification of median rules robust to designer uncertainty.

Application to various belief structures of the designer.

Abstract

This paper studies single-peaked domains where the designer is uncertain about the underlying alignment according to which the domain is single-peaked. The underlying alignment is common knowledge amongst agents, but preferences are private knowledge. Thus, the state of the world has both a public and private element, with the designer uninformed of both. I first posit a relevant solution concept called implementation in mixed information equilibria, which requires Nash implementation in the public information and dominant strategy implementation in the private information given the public information. I then identify necessary and sufficient conditions for social rules to be implementable. The characterization is used to identify unanimous and anonymous implementable social rules for various belief structures of the designer, which basically boils down to picking the right rules from the large class of median rules identified by Moulin (1980), and hence this result can be seen as identifying which median rules are robust to designer uncertainty.