Single-peaked domains with designer uncertainty

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 choice rules (SCRs) to be implementable. The characterization is used to identify unanimous and anonymous implementable SCRs for different forms of designer uncertainty, which basically boils down to picking the right SCRs from the large class identified by Moulin (Public Choice 35(4):437–455, 1980), and hence this result can be seen as identifying which of Moulin’s SCRs are robust to designer uncertainty.