  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.
