We characterize the maximal sets of preferences under which generalized median voter schemes are strategy-proof. Those domains are defined by a qualified version of single-peakedness, which depends on the distribution of power among agents implied by each generalized median voter scheme.

The division problem consists of allocating an amount M of a perfectly divisible good among a group of n agents. Sprumont (1991) showed that if agents have single-peaked preferences over their shares, the uniform rule is the unique strategy-proof, efficient, and anonymous rule. Ching and...

We study the problem of a society choosing a subset of new members from a finite set of candidates (as in Barberà et al. 1991). However, we explicitly consider the possibility that initial members of the society (founders) may want to leave it if they do not like the resulting new society. We...