Following Barbera, Sonnenschein, and Zhou (1991, Econometrica 59, 595-609), we study rules (or social choice functions) through which agents select a subset from a set of objects. We investigate domains on which there exist nontrivial strategy-proof rules. We establish that the set of separable...

Domains of individual preferences for which the well-known impossibility theorems of Gibbard-Satterthwaite and Muller-Satterthwaite do not hold are studied. To comprehend the limitations these results imply for social choice rules, we search for the largest domains that are possible. Here, we...

The division problem consists of allocating a given amount of an homogeneous and perfectly divisible good among a group of agents with singlepeaked preferences on the set of their potential shares. A rule proposes a vector of shares for each division problem. Most of the literature has...