We study axioms which define "representative democracy" in an environment in which agents vote over a finite set of alternatives. We focus on a property that states that whether votes are aggregated directly or indirectly make no difference. We call this property 'representative consistency'....

We show that in the context of repeated implementation, any social choice rule which realizes all alternatives for a positive (yet arbitrarily small) amount of time is Nash implementable. The results complement those of the virtual implementation literature.

We introduce a new class of rules for resolving quasilinear social choice problems. These rules extend those of Green [7]. We call such rules multi-utilitarian rules. Each multi-utilitarian rule is associated with a probability measure over the set of weighted utilitarian rules, and is derived...