Pareto efficiency in multiple referendum

We consider situations of multiple referendum: finitely many yes‐or‐no issues have to be socially assessed from a set of approval ballots, where voters approve as many issues as they want. Each approval ballot is extended to a complete preorder over the set of outcomes by means of a preference extension. We characterize, under a mild richness condition, the largest domain of top‐consistent and separable preference extensions for which issue‐wise majority voting is Pareto efficient, i.e., always yields out a Pareto‐optimal outcome. Top‐consistency means that voters’ ballots are their unique most preferred outcome. It appears that the size of this domain becomes negligible relative to the size of the full domain as the number of issues increases.