Full Information Equivalence in Large Elections

We study the problem of aggregating private information in elections with two or more alternatives for a large family of scoring rules. We introduce a feasibility condition, the linear refinement condition, that characterizes when information can be aggregated asymptotically as the electorate grows large: there must exist a utility function, linear in distributions over signals, sharing the same top alternative as the primitive utility function. Our results complement the existing work where strong assumptions are imposed on the environment, and caution against potential false positives when too much structure is imposed.