On the informational efficiency of simple scoring rules

We study information aggregation in large elections. With two candidates, efficient information aggregation is possible in a large election (e.g., Feddersen and Pesendorfer [4, 5, 6], among others). We find that this result does not extend to large elections with more than two candidates. More precisely, we study a class of simple scoring rules in large voting games with Poisson population uncertainty and three candidates. We show that there is no simple scoring rule that aggregates information efficiently, even if preferences are dichotomous and a unique Condorcet winner always exists. We introduce a weaker criterion of informational efficiency that requires a voting rule to have at least one efficient equilibrium. Only approval voting satisfies this criterion.