We compare approval voting with other scoring rules for environments with common values and private information. For finite electorates, the best equilibrium under approval voting is superior to plurality rule or negative voting. For large electorates, if any scoring rule yields a sequence of equilibria that efficiently aggregates information, then approval voting must do so as well.
Ahn, D. S., & Oliveros, S. (2016). Approval voting and scoring rules with common values. Journal of Economic Theory, 166, 304–310. https://doi.org/10.1016/j.jet.2016.09.002