One Person, Many Votes: Divided Majority and Information Aggregation

In elections, majority divisions pave the way to focal manipulations and coordination failures, which can lead to the victory of the wrong candidate. This paper shows how this flaw can be addressed if voter preferences over candidates are sensitive to information. We consider two potential sources of divisions: majority voters may have similar preferences but opposite information about the candidates, or opposite preferences. We show that when information is the source of majority divisions, Approval Voting features a unique equilibrium with full information and coordination equivalence. That is, it produces the same outcome as if both information and coordination problems could be resolved. Other electoral systems, such as Plurality and Two-Round elections, do not satisfy this equivalence. The second source of division is opposite preferences. Whenever the fraction of voters with such preferences is not too large, Approval Voting still satisfies full information and coordination equivalence.