Measuring Majority Power and Veto Power of Voting Rules
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We study voting rules with respect to how they allow or limit a majority to dominate minorities: whether a voting rule makes a majority powerful, and whether minorities can veto candidates that they do not prefer. For a given voting rule, the minimal share of voters that guarantees a victory to one of their most preferred candidates is the measure of majority power, and the minimal share of voters that allows to veto each of their least preferred candidates is the measure of veto power. We find tight bounds on these minimal shares for voting rules that are popular in the literature and real elections. We order these rules according to majority power and veto power. The instant-runoff rule has both the highest majority power and the highest veto power and the plurality rule has the lowest. In general, the higher majority power of a voting rule is, the higher is its veto power. The two exceptions are Black's rule and Borda rule that have a relatively low level of majority power and a high level of veto power and thus provide minority protection.
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