Communication Complexity of Common Voting Rules

We determine the communication complexity of the com- mon voting rules. The rules (sorted by their communication complexity from low to high) are plurality, plurality with runoff, single transferable vote (STV), Condorcet, approval, Bucklin, cup, maximin, Borda, Copeland, and ranked pairs. For each rule, we first give a deterministic communication protocol and an upper bound on the number of bits com- municated in it; then, we give a lower bound on (even the nondeterministic) communication requirements of the vot- ing rule. The bounds match for all voting rules except STV and maximin.