Communication complexity of common voting rules

Vincent Conitzer,Tuomas Sandholm

doi:10.1145/1064009.1064018

Abstract

We determine the communication complexity of the common 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 communicated in it; then, we give a lower bound on (even the nondeterministic) communication requirements of the voting rule. The bounds match for all voting rules except STV and maximin.

Highlights

One key factor in the practicality of any preference aggregation rule is its communication burden
Most of the work on reducing the communication burden in preference aggregation has focused on resource allocation settings such as combinatorial auctions, in which an auctioneer auctions off a number of items in a single event
Segal studies social choice rules in general, and shows that for a large class of social choice rules, supporting budget sets must be revealed such that if every agent prefers the same outcome in her budget set, this proves the optimality of that outcome

Summary

Introduction

One key factor in the practicality of any preference aggregation rule is its communication burden. Because in a combinatorial auction, bidders can have separate valuations for each of an exponential number of possible bundles of items, this is a setting in which reducing the communication burden is especially crucial. This can be accomplished by supplementing the auctioneer with an elicitor that incrementally elicits parts of the bidders’ preferences on an as-needed basis, based on what the bidders have revealed about their preferences so far, as suggested by Conen and Sandholm [5]. Segal uses this characterization to prove bounds on the communication required in resource allocation as well as matching settings [20]

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Conclusion