The unavailable candidate model

Abstract

One of the fundamental problems in the theory of social choice is aggregating the rankings of a set of agents (or voters) into a consensus ranking. Rank aggregation has found application in a variety of computational contexts. However, the goal of constructing a consensus ranking rather than, say, a single outcome (or winner) is often left unjustified, calling into question the suitability of classical rank aggregation methods. We introduce a novel model which offers a decision-theoretic motivation for constructing a consensus ranking. Our unavailable candidate model assumes that a consensus choice must be made, but that candidates may become unavailable after voters express their preferences. Roughly speaking, a consensus ranking serves as a compact, easily communicable representation of a decision policy that can be used to make choices in the face of uncertain candidate availability. We use this model to define a principled aggregation method that minimizes expected voter dissatisfaction with the chosen candidate. We give exact and approximation algorithms for computing optimal rankings and provide computational evidence for the effectiveness of a simple greedy scheme. We also describe strong connections to popular voting protocols such as the plurality rule and the Kemeny consensus, showing specifically that Kemeny produces optimal rankings in the unavailable candidate model under certain conditions.