Consensus rules for committee elections

The committee election problem is to choose from a finite set S of candidates a nonempty subset T of committee members as the consequence of an election in which each voter expresses a preference for a candidate in S . Consensus rules for electing committees can be modeled as optimization problems based on criteria involving distances, angles or ratios of quantities derived from the election tallies. We describe three such consensus rules and discuss their features and interrelationships.