A Minimax Procedure for Electing Committees

A new voting procedure for electing committees, called the minimax procedure, is described. Based on approval voting (AV), it chooses the committee that minimizes the maximum “Hamming distance” to all voters (minimax outcome). Such an outcome may be diametrically opposed to the outcome obtained from aggregating votes in the usual manner, which minimizes the sum of the Hamming distances to all voters (minisum outcome). Computer simulation is used to assess how much minimax and minisum outcomes tend to diverge. The manipulability of the minimax procedure is also investigated. The minimax procedure is applied to the 2003 Game Theory Society (GTS) election of a council of 12 new members from a list of 24 candidates. The 9 and 10 biggest vote-getters would have been displaced by the 16 and 17 biggest vote-getters if the minimax procedure had been used; there would have been more substantial differences if the size of the council had been made endogenous rather than being fixed at 12. It is argued that when few if any voters cast identical AV ballots, as was true in the GTS election (there were 2 ≈ 16.8 million possible ballots), a minimax committee will better represent the interests of all voters than a minisum committee.