A minimax procedure for electing committees

A new voting procedure for electing committees, called the minimax procedure, is described. Based on approval balloting, it chooses the committee that minimizes the maximum Hamming distance to voters' ballots, where these ballots are weighted by their proximity to other voters' ballots. This minimax outcome may be diametrically opposed to the outcome obtained by aggregating approval votes in the usual manner, which minimizes the sum of the Hamming distances and is called the minisum outcome. The manipulability of these procedures, and their applicability when election outcomes are restricted in various ways, are also investigated. The minimax procedure is applied to the 2003 Game Theory Society election of a council of 12 new members from a list of 24 candidates. By rendering outlying voters less influential and not antagonizing any voters too much, it arguably would have produced a committee more representative of the interests of all voters than the minisum committee that was elected.