Computer-assisted constrained approval voting

Approval voting, proposed independently by several analysts in the 1970s, is a voting system in which voters can vote for as many candidates as they like in multicandidate elections. Recently, S.J. Brams modified this system, introducing so-called constrained approval voting. It is designed for a professional association to ensure equitable representation of different interests. In his new system approval voting is combined with the constraints on the number of persons that can be elected from different categories of members. In the present paper the problem of constrained approval voting is formulated (following the work of R.F. Potthoff) as an integer programming problem. Some computational aspects of this problem are discussed. The paper presents a numerical example illustrating a possibility to apply the discussed voting procedure in the election of members of the Committee for Organization and Management Sciences of the Polish Academy of Sciences.