Committee Selection with a Weight Constraint Based on Lexicographic Rankings of Individuals

We investigate the problem of selecting a committee consisting of k members from a list of m candidates. The selection of each candidate consumes a certain weight (or cost). Hence, the choice of the k-committee has to satisfy a weight (or budget) constraint: The sum of the weights of all selected committee members must not exceed a given value W . While the former part of the problem is a typical question in Social Choice Theory, the latter stems from Discrete Optimization. The purpose of our contribution is to link these two research fields: We first define reasonable ways of ranking sets of objects, i.e. candidates, and then develop efficient algorithms for the actual computation of optimal committees. We focus in particular on the running time complexity of the developed algorithms.