Alice and Bob will fight: the problem of electing a committee in the presence of candidate interdependence

The problem of electing a committee which satisfies voters is one for which good solutions are scarce. Extending single-winner voting rules to the multi-winner case works well only when voters have no preferential dependencies among candidates for the committee. (Our motivating example is a voter who believes that Alice and Bob are the best candidates, but also that the worst possible committee is one with both Alice and Bob.) In order to tackle the interdependence problem, we propose a voting rule called the Goalbase Summation Rule (GSR), which uses goalbases (sets of weighted propositional formulas) as ballots. Using goalbases as ballots lets voters express complex preferences in a compact fashion, while the computational complexity of finding winning committees remains reasonable when the number of seats is fixed. Additionally, the GSR is able to simulate and extend many existing voting rules.