Many collective decision making problems have a combinatorial structure: the agents involved must decide on multiple issues and their preferences over one issue may depend on the choices adopted for some of the others. Voting is an attractive method for making collective decisions, but conducting a multi-issue election is challenging. On the one hand, requiring agents to vote by expressing their preferences over all combinations of issues is computationally infeasible; on the other, decomposing the problem into several elections on smaller sets of issues can lead to paradoxical outcomes. Any pragmatic method for running a multi-issue election will have to balance these two concerns. We identify and analyse the problem of generating an agenda for a given election, specifying which issues to vote on together in local elections and in which order to schedule those local elections.

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.