Hypercubewise Preference Aggregation in Multi-Issue Domains

We consider a framework for preference aggregation on multiple binary issues, where agents' preferences are represented by (possibly cyclic) CP-nets. We focus on the majority aggregation of the individual CP-nets, which is the CP-net where the direction of each edge of the hypercube is decided according to the majority rule. First we focus on hypercube Condorcet winners (HCWs); in particular, we show that, assuming a uniform distribution for the CP-nets, the probability that there exists at least one HCW is at least 1-1/e, and the expected number of HCWs is 1. Our experimental results confirm these results. We also show experimental results under the Impartial Culture assumption. We then generalize a few tournament solutions to select winners from (weighted) majoritarian CP-nets, namely Copeland, maximin, and Kemeny. For each of these, we address some social choice theoretic and computational issues.