Hypercubewise Preference Aggregation in Multi-issue Domains
Vincent Conitzer, Jérôme Lang and Lirong Xia
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 if assuming a uniform distribution of 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 {\em 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.