A distributed protocol for collective decision-making in combinatorial domains

In this paper, we study the problem of collective decisionmaking over combinatorial domains, where the set of possible alternatives is a Cartesian product of (finite) domain values for each of a given set of variables, and these variables are not preferentially independent. Due to the large alternative space, most common rules for preference aggregation cannot be directly applied to compute a winner. In this paper, we focus on a particular social choice rule, namely Smith/Minimax. We introduce a distributed protocol for collective decisionmaking, which enjoys the following desirable properties: i) the final decision chosen is guaranteed to be a Smith member, and is sufficiently close to the Smith/Minimax candidate; ii) it enables distributed decision-making and works under incomplete information settings, i.e., the agents are not required to reveal their preferences explicitly; iii) it significantly reduces the amount of dominance testings (individual outcome comparisons) that each agent needs to conduct, as well as the number of pairwise comparisons; iv) it is sufficiently general and does not restrict the choice of preference representation languages.