Voting on Multiattribute Domains with Cyclic Preferential Dependencies

In group decision making, often the agents need to decide on multiple attributes at the same time, so that there are exponentially many alternatives. In this case, it is unrealistic to ask agents to communicate a full ranking of all the alternatives. To address this, earlier work has proposed decomposing such voting processes by using local voting rules on the individual attributes. Unfortunately, the existing methods work only with rather severe domain restrictions, as they require the voters' preferences to extend acyclic CP-nets compatible with a common order on the attributes. We first show that this requirement is very restrictive, by proving that the number of linear orders extending an acyclic CP-net is exponentially smaller than the number of all linear orders. Then, we introduce a very general methodology that allows us to aggregate preferences when voters express CP-nets that can be cyclic. There does not need to be any common structure among the submitted CP-nets. Our methodology generalizes the earlier, more restrictive methodology. We study whether properties of the local rules transfer to the global rule, and vice versa. We also address how to compute the winning alternatives.