Aggregation of equivalence relations

Each of n attributes partitions a set of items into equivalence classes. A consistent aggregator of the n partitions is defined as an aggregate partition that satisfies an independence condition and a unanimity condition. It is shown that the class of consistent aggregators is precisely the class of conjunctive aggregators. That is, for each consistent aggregator there is a nonempty subset N of the attributes such that two items are equivalent in the aggregate partition if and only if they are equivalent with respect to each attribute in N.