Domain Restrictions in the Aggregation of Classifications

Abstract

AbstractThe possibility of domain restrictions that allow the consistent use of majority-based aggregators for rankings of objects has been widely explored. This paper extends this exploration to structures in which equivalence relations or classifications are aggregated, and shows that there is very limited scope for such restrictions in the binary structure of Mirkin and in the unary structure of Maniquet and Mongin. We develop a hybrid structure that combines binary and unary conditions on the aggregator, and that allows the use of a majority-based aggregator if and only if each object is eligible for inclusion in no more than two categories out of some greater number. We also show that in many circumstances, the surjectivity requirement of Maniquet and Mongin implicitly introduces binary conditions on the aggregator, and that their structure is entailed by the hybrid structure introduced here.