ABSTRACT
Equivalence relations An equivalence relation ~ 0 ° n X is a reflexive ( x ~ 0x), symmetric
and transitive binary relation on X. We consider the aggregation of equivalence relations . . . , on X into a consensus equivalence relation « on X. Each could refer to a strong similarity relation on X for a particular criterion used to judge similarity. Then « says which items in X are similar on the basis of « i through
Although there need be no underlying notions of asymmetric orderings behind the equivalence relations, the ensuing theorem will be stated in the choice function mode to show clearly the connections to Theorem 1. Profiles of equivalence relations will be denoted by E and E ' , with corresponding individual equivalence relations and In terms of C, we define aggregate equivalence
by
x ^ Ey if x =y, or if x ¥^y and C({x, y}, E) = {x, y}.
