Democracy and efficiency: A note on ‘Arrow’s theorem is not a surprising result’

It has been shown that Arrow’s impossibility result can be avoided when the notion of aggregation procedure is extended to include procedures leading to more than one relation on the set of alternatives. The purpose of this note is to study the structure of these aggregation procedures, generalizing previous results obtained by Phillipe Vincke. Under ‘Arrowian’ conditions, the paper proves that such procedures lead to oligarchies. The size of these oligarchies is discussed.