On the aggregation of incomplete preferences

Assume a set of objects is given with information about their bilateral relationships, allowing for incomplete and multiple comparisons as well as different preference intensities. An axiomatic approach is applied for the problem of ranking the objects. Consistency requires the preservation of relative ranking if two sets of such preferences are aggregated. Self-consistency prohibits to assign a lower rank for an object with a better or equivalent performance than another. It is revealed that these two properties cannot be satisfied simultaneously. The impossibility holds under various restrictions on the domain. However, a positive result emerges if only aggregation of ranking problems with the same comparison structure is allowed, which implies possibility in the case of round-robin tournaments. JEL classification number: C44, D71 AMS classification number: 15A06, 91B14