An Axiomatic Theory of Tournament Aggregation

An axiomatic theory for aggregation of individual preferences is developed. Many authors, since K. J. Arrow, have studied the case where every individual preference is an ordering. We study here the case where every individual preference is a tournament (for instance, in “paired comparisons”). The original results obtained can be compared to those of the classic theory. For example, we prove, in this context, a generalisation of Arrow's theorem and we emphasize duality between Arrow's results and Black-Inada-Sen's results (technically by means of a Galois connection between two lattices). We used social functions defined by means of “families of majorities” (simple games),