Priority Ranking and Consensus Formation

This paper investigates the problem of combining ordinal preferences, expressed as priority vectors, to form a consensus. An axiomatic structure relating to the concept of distance between rankings is developed, uniqueness of the distance measure is proven and its form derived. Adopting the median ranking as a form of consensus, it is shown that this ranking can be determined, in the case of complete rankings, by solving a certain assignment problem. The results are compared and contrasted to earlier work due to Arrow, Kendall, Kemeny and Snell, and Bogart.