A Generalized Network Formulation of the Pairwise Comparison Consensus Ranking Model

This paper shows how the consensus formation problem for strict linear orderings can be modelled as a generalized network and will permit the solution of much larger problems than has been the case previously.

Abstract

One of the best known and most widely referenced models for representing ordinal preferences is that due to Kemeny and Snell (Kemeny, J. G., L. J. Snell. 1962. Preference ranking: an axiomatic approach. Mathematical Models in the Social Sciences. Glnn, New York, 9–23.). This model is designed to accommodate pairwise comparison data with an l 1 norm used to measure voter disagreement. While this model possesses many of the necessary properties for a social choice function, solution procedures developed to date have been capable of handling only small problems due to the difficulty of modelling the transitivity requirements of an optimal consensus ranking. This paper shows how the consensus formation problem for strict linear orderings can be modelled as a generalized network. Since efficient computer codes already exist for handling this special structure, this approach will permit the solution of much larger problems than has been the case previously.