Outranking methods for multicriterion decision making: Arrow's and Raynaud's conjecture

Outranking methods constitute a class of ordinal ranking algorithms for multicriterion decision making. This paper is concerned with four such methods: Kohler's primal and dual algorithms, and Arrow-Raynaud's primal and dual algorithms. Arrow and Raynaud made the conjecture that these four methods yield the totality of ''prudent orders'' whenever the outranking matrix has the ''constant sum'' property. This paper shows that their conjecture is not valid.