Ranking in Tournaments and Group Decisionmaking

Abstract

This paper fully discusses methods for ranking a set of alternatives in the fairest possible way according to a minimum violations criterion. New methods, based on finding paths and circuits in graphs, are presented for ranking participants in round-robin and generalized tournaments, and for consensus and group decisionmaking problems. The objective of the paper is to review existing methods for tackling these problems, and compare them with the new methods, according to a “fairness” criterion, and the amount of computing required to reach a solution. It is shown that the new methods often exceed the existing methods in both fairness and reduced computing requirements. In particular, the new methods are generally more versatile than existing methods. This allows organizations to obtain the fairest ranking of a number of alternatives, according to their managers' or employees' wishes. Particular attention is given to incomplete rankings where insufficient exposure of an individual to some alternatives restricts that individual to ranking only the remaining alternatives.