Ranking in Tournaments and Group Decisionmaking
讨论如何根据最小违规准则对一组备选方案进行最公平排名，提出基于图论路径和回路的新方法，用于循环赛、广义锦标赛及群体决策问题，并与现有方法比较公平性和计算量。
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.