"Evaluation of
Rankings With Regard to the Possible Number of Agreements and
Conflicts"
European Journal of Operational
Research, Vol. 106, No. 1, p. 129-136, 1998.
by Thomas G. Ray and Evangelos Triantaphyllou
Abstract:
An interesting problem in group decision analysis is how many
different agreements can occur, or conversely disagreements may
exist, between two or more different rankings of a set of
alternatives. In this paper it is assumed that a reference
ranking has been established for the set of alternatives. This
reference ranking may represent the ranking of a high authority
decision maker or be just a virtual ranking to be used in
determining the discrepancy between pairs of rankings. Then, the
problem examined here is to evaluate the number of possible
rankings when the ranking method is the number of agreements with
some reference ranking. The analysis presented here illustrates
that this problem is not trivial and moreover, its simple context
conceals complexity in its depth.
The purpose of this paper is to provide an evaluation of the
number of possible agreements in rankings given to a set of
concepts, alternatives or ideas, by two or more decision makers.
The number of possible agreements takes on the values 0, 1, 2,
..., n-2, or n when n concepts are
compared. This paper develops a recursive closed form formula
for calculating the frequencies for the various numbers of
agreements.
Key Words:
Decision analysis, ranking of alternatives, multi-
criteria decision making, group decision making, combinatorics,
conflict resolution.
