Modeling hierarchy: Transitivity and the linear ordering problem

Abstract

For dominance data, the problem of creating a transitive model of a system is considered. In particular the minimum errors criterion of the linear ordering problem for tournaments is discussed, and its relation to the probabilistic model of dominance data is examined. A heuristic is proposed for ranking actors by dominance which combines computational speed, intuitive appeal, and reasonable performance on the minimum errors criterion. In addition, one statistical approach, the Bradley‐Terry model, is discussed, and its appropriateness for dominance data is considered.

Key words:

• Linear ordering problem
• tournaments
• transitivity