A Note on Ranking in the Plackett-Luce Model for Multiple Comparisons

摘要: Ranking and rating individuals is a fundamental problem in multiple comparisons. One of the most well-known approaches Plackett-Luce model, which ordering decided by maximum likelihood estimator. However, estimate (MLE) does not exist when some are never ranked lower than others or lose all their races. In this note, we proposed penalized method to address problem. As parameter goes zero, MLE converges original MLE. Further, there exists critical point ranking independent choice parameter. Several numerical examples provided.