A GENERAL FRAMEWORK FOR DISTANCE-BASED CONSENSUS IN ORDINAL RANKING MODELS

The problem of aggregating a set of ordinal rankings of n alternatives has given rise to a number of consensus models. Among the most common of these models are those due to Borda and Kendall, which amount to u sing average ranks, and the l(1) and l(2) distance models. A common cr iticism of these approaches is their use of ordinal rank position numb ers directly as the values of being ranked at those levels. This paper presents a general framework for associating value or worth with ordi nal ranks, and develops models for deriving a consensus based on this framework. It is shown that the l(p) distance models using this framew ork are equivalent to the conventional ordinal models for any p greate r than or equal to 1. This observation can be seen as a form of valida tion of the practice of using ordinal data in a manner for which it wa s presumably not designed. In particular, it establishes the robustnes s of the simple Borda, Kendall and median ranking models.