A maximum entropy approach to recovering information from ranking data

Abstract

In this paper, we investigate a maximum entropy (ME) approach to recover the conditional choice proba- bilities and hence recover the ranking probabilities. The beauty of this approach is that it is onparametric in nature in the sense that no distributional assumption on the data is required. Moreover, we show that the ranking probabilities recovered by using the ME method satisfy the well known Luce model for ranking data. In particular, the ME estimates of the choice probabilities are the same as the corresponding maximum likelihood estimates under the Luce model. In addition, we propose a generalized ME (GME) approach which requires weaker moment constraints used in entropy maximization. Based on a simulation study, we ¯nd that the GME method produces estimates of smaller MSE and smaller bias as compared with the ME method. The proposed methods are applied to analyse the data given in Dansie (1986) in which 800 people were asked to indicate their preference on 4 motor cars.