Abstract
A probabilistic approach to build a model for the paired comparisons experimentation based on the comparison of two Cauchy random variables is considered. The Cauchy distribution may be used to model a variety of phenomena, such as the impact of light particles being emitted from a point source on a plane surface. By basing the preference criterion on such impact, the device with greater impact may be preferred to the device with the lower impact (or as the theory suggests). Moreover, Adams (2005) also discusses the Cauchy model while studying dominance hierarchies in social animals. The paired comparison model is built and is then studied in Bayesian framework. The inferences about the proposed model parameters are made using the non-informative priors (uniform and Jeffreys), as well as informative and the conjugate priors. The hyperparameters are also elicited. Although any group of individuals may be ranked using the Cauchy model, we illustrate the Bayesian inferential procedure with real data on five top-ranked one-day international (ODI) cricket teams.