Comparing and choosing between two models with a third model in the background

This study discusses from the Bayesian standpoint whether the comparison or choice between two competing models depends on the characteristics of a third model lurking in the background. In the qualitative choice literature an obvious analog is the independence of irrelevant alternatives property. Usually, Bayesian posterior odds analysis satisfies a similar property, but standard Bayesian model selection does not. The analysis also considers a random utility model in which the utility function of the reader is only partially known to the statistician. The implications of this framework for estimation and prediction are explored.