  In objective Bayesian model selection, no single criterion has emerged as
dominant in defining objective prior distributions. Indeed, many criteria have
been separately proposed and utilized to propose differing prior choices. We
first formalize the most general and compelling of the various criteria that
have been suggested, together with a new criterion. We then illustrate the
potential of these criteria in determining objective model selection priors by
considering their application to the problem of variable selection in normal
linear models. This results in a new model selection objective prior with a
number of compelling properties.
