Likelihoodism,Bayesianism, and relational confirmation

Likelihoodists and Bayesians seem to have a fundamental disagreement about the proper probabilistic explication of relational (or contrastive) conceptions of evidential support (or confirmation). In this paper, I will survey some recent arguments and results in this area, with an eye toward pinpointing the nexus of the dispute. This will lead, first, to an important shift in the way the debate has been couched, and, second, to an alternative explication of relational support, which is in some sense a “middle way” between Likelihoodism and Bayesianism. In the process, I will propose some new work for an old probability puzzle: the “Monty Hall” problem. Thanks to the participants of the Philosophy, Probability, and Modeling (PPM) Seminar at the University of Konstanz (especially Stephan Hartmann, Franz Huber, Wolfgang Spohn, and Teddy Seidenfeld), for a very fruitful discussion of an early draft of this paper in July, 2004. Since then, discussions and correspondences with Prasanta Bandyopadhyay, Luc Bovens, Alan Hájek, Jim Hawthorne, Jim Joyce, Jon Kvanvig (and other participants of his “Certain Doubts” blog, which had a thread on a previous draft of this paper), Patrick Maher, Sherri Roush, Richard Royall, Elliott Sober, Dan Steel, and an anonymous referee of Synthese has been very valuable.