Professor Seidenfeld's article is a critique of the objectivist principles of Jeffreys and Jaynes and is, at best, peripherally concerned with my book. Nevertheless, it lodges the very strong claim that the Bayesian approach to theory appraisal developed therein is founded on their principles (as in 'founded on quicksand'). No attempt is made to substantiate this claim, and readers unfamiliar with my work could easily gather the false impression that my own view of the enterprise is being presented. I have therefore availed myself of the editors' kind invitation to set the record straight. In addition, I want to respond briefly to Seidenfeld's attempt to show that the Jaynes-Jeffreys program is incompatible with conditionalization.
1. THE LIKELIHOOD PRINCIPLE EXTENDED
Bayesians of all stripes are committed to appraising and comparing hypotheses by their probabilities, and to updating probability assignments by Bayes' Rule (conditionalization). My book is concerned with the implications of this approach for theories with adjustable parameters. I want to begin with a very simple discrete example that will illustrate the very straightforward concepts and claims Professor Seidenfeld professes not to understand.
A deck of cards may be normal (containing 52 distinct cards) or anomalous (containing 52 replicas of a single card). In statistical parlance, the former hypothesis is 'simple', while the latter is 'composite'. We can also think of the latter as containing an adjustable parameter which takes 52 possible values. A widely shared intuition holds that a theory is complicated when its stock of adjustable parameters is enlarged, and I think that any concept or measure of simplicity that is to be taken seriously must respect that intuition. Applied to the card example, the hypothesis K that Theory and Decision 11 (1979) 441-