The theory of personal probability must be explored with circumspection and imagination. For example, applying the theory naively one quickly comes to the conclusion that randomization is without value to statistics. This conclusion does not sound right; and it is not right.L. J. Savage (1961, p. 585).
Randomization is a generally accepted principle of sound experimental design and common practice among working scientists. But many philosophers and some theoretical statisticians have rejected it. Bayesians have most often stated their opposition to randomization in terms of a decision theoretic argument. Not all Bayesians, however, could go along with that argument, as the above quotation by Leonard Savage testifies.
In this paper I will examine the Bayesian decision theoretic argument against randomization and show why it fails. By means of an example I will then give a partial justification of randomization in Bayesian terms.