In part the problem of the subjectivity of Bayesian analysis may be resolved by taking a different attitude to scientific theory, and by giving up the ideal of absolute objectivity. Indeed, some will argue that it is just right that the statistical methods accommodate differences of opinion among scientists. However, this response misses the mark if the prior distribution expresses ignorance rather than opinion: it seems harder to defend the rationality of differences of opinion that stem from different ways of spelling out ignorance. Now there is also a more positive answer to worries over objectivity, based on so-called convergence results (e.g., Blackwell and Dubins 1962 and Gaifman and Snir 1982). It turns out that the impact of prior choice diminishes with the accumulation of data, and that in the limit the posterior distribution will converge to a set, possibly a singleton, of best hypotheses, determined by the sampled data and hence completely independent of the prior distribution.  However, in the short and medium run the influence of subjective prior choice remains.