Inference using conditional probabilities despite prior ignorance

Some assumptions are introduced about ignorance and heuristic inference based only upon evidence and without prior probabilities. The consistency of the assumptions is checked by presenting a model of them. The assumptions imply a decision procedure for orderings between exclusive sentences which works equally well with subjectivist Bayes factors or the kind of functions commonly found in classical objectivist tests of statistical significance. Within this framework for representing ignorance, the sometimes contentious schools of statistical objectivism and subjectivism appear to share much in common. Two statistical applications are presented: significance testing of a sharp null hypothesis, and the “perfect working” parameter estimation problem of reliability engineering. Finally, the decision procedure for exclusive sentences is adapted to more general cases of reasoning under uncertainty