Expected Accuracy Supports Conditionalization—and Conglomerability and Reflection

Expected accuracy arguments have been used by several authors (Leitgeb and Pettigrew and Greaves and Wallace) to support the diachronic principle of conditionalization, in updates where there are only finitely many possible propositions to learn. I show that these arguments can be extended to infinite cases, giving an argument not just for conditionalization but also for principles known as ‘conglomerability’ and ‘reflection’. This shows that the expected accuracy approach is stronger than has been realized. I also argue that we should be careful to distinguish diachronic update principles from related synchronic principles for conditional probability.