| Abstract |
There are many real-world situations where evidence is uncertain, arising from factors such as noisy measurements, incomplete data, or ambiguous observations. In such cases, Bayesian Conditionalization (BC), which assumes evidence is fully certain, is not an appropriate method for belief updating. Instead, Jeffrey Conditionalization (JC) offers a flexible alternative that accommodates uncertain evidence by allowing probabilistic updates. However, a key problem with JC, not present in BC, is its noncommutative nature: the order in which evidence is received affects the resulting posterior probabilities. This feature has significant implications for the agreement of posterior probabilities between agents. Specifically, two agents with identical priors and access to the same total evidence can reach different posterior beliefs if they process the evidence in different sequences. |
