An Axiomatic Characterization of Bayesian Updating
将贝叶斯更新视为从先验信念和新信息到后验的映射,用三条公理(非创新性、丢弃、比例性)刻画其本质,有助于理解规范贝叶斯基准与替代模型及实际人类行为的差异。
We provide an axiomatic characterization of Bayesian updating, viewed as a mapping from prior beliefs and new information to posteriors, which is disentangled from any reference to preferences. Bayesian updating is characterized by Non-Innovativeness (events considered impossible in the prior remain impossible in the posterior), Dropping (events contradicted by new evidence are considered impossible in the posterior), and Proportionality (for other events, the posterior simply rescales the prior’s probabilities proportionally). The result clarifies the differences between the normative Bayesian benchmark, alternative models, and actual human behavior.