Reverse Bayesianism and act independence

Karni and Vierø (2013) propose a model of belief revision under growing awareness-reverse Bayesianism-which posits that as a person becomes aware of new acts, consequences , or act-consequence links, she revises her beliefs over an expanded state space in a way that preserves the relative likelihoods of events in the original state space. A key feature of the model is that reverse Bayesianism does not fully determine the revised probability distribution. We provide an assumption-act independence-that imposes additional restrictions on reverse Bayesian belief revision. We show that with act independence knowledge of the probabilities of the new act events in the expanded state space is sufficient to fully determine the revised probability distribution in each case of growing awareness. We also explore what additional knowledge is required for reverse Bayesianism to pin down the revised probabilities without act independence