Anchored belief updating from recommendations

We study a belief updating behavior in a framework where information is presented as a recommendation from a menu of actions. We introduce a property on belief updating called order independence of recommendations, which is analogous to the Bayes’ Rule property of path independence of signals. We show that order independence and the properties that characterize the contraction rule of Ke et al. (2021) lead to an impossibility result on the general domain of recommendations. We then show that such a rule exists if and only if the domain is substantially restricted. Lastly, we propose the anchored contraction rule, which satisfies order independence on the general domain. The anchored contraction rule gives a theoretical ground for the asymmetric confirmation bias in the general domain of recommendations that a belief is updated if and only if information supports an ideal point.