Built upon statistics insights, we illustrate that Bayesian decision theory combined with a non-informative prior may lead to a strictly dominated decision rule, which can be improved by shrinking the decision towards an arbitrary-chosen reference point. By doing so, one incurs a bias but reduces the variance of the decision and decreases the expected loss. This revelation suggests that anchoring may have a rational explanation. The examination of the known features of the anchoring effect provides additional support to this view.
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