A Note on Learning under the Knightian Uncertainty

In contrast to the traditional model of uncertainty, where the uncertainty is characterized by a single distribution function that a decision maker faces, the Knightian-uncertainty approach characterizes it as a set of distributions rather than a single one. Hence, learning in the context of Knightian uncertainty is characterized by an update process of the set of distributions after each of random sampling. This note presents two examples in which the Dempster-Shafer update rule, the one which attracts much attention since it seems intuitive, does not at all reduce the Knightian uncertainty (Example 1) and it actually increases the Knightian uncertainty (Example 2). Thus, what is a sensible update process is still an open question under the Knightian uncertainty.