We axiomatically characterise a class of updating rules in the contexts of: (a) consumer's equilibrium; and (b) random choice by a decision maker. The updating rule captures the effect of absence of a product on the expenditure-share function in (a) and the effect of removal of an alternative on the choice probabilities of the remaining alternatives in (b). The class of updating rules, called hemi-Bayesian random choice rule can be described as follows: the expenditure-share or the probability-weight of the alternative that is removed is distributed proportionately to the alternatives belonging to its lower contour set according to some linear order. We show that this class of rules is the same as random consideration set rule as in Manzini and Mariotti (2014). © 2020 Elsevier B.V.