# Adaptive Sampling Policies Imply Biased Beliefs: A Generalization of the Hot Stove Effect

- Jerker Denrell, Warwick Business School, University of Warwick, Coventry, West Midlands, United Kingdom

**Abstract**The Hot Stove Effect is a negativity bias resulting from the adaptive character of learning. The mechanism is that learning algorithms that pursue alternatives with positive estimated values, but avoid alternatives with negative estimated values, will correct errors of overestimation but fail to correct errors of underestimation. Here we generalize the theory behind the Hot Stove Effect to settings in which negative estimates do not necessarily lead to avoidance but to a smaller sample size (i.e, a learner selects fewer of alternative B if B is believed to be inferior but does not entirely avoid B). We demonstrate formally that the negativity bias remains in this set-up. We also show that there is a negativity bias for Bayesian learners in the sense that most such learners underestimate the expected value of an alternative.