Likelihood neglect bias and the mental simulations approach: An illustration using the old and new Monty Hall problems

Abstract

Abstract This article introduces a new violation of a law of probability, likelihood neglect bias. The bias occurs when one is (i) aware that some evidence is more likely given one hypothesis rather than another but (ii) that evidence does not cause them to raise their probability for the former hypothesis relative to the latter. The Monty Hall problem illustrates this bias, although the bias is potentially present in other contexts as well. Unlike previous studies, the present study shows that incorrect responses to the problem are attributable to failure to realize the implications of likelihoods (i.e., likelihood neglect) instead of unawareness of what the likelihoods are. Likelihood neglect is also distinguished from other biases which it is occasionally confused with, and a theoretical explanation of likelihood neglect is proposed. Experimental results further indicate that a new approach—the mental simulations approach—showed a large effect in reducing likelihood neglect and increasing correct probabilities when encountering the Monty Hall problem. The approach also increased correct probabilities for a new modification called the ‘new Monty Hall problem’, unlike two prominent alternative approaches to the original Monty Hall problem. The new Monty Hall problem also illustrates that humans can fail to recognize objectively strong evidence for a hypothesis if they neglect likelihoods.