# Explaining Away, Augmentation, and the Assumption of Independence

November, 2020

Imagine you are on a tropical island in which there are three types of mosquito (Reb, Mar, and Murb) that carry a certain disease, called Ling fever. For each mosquito type, there is a certain risk of being bitten by an infected mosquito, and a certain risk of contracting the disease when bitten. One day during a routine health check, it turns out that you have Ling fever, prompting you to increase your degree of belief that you were bitten by an infected mosquito. Further tests show that you were bitten by an infected mosquito of the Reb type. How does this additional information affect your degree of belief that you were bitten by an infected mosquito of the Mar type?

In this situation, the presence of a bite from Reb "explains away" the finding of Ling fever, suggesting you can reduce your degree of belief in a bite from Mar. Now imagine the further test showed instead that you were not bitten by an infected mosquito of the Reb type. How does this additional piece of information affect your degree of belief that you were bitten by an infected mosquito of the Mar type? In the absence of a bite from Reb, the finding of Ling fever  still needs an explanation, suggesting you can "augment" your degree of belief in a bite from Mar.

The above reasoning is called intercausal because it involves inferring the likelihood that one cause is present or absent, based on knowledge about one or more further causes. People tend to show this explaining away effect in their probability judgments, but to a lower extent than predicted by the causal structure of the situation.

This study investigates further the conditions under which explaining away is observed. A total of 37 participants estimated the probability of a cause, given the presence or the absence of another cause, for situations in which the effect was either present or absent, and the evidence about the effect was either certain or uncertain. Responses were compared to predictions obtained using Bayesian network modelling techniques as well as a sensitivity analysis of the size of normative changes in probability under different information conditions. The findings suggest that alongside earlier explanations brought forward in the literature, explaining away may occur less often when the causes are assumed to interact in their contribution to the effect, and when the normative size of the probability change is not large enough to be subjectively meaningful. Further, people struggled when given evidence against negative evidence, resembling a double negation effect.

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