Misinformation, and its impact on society, has become anincreasingly topical field of study of late. A body of literatureexists that suggests misinformation can retain an influenceover beliefs despite subsequent retraction, known as theContinued Influence Effect (CIE). Researchers have arguedthis to be irrational. However, we show using a Bayesianformalism why this argument is overly assumptive, pointingto (previously overlooked) considerations of reliability of, anddependence between, misinforming and retracting sources.We demonstrate that lay reasoners intuitively endorseassumptions that demarcate CIE as a rational process, basedon the fact misinformation precedes its retraction. Moreover,despite using established CIE materials, we further upturn theapplecart by finding participants show CIE, and appropriatelypenalize the reliabilities of contradicting sources.

The studies apply a Bayesian source credibility model to a legal setting to test epistemic influence of witnesstestimonies. The model amalgamates perceived witness trustworthiness and access to accurate information as independentelements that describe and predict the impact of the testimony of that particular witness.Across two studies, the model enjoys a good fit with observed posterior ratings of the likelihood of guilt (study 1: R2 = .867,study 2: R2 = .701). Study 1 (n = 101) employs different witness types and reports whilst study 2 (n = 102) employs differentwitness types, access to accurate information, and reports.The studies suggest the applicability of a Bayesian source credibility model in a legal setting to account for the impactof different witness types. We show that participants are sensitive to the type of witness and that different witnesses have apredictable impact on the perception of the testimony.

Is the nested sets approach to improving accuracy on Bayesian word problems simply a way of prompting a natural frequencies solution, as its critics claim? Conversely, is it in fact, as its advocates claim, a more fundamental explanation of why the natural frequency approach itself works? Following recent calls, we use a process-focused approach to contribute to answering these long-debated questions. We also argue for a third, pragmatic way of looking at these two approaches and argue that they reveal different truths about human Bayesian reasoning. Using a think aloud methodology we show that while the nested sets approach does appear in part to work via the mechanisms theorised by advocates (by encouraging a nested sets representation), it also encourages conversion of the problem to frequencies, as its critics claim. The ramifications of these findings, as well as ways to further enhance the nested sets approach and train individuals to deal with standard probability problems are discussed.