Open-ended questions, in which participants write or type their responses, are used in many areas of the behavioral sciences. Although effective in the lab, they are relatively untested in online experiments, and the quality of responses is largely unexplored. Closed-ended questions are easier to use online because they generally require only single key- or mouse-press responses and are less cognitively demanding, but they can bias the responses. We compared the data quality obtained using open and closed response formats using the continued-influence effect (CIE), in which participants read a series of statements about an unfolding event, one of which is unambiguously corrected later. Participants typically continue to refer to the corrected misinformation when making inferential statements about the event. We implemented this basic procedure online (Exp. 1A, n = 78), comparing standard open-ended responses to an alternative procedure using closed-ended responses (Exp. 1B, n = 75). Finally, we replicated these findings in a larger preregistered study (Exps. 2A and 2B, n = 323). We observed the CIE in all conditions: Participants continued to refer to the misinformation following a correction, and their references to the target misinformation were broadly similar in number across open- and closed-ended questions. We found that participants' open-ended responses were relatively detailed (including an average of 75 characters for inference questions), and almost all responses attempted to address the question. The responses were faster, however, for closed-ended questions. Overall, we suggest that with caution it may be possible to use either method for gathering CIE data.

Misinformation has become an increasingly topical field of research. Studies on the 'Continued Influence Effect' (CIE) show that misinformation continues to influence reasoning despite subsequent retraction. Current explanatory theories of the CIE tacitly assume continued reliance on misinformation is the consequence of a biased process. In the present work, we show why this perspective may be erroneous. Using a Bayesian formalism, we conceptualize the CIE as a scenario involving contradictory testimonies and incorporate the previously overlooked factors of the temporal dependence (misinformation precedes its retraction) between, and the perceived reliability of, misinforming and retracting sources. When considering such factors, we show the CIE to have normative backing. We demonstrate that, on aggregate, lay reasoners (N = 101) intuitively endorse the necessary assumptions that demarcate CIE as a rational process, still exhibit the standard effect, and appropriately penalize the reliability of contradicting sources. Individuallevel analyses revealed that although many participants endorsed assumptions for a rational CIE, very few were able to execute the complex model update that the Bayesian model entails. In sum, we provide a novel illustration of the pervasive influence of misinformation as the consequence of a rational process.

Consensus between informants is a valuable cue to a claim's epistemic value, when informants' beliefs are developed independently of each other. Recent work (Yousif et al., 2019) described an illusion of consensus such that people did not generally discriminate between the epistemic warrant of true consensus, where a majority claim is supported by multiple independent sources, and false consensus arising from a single source's repeated claim. Four experiments tested a novel account of the illusion of consensus; that it arises when people are unsure about the independence of the primary sources on which informant claims are based. When this independence relationship was ambiguous we found evidence for the illusion. However, when steps were taken to highlight the independence between data sources in the true consensus conditions, and confidence in a claim was measured against a no consensus baseline (where there was an equal number of reports supporting and opposing a claim), we eliminated the illusion of consensus. Under these conditions, more weight was given to claims based on true consensus than false consensus. These findings show that although the illusion of consensus is prevalent, people do have the capacity to distinguish between true and false consensus.

Bayesian reasoning and decision making is widely considered normative because it minimizes prediction error in a coherent way. However, it is often difficult to apply Bayesian principles to complex real world problems, which typically have many unknowns and interconnected variables. Bayesian network modeling techniques make it possible to model such problems and obtain precise predictions about the causal impact that changing the value of one variable may have on the values of other variables connected to it. But Bayesian modeling is itself complex, and has until now remained largely inaccessible to lay people. In a large scale lab experiment, we provide proof of principle that a Bayesian network modeling tool, adapted to provide basic training and guidance on the modeling process to beginners without requiring knowledge of the mathematical machinery working behind the scenes, significantly helps lay people find normative Bayesian solutions to complex problems, compared to generic training on probabilistic reasoning. We discuss the implications of this finding for the use of Bayesian network software tools in applied contexts such as security, medical, forensic, economic or environmental decision making.

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