From mere coincidences to meaningful discoveries

Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States
Cognition (Impact Factor: 3.63). 06/2007; 103(2):180-226. DOI: 10.1016/j.cognition.2006.03.004
Source: PubMed


People's reactions to coincidences are often cited as an illustration of the irrationality of human reasoning about chance. We argue that coincidences may be better understood in terms of rational statistical inference, based on their functional role in processes of causal discovery and theory revision. We present a formal definition of coincidences in the context of a Bayesian framework for causal induction: a coincidence is an event that provides support for an alternative to a currently favored causal theory, but not necessarily enough support to accept that alternative in light of its low prior probability. We test the qualitative and quantitative predictions of this account through a series of experiments that examine the transition from coincidence to evidence, the correspondence between the strength of coincidences and the statistical support for causal structure, and the relationship between causes and coincidences. Our results indicate that people can accurately assess the strength of coincidences, suggesting that irrational conclusions drawn from coincidences are the consequence of overestimation of the plausibility of novel causal forces. We discuss the implications of our account for understanding the role of coincidences in theory change.

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    • "In addition, to ascertain that participants did in fact behave in a way that is correctly modeled by this framework , we compared subjective randomness with the normative value arising from algorithmic information theory (as suggested elsewhere; Gauvrit, Soler-Toscano, & Zenil, 2014; Griffiths & Tenenbaum, 2007). In this formal approach, p(s|D)—the algorithmic probability of s—is the probability that a randomly chosen deterministic algorithm would produce s (Gauvrit, Soler-Toscano, Zenil, & Delahaye, 2014; Soler-Toscano, Zenil, Delahaye, & Gauvrit, 2014). "
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    ABSTRACT: Belief in conspiracy theories has often been associated with a biased perception of randomness, akin to a nothing-happens-by-accident heuristic. Indeed, a low prior for randomness (i.e., believing that randomness is a priori unlikely) could plausibly explain the tendency to believe that a planned deception lies behind many events, as well as the tendency to perceive meaningful information in scattered and irrelevant details; both of these tendencies are traits diagnostic of conspiracist ideation. In three studies, we investigated this hypothesis and failed to find the predicted association between low prior for randomness and conspiracist ideation, even when randomness was explicitly opposed to malevolent human intervention. Conspiracy believers' and nonbelievers' perceptions of randomness were not only indistinguishable from each other but also accurate compared with the normative view arising from the algorithmic information framework. Thus, the motto "nothing happens by accident," taken at face value, does not explain belief in conspiracy theories.
    Psychological Science 11/2015; 26(11):1762-1770. DOI:10.1177/0956797615598740 · 4.43 Impact Factor
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    • "In a study by Gopnik et al. (2004), there were only three relevant entities (an experimenter and two puppets), and only two causal hypotheses, which the children were explicitly informed about. Other studies have used systems scarcely more complex than that (Gopnik et al., 2004; Gopnik & Schulz, 2004; Gopnik, Sobel, Schulz, & Glymour, 2001; Gweon & Schulz, 2012; Kushnir & Gopnik, 2005; Schulz, Bonawitz, & Griffiths, 2007; Schulz, Gopnik, & Glymour, 2007; Sobel & Kirkham, 2006, 2007; Sobel & Munro, 2009). Even older children fail to appreciate the importance of control of variables in causal hypothesis testing (Chen & Klahr, 1999; Kuhn, Schauble, & Garcia-Mila, 1992; Schauble, 1990; Zimmerman, 2007). "
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    ABSTRACT: It is argued that causal understanding originates in experiences of acting on objects. Such experiences have consistent features that can be used as clues to causal identification and judgment. These are singular clues, meaning that they can be detected in single instances. A catalog of 14 singular clues is proposed. The clues function as heuristics for generating causal judgments under uncertainty and are a pervasive source of bias in causal judgment. More sophisticated clues such as mechanism clues and repeated interventions are derived from the 14. Research on the use of empirical information and conditional probabilities to identify causes has used scenarios in which several of the clues are present, and the use of empirical association information for causal judgment depends on the presence of singular clues. It is the singular clues and their origin that are basic to causal understanding, not multiple instance clues such as empirical association, contingency, and conditional probabilities.
    Cognitive Science A Multidisciplinary Journal 08/2013; 38(1). DOI:10.1111/cogs.12075 · 2.59 Impact Factor
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    • "If the complexity-based model proposed here is correct, why would probabilistic or Bayesian accounts have partial predictive power? And why are coincidences systematically accompanied by a subjective feeling of low probability (Griffiths & Tenenbaum, 2007)? The relation between descriptive complexity and probability has always been noticed (Solomonoff, 1997), but its usual formulation as p = 2 –C(D) is unsatisfactory for our purpose. "
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    ABSTRACT: Individuals have an intuitive perception of what makes a good coincidence. Though the sensitivity to coincidences has often been presented as resulting from an erroneous assessment of probability, it appears to be a genuine competence, based on non-trivial computations. The model presented here suggests that coincidences occur when subjects perceive complexity drops. Co-occurring events are, together, simpler than if considered separately. This model leads to a possible redefinition of subjective probability.
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