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

ABSTRACT 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.

  • Source
    • "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). "
    [Show abstract] [Hide abstract]
    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
  • Source
    • "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. "
    [Show abstract] [Hide abstract]
    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.
  • Source
    • "Bayesian models of cognitive inference are increasingly prominent is several areas of cognitive psychology, including animal and human learning (Courville et al. 2006, Tenenbaum et al. 2006, Steyvers et al. 2003, Griffiths and Tenenbaum 2008), visual perception and motor control (Yuille and Kersten 1006, Kording and Wolpert 2006),semantic memory and language processing (Steyvers et al. 2006, Chater and Manning 2006, Xu and Tenenbaum in press), and social cognition (Baker et al. 2007). For a recent overview of Bayesian models of cognition, see Griffiths et al. (2008). "
    [Show abstract] [Hide abstract]
    ABSTRACT: Ken Binmore needs no introduction to readers of THE ECONOMIC JOURNAL. In RATIONAL DECISIONS, this mathematician turned economist turned philoso- pher combines brief introductions to Bayesian decision theory and game theory with a far-reaching and synthetic assessment of the limits of Bayesian decision theory and offer new directions in extending decision theory to situations where the traditionalapproach doesnotapply. Binmore'sarguments are generallysketchy and impressionistic,seeking to convey ideas rather than rigorouslyjustifyingthem. His references to the literature are broad and deep, hence likely to keep the inter- ested reader busy for a good period of time. This book is thus not for the economist who is blissfullycontented with the usual version of the theory learned in graduate school (Varian 1992, Mas-Colell et al. 1995). Nor is this book for the beginner, who would do better reading Savage (1954) directly, or a more recent didactic ex- position (Kreps 1988, Gintis 2009b). For instance, Binmore follows Anscombe and Aumann (1963) in axiomatically deriving the expected utility theorem, thus side-stepping the behaviorally important issue as how consistent preferences lead to probabilitydistributionswhen the choices involved do not include lotteries with objective probabilities. More generally, Binmore passes seamlessly from elemen- tary exposition to deep and complex issues that are bound to leave the novice in the dust.
    The Economic Journal 01/2010; 120(542):F162 - F180. DOI:10.1111/j.1468-0297.2009.02342.x · 1.95 Impact Factor
Show more


Available from