The natural frequency hypothesis and evolutionary arguments

Abstract In the rationality debate, Gerd Gigerenzer and his colleagues have argued that human’s apparent inability to follow probabilistic principles does not mean our irrationality, because we can do probabilistic reasoning successfully if probability information is given in frequencies, not percentages (the natural frequency hypothesis). They also offered an evolutionary argument to this hypothesis, according to which using frequencies was evolutionarily more advantageous to our hominin ancestors than using percentages, and this is why we can reason correctly about probabilities in the frequency format. This paper offers a critical review of this evolutionary argument. I show that there are reasons to believe using the frequency format was not more adaptive than using the standard (percentage) format. I also argue that there is a plausible alternative explanation (the nested-sets hypothesis) for the improved test performances of experimental subjects—one of Gigerenzer’s key explananda—which undermines the need to postulate mental mechanisms for probabilistic reasoning tuned to the frequency format. The explanatory thrust of the natural frequency hypothesis is much less significant than its advocates assume.

[1]  Vittorio Girotto,et al.  Intuitions of probabilities shape expectations about the future at 12 months and beyond , 2007, Proceedings of the National Academy of Sciences.

[2]  Gary L. Brase Omissions, conflations, and false dichotomies: Conceptual and empirical problems with the Barbey & Sloman account. , 2007 .

[3]  Lynn Hasher,et al.  Frequency processing: A twenty-five year perspective. , 2002 .

[4]  Peter Salmon,et al.  Health professionals' and service users' interpretation of screening test results: experimental study , 2006, BMJ : British Medical Journal.

[5]  David E. Over,et al.  The logic of natural sampling , 2007 .

[6]  Jeffrey M. Stibel,et al.  Frequency illusions and other fallacies , 2003 .

[7]  Gary L. Brase,et al.  Individuation, counting, and statistical inference: The role of frequency and whole-object representations in judgment under uncertainty , 1998 .

[8]  Lynn Hasher,et al.  The Processing of Frequency Information: An Automatic Mechanism?. , 1977 .

[9]  Ilkka Niiniluoto,et al.  Handbook of Epistemology , 2004 .

[10]  V. Girotto,et al.  Solving probabilistic and statistical problems: a matter of information structure and question form , 2001, Cognition.

[11]  Peter B. M. Vranas,et al.  Gigerenzer's normative critique of Kahneman and Tversky , 2000, Cognition.

[12]  Colin Allen,et al.  The evolution of mind , 1998 .

[13]  Gerd Gigerenzer,et al.  How to Improve Bayesian Reasoning Without Instruction: Frequency Formats , 1995 .

[14]  G. Gigerenzer The bounded rationality of probabilistic mental models. , 1993 .

[15]  Bonnie Grossen,et al.  Diagramming a Logic Strategy: Effects on Difficult Problem Types and Transfer , 1990 .

[16]  K. Stanovich,et al.  Evolutionary versus instrumental goals: How evolutionary psychology misconceives human rationality , 2003 .

[17]  R. Nozick THE NATURE OF RATIONALITY , 1995 .

[18]  K. Stanovich,et al.  Individual differences in reasoning: Implications for the rationality debate? , 2000, Behavioral and Brain Sciences.

[19]  Stephen E. Newstead,et al.  The role of problem structure in a deductive reasoning task. , 1982 .

[20]  Gerd Gigerenzer,et al.  The role of representation in Bayesian reasoning: Correcting common misconceptions , 2007 .

[21]  Jeffrey R. Stevens,et al.  A statistical taxonomy and another “chance” for natural frequencies , 2007 .

[22]  Benton J. Underwood,et al.  Retention of Frequency Information with Observations on Recognition and Recall. , 1971 .

[23]  Gerd Gigerenzer,et al.  Content-blind norms, no norms, or good norms? A reply to Vranas , 2001, Cognition.

[24]  Gerd Gigerenzer,et al.  Children can solve Bayesian problems: the role of representation in mental computation , 2006, Cognition.

[25]  Kimihiko Yamagishi,et al.  Facilitating normative judgments of conditional probability: frequency or nested sets? , 2003, Experimental psychology.

[26]  John Woods,et al.  Argument: Critical Thinking, Logic and the Fallacies , 2002 .

[27]  Deborah J. Bennett Logic Made Easy : How to Know When Language Deceives You , 2004 .

[28]  Gary L. Brase Which Statistical Formats Facilitate What Decisions? The Perception and Influence of Different Statistical Information Formats , 2002 .

[29]  William P. Neace,et al.  Frequency formats, probability formats, or problem structure? A test of the nested-sets hypothesis in an extensional reasoning task , 2008 .

[30]  Gary L. Brase,et al.  Frequency interpretation of ambiguous statistical information facilitates Bayesian reasoning , 2008, Psychonomic bulletin & review.

[31]  S. Sloman,et al.  Base-rate respect: From ecological rationality to dual processes. , 2007, The Behavioral and brain sciences.

[32]  A. Tversky,et al.  Extensional versus intuitive reasoning: the conjunction fallacy in probability judgment , 1983 .

[33]  Gary L. Brase Pictorial representations in statistical reasoning , 2009 .

[34]  A. Tversky,et al.  Judgment under Uncertainty: Heuristics and Biases , 1974, Science.

[35]  D Kahneman,et al.  On the reality of cognitive illusions. , 1996, Psychological review.

[36]  G Gigerenzer,et al.  Using natural frequencies to improve diagnostic inferences , 1998, Academic medicine : journal of the Association of American Medical Colleges.

[37]  Gerd Gigerenzer,et al.  Overcoming Difficulties in Bayesian Reasoning: A Reply to Lewis & Keren and Mellers & McGraw , 1998 .

[38]  Ronald de Sousa Why Do We Think , 2007 .

[39]  Vittorio Girotto,et al.  Chances and frequencies in probabilistic reasoning: rejoinder to Hoffrage, Gigerenzer, Krauss, and Martignon , 2002, Cognition.

[40]  Douglas Walton,et al.  Argument: Critical Thinking, Logic and the Fallacies (M. Hogan) , 2002 .

[41]  Andrea Polonioli,et al.  Gigerenzer’s ‘external validity argument’ against the heuristics and biases program: an assessment , 2012 .

[42]  G. Gigerenzer How to Make Cognitive Illusions Disappear: Beyond “Heuristics and Biases” , 1991 .

[43]  G. Keren,et al.  On the difficulties underlying Bayesian reasoning: A comment on Gigerenzer and Hoffrage , 1999 .

[44]  David E. Over,et al.  Evolution and the Psychology of Thinking: The Debate , 2004 .

[45]  Gerhard H. Fischer,et al.  "Contributions to Mathematical Psychology, Psychometrics, and Methodology" , 1993 .

[46]  Richard Patterson The versatility and generality of nested set operations , 2007 .

[47]  K. Manktelow,et al.  Rationality: Psychological and Philosophical Perspectives , 1993 .

[48]  S. Pinker How the Mind Works , 1999, Philosophy after Darwin.

[49]  Richard Samuels,et al.  Reason and Rationality , 2004 .

[50]  Gerd Gigerenzer,et al.  Adaptive Thinking: Rationality in the Real World , 2000 .

[51]  S. Stich,et al.  Ending the Rationality Wars: How to Make Disputes About Human Rationality Disappear , 2002 .

[52]  G. Gigerenzer Ecological intelligence: An adaptation for frequencies , 1997 .

[53]  Gernot D. Kleiter,et al.  Natural Sampling: Rationality without Base Rates , 1994 .

[54]  Renée Elio Common Sense, Reasoning, and Rationality , 2002 .

[55]  Ronald de Sousa,et al.  Why Think?: Evolution and the Rational Mind , 2007 .

[56]  G. Gigerenzer,et al.  Overcoming difficulties in Bayesian reasoning: A reply to Lewis and Keren (1999) and Mellers and McGraw (1999). , 1999 .

[57]  Tilmann Betsch,et al.  Etc. frequency processing and cognition , 2002 .

[58]  Leo Groarke Good reasoning matters , 1989 .

[59]  L Hasher,et al.  Automatic processing of fundamental information: the case of frequency of occurrence. , 1984, The American psychologist.

[60]  L. Cosmides,et al.  Are humans good intuitive statisticians after all? Rethinking some conclusions from the literature on judgment under uncertainty , 1996, Cognition.

[61]  Vittorio Girotto,et al.  Children’s understanding of posterior probability , 2008, Cognition.

[62]  David E. Over,et al.  Ecological issues: A reply to Todd, Fiddick, & Krauss , 2000 .

[63]  Edward Vul,et al.  Pure Reasoning in 12-Month-Old Infants as Probabilistic Inference , 2011, Science.

[64]  Peter B. M. Vranas,et al.  Single-case probabilities and content-neutral norms: a reply to Gigerenzer , 2001, Cognition.

[65]  Philip N. Johnson-Laird,et al.  Naive Probability: A Mental Model Theory of Extensional Reasoning , 1999 .

[66]  G. Gigerenzer,et al.  Representation facilitates reasoning: what natural frequencies are and what they are not , 2002, Cognition.