NBER WORKING PAPER SERIES ERRORS IN PROBABILISTIC REASONING AND JUDGMENT BIASES Daniel J. Benjamin Working Paper 25200 http://www.nber.org/papers/w25200 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 October 2018 This chapter will appear in the forthcoming Handbook of Behavioral Economics (eds. Doug Bernheim, Stefano DellaVigna, and David Laibson), Volume 2, Elsevier, 2019. For helpful comments, I am grateful to Andreas Aristidou, Nick Barberis, Pedro Bordalo, Colin Camerer, Christopher Chabris, Samantha Cherney, Bob Clemen, Gary Charness, Alexander Coutts, Chetan Dave, Juan Dubra, Craig Fox, Nicola Gennaioli, Tom Gilovich, David Grether, Zack Grossman, Ori Heffetz, Jon Kleinberg, Lawrence Jin, Annie Liang, Chuck Manski, Josh Miller, Don Moore, Ted O’Donoghue, Jeff Naecker, Collin Raymond, Alex Rees-Jones, Rebecca Royer, Josh Schwartzstein, Tali Sharot, Andrei Shleifer, Josh Tasoff, Richard Thaler, Joël van der Weele, George Wu, Basit Zafar, Chen Zhao, Daniel Zizzo, conference participants at the 2016 Stanford Institute for Theoretical Economics, and the editors of this Handbook, Doug Bernheim, Stefano DellaVigna, and David Laibson. I am grateful to Matthew Rabin for extremely valuable conversations about the topics in this chapter over many years. I thank Peter Bowers, Rebecca Royer, and especially Tushar Kundu for outstanding research assistance. The views expressed herein are those of the author and do not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulated for discussion and comment purposes. They have not been peer- reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications. © 2018 by Daniel J. Benjamin. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. Errors in Probabilistic Reasoning and Judgment Biases Daniel J. Benjamin NBER Working Paper No. 25200 October 2018 JEL No. D03,D90 ABSTRACT Errors in probabilistic reasoning have been the focus of much psychology research and are among the original topics of modern behavioral economics. This chapter reviews theory and evidence on this topic, with the goal of facilitating more systematic study of belief biases and their integration into economics. The chapter discusses biases in beliefs about random processes, biases in belief updating, the representativeness heuristic as a possible unifying theory, and interactions between biased belief updating and other features of the updating situation. Throughout, I aim to convey how much evidence there is for (and against) each putative bias, and I highlight when and how different biases may be related to each other. The chapter ends by drawing general lessons for when people update too much or too little, reflecting on modeling challenges, pointing to areas of economics to which the biases are relevant, and highlighting some possible directions for future work. Daniel J. Benjamin Center for Economics and Social Research University of Southern California 635 Downie Way, Suite 312 Los Angeles, CA 90089-3332 and NBER [email protected] Table of Contents Section 1. Introduction ............................................................................................................ 1 Section 2. Biased Beliefs About Random Sequences .............................................................. 9 2.A. The Gambler’s Fallacy and the Law of Small Numbers ................................................. 9 2.B. The Hot-Hand Bias ....................................................................................................... 16 2.C. Additional Biases in Beliefs About Random Sequences ............................................... 21 Section 3. Biased Beliefs About Sampling Distributions .......................................................24 3.A. Partition Dependence.................................................................................................... 24 3.B. Sample-Size Neglect and Non-Belief in the Law of Large Numbers ............................ 33 3.C. Sampling-Distribution-Tails Diminishing Sensitivity ................................................... 41 3.D. Overweighting the Mean and the Fallacy of Large Numbers ....................................... 43 3.E. Sampling-Distribution Beliefs for Small Samples ........................................................ 46 3.F. Summary and Comparison of Sequence Beliefs Versus Sampling-Distribution Beliefs 48 Section 4. Evidence on Belief Updating .................................................................................50 4.A. Conceptual Framework ................................................................................................ 54 4.B. Evidence from Simultaneous Samples .......................................................................... 57 4.C. Evidence from Sequential Samples ............................................................................... 78 Section 5. Theories of Biased Inference .................................................................................86 5.A. Biased Sampling-Distribution Beliefs ........................................................................... 87 5.B. Conservatism Bias ........................................................................................................ 96 5.C. Extreme-Belief Aversion ............................................................................................... 98 5.D. Summary .....................................................................................................................102 Section 6. Base-Rate Neglect ................................................................................................ 104 Section 7. The Representativeness Heuristic ....................................................................... 116 7.A. Representativeness ......................................................................................................116 7.B. The Strength-Versus-Weight Theory of Biased Updating ...........................................122 7.C. Economic Models of Representativeness ....................................................................125 7.D. Modeling Representativeness Versus Specific Biases .................................................134 Section 8. Prior-Biased Inference ........................................................................................ 136 8.A. Conceptual Framework ...............................................................................................136 8.B. Evidence and Models ...................................................................................................138 Section 9. Preference-Biased Inference ............................................................................... 149 9.A. Conceptual Framework ...............................................................................................149 9.B. Evidence and Models ...................................................................................................151 Section 10. Discussion........................................................................................................... 158 10.A. When Do People Update Too Much or Too Little? ...................................................158 10.B. Modeling Challenges ................................................................................................160 10.C. Generalizability from the Lab to the Field ................................................................163 10.D. Connecting With Other Areas of Economics ............................................................167 10.E. Some Possible Directions For Future Research .......................................................169 Section 1. Introduction Probabilistic beliefs are central to decision-making under risk. Therefore, systematic errors in probabilistic reasoning can matter for the many economic decisions that involve risk, including investing for retirement, purchasing insurance, starting a business, and searching for goods, jobs, or workers. This chapter reviews what psychologists and economists have learned about such systematic errors. At the cost of some precision, throughout this chapter I will use the term “belief biases” as shorthand for “errors in probabilistic reasoning.” By “bias,” in this chapter I will mean any deviation from correct reasoning about probabilities or Bayesian updating.1 This chapter’s area of research—which is often called “judgment under uncertainty” or “heuristics and biases” in psychology—was introduced by the psychologist Ward Edwards and his students and colleagues in the 1960s (e.g., Phillips and Edwards, 1966). This topic was the starting point of the collaboration between Daniel Kahneman and Amos Tversky. Their seminal early papers (e.g., Tversky and Kahneman, 1971, 1974) jumpstarted an enormous literature in psychology and influenced thinking in many other disciplines, including economics. Despite so much work by psychologists and despite being one of the original topics of modern behavioral economics, to date belief biases have received less attention from behavioral economists than time, risk, and social preferences. Belief biases have also made 1 My use of the same term “bias” for all of these deviations is not meant to obscure the distinctions between them in terms of their psychological origins. For example,