Biased Beliefs about Random Samples: Evidence from Two Integrated Experiments

65 Pages Posted: 5 Oct 2017 Last revised: 12 Oct 2017

See all articles by Daniel J. Benjamin

Daniel J. Benjamin

Anderson School of Management; USC, Center for Economic and Social Research (CESR); National Bureau of Economic Research (NBER); Human Genetics Department, David Geffen School of Medicine

Don A. Moore

University of California, Berkeley - Haas School of Business

Matthew Rabin

Harvard University - Department of Economics

Multiple version iconThere are 3 versions of this paper

Date Written: October 3, 2017

Abstract

This paper describes results of a pair of incentivized experiments on biases in judgments about random samples. Consistent with the Law of Small Numbers (LSN), participants exaggerated the likelihood that short sequences and random subsets of coin flips would be balanced between heads and tails. Consistent with the Non-Belief in the Law of Large Numbers (NBLLN), participants underestimated the likelihood that large samples would be close to 50% heads. However, we identify some shortcomings of existing models of LSN, and we find that NBLLN may not be as stable as previous studies suggest. We also find evidence for exact representativeness (ER), whereby people tend to exaggerate the likelihood that samples will (nearly) exactly mirror the underlying odds, as an additional bias beyond LSN. Our within-subject design of asking many different questions about the same data lets us disentangle the biases from possible rational alternative interpretations by showing that the biases lead to inconsistency in answers. Our design also centers on identifying and controlling for bin effects, whereby the probability assigned to outcomes systematically depends on the categories used to elicit beliefs in a way predicted by support theory. The bin effects are large and systematic and affect some results, but we find LSN, NBLLN, and ER even after controlling for them.

Keywords: Law of Small Numbers, Gambler’s Fallacy, Non-Belief in the Law of Large Numbers, Big Data, Support Theory

JEL Classification: B49

Suggested Citation

Benjamin, Daniel J. and Moore, Don A. and Rabin, Matthew, Biased Beliefs about Random Samples: Evidence from Two Integrated Experiments (October 3, 2017). CESR-Schaeffer Working Paper No. 2017-008, Available at SSRN: https://ssrn.com/abstract=3048053 or http://dx.doi.org/10.2139/ssrn.3048053

Daniel J. Benjamin (Contact Author)

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Don A. Moore

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Matthew Rabin

Harvard University - Department of Economics ( email )

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