Unraveling the Conjunction Paradox

15 Law, Probability and Risk 259 (2016)

FSU College of Law, Public Law Research Paper No. 792

61 Pages Posted: 7 Mar 2016 Last revised: 23 Dec 2016

See all articles by Mark Spottswood

Mark Spottswood

Florida State University College of Law

Date Written: March 4, 2016


The conjunction paradox arises when a claim requires proof of multiple elements and the likelihood of some elements are at least partially independent of the likelihood of others. In that situation, probability theory may dictate that the conjunction of the elements is less likely than their disjunction, implying that a defendant should not be found liable, even though each element is probably true when considered in isolation. Nonetheless, American jury instructions reject this implication, and many scholars of proof have sought to construct normative theories to justify that rejection.

This article collects and critiques two families of arguments about the conjunction paradox. First, I explain why an explanatory conception of proof cannot eliminate the paradox. Second, I show why various mathematical alternatives to standard probability theory are normatively deficient when applied to legal fact-finding. Instead, I suggest that the best way to resolve the paradox is through instructions that encourage juries to make appropriate adjustments for conjunctive and disjunctive likelihoods without having to frame their analyses in mathematical terms.

Keywords: conjunction paradox, probability, evidence, burdens of proof, fact-finding, Bayesian, inference to the best explanation, belief functions

Suggested Citation

Spottswood, Mark, Unraveling the Conjunction Paradox (March 4, 2016). 15 Law, Probability and Risk 259 (2016) ; FSU College of Law, Public Law Research Paper No. 792. Available at SSRN: https://ssrn.com/abstract=2742408 or http://dx.doi.org/10.2139/ssrn.2742408

Mark Spottswood (Contact Author)

Florida State University College of Law ( email )

425 W. Jefferson Street
Tallahassee, FL Florida 32306
United States
8506444248 (Phone)

HOME PAGE: http://www.law.fsu.edu/our-faculty/profiles/spottswood

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