Editing Base rate fallacy (section)

{{Short description|Logic error due to ignoring the base rate}}
{{Lead rewrite|date=July 2023}}
[[File:Base rate fallacy with vaccines.svg|thumb|upright=1.3|A hospital receiving more vaccinated [[COVID-19]] patients than unvaccinated ones might suggest that the vaccine is ineffective, but such an imbalance is to be expected within a highly vaccinated population.<ref>{{cite web |date=2023-01-18 |title=COVID-19 Cases, Hospitalizations, and Deaths by Vaccination Status |url=https://doh.wa.gov/sites/default/files/2022-02/421-010-CasesInNotFullyVaccinated.pdf |url-status=live |archive-url=https://web.archive.org/web/20230126022307/https://doh.wa.gov/sites/default/files/2022-02/421-010-CasesInNotFullyVaccinated.pdf |archive-date=2023-01-26 |access-date=2023-02-14 |publisher=Washington State Department of Health |quote=If the exposure to COVID-19 stays the same, as more individuals are vaccinated, more cases, hospitalizations, and deaths will be in vaccinated individuals, as they will continue to make up more and more of the population. For example, if 100% of the population was vaccinated, 100% of cases would be among vaccinated people.}}</ref>]]
The '''base rate fallacy''', also called '''base rate neglect'''<ref>{{Cite journal |last1=Welsh |first1=Matthew B. |last2=Navarro |first2=Daniel J. |date=2012 |title=Seeing is believing: Priors, trust, and base rate neglect |url=http://dx.doi.org/10.1016/j.obhdp.2012.04.001 |journal=Organizational Behavior and Human Decision Processes |volume=119 |issue=1 |pages=1–14 |doi=10.1016/j.obhdp.2012.04.001 |issn=0749-5978 |hdl-access=free |hdl=2440/41190}}</ref> or '''base rate bias''', is a type of [[fallacy]] in which people tend to ignore the [[base rate]] (e.g., general [[prevalence]]) in favor of the individuating information (i.e., information pertaining only to a specific case).<ref>{{cite web |title=Logical Fallacy: The Base Rate Fallacy |url=http://www.fallacyfiles.org/baserate.html |access-date=2013-06-15 |publisher=Fallacyfiles.org}}</ref> For example, if someone hears that a friend is very shy and quiet, they might think the friend is more likely to be a librarian than a salesperson. However, there are far more salespeople than librarians overall—hence making it more likely that their friend is actually a salesperson, even if a greater proportion of librarians fit the description of being shy and quiet. Base rate neglect is a specific form of the more general [[extension neglect]].

It is also called the '''prosecutor's fallacy''' or '''defense attorney's fallacy''' when applied to the results of statistical tests (such as DNA tests) in the context of law proceedings. These terms were introduced by William C. Thompson and Edward Schumann in 1987,<ref name="TS">{{cite journal |last1=Thompson |first1=W.C. |last2=Schumann |first2=E.L. |year=1987 |title=Interpretation of Statistical Evidence in Criminal Trials: The Prosecutor's Fallacy and the Defense Attorney's Fallacy |journal=Law and Human Behavior |volume=11 |issue=3 |page=167 |doi=10.1007/BF01044641 |jstor=1393631 |s2cid=147472915}}</ref><ref>{{cite web |last1=Fountain |first1=John |last2=Gunby |first2=Philip |date=February 2010 |title=Ambiguity, the Certainty Illusion, and Gigerenzer's Natural Frequency Approach to Reasoning with Inverse Probabilities |url=http://uctv.canterbury.ac.nz/viewfile.php/4/sharing/55/74/74/NZEPVersionofImpreciseProbabilitiespaperVersi.pdf |publisher=[[University of Canterbury]] |page=6}}{{Dead link|date=May 2020|bot=InternetArchiveBot|fix-attempted=yes}}</ref> although it has been argued that their definition of the prosecutor's fallacy extends to many additional invalid imputations of guilt or liability that are not analyzable as errors in base rates or [[Bayes's theorem]].<ref>{{Cite journal |last=Suss |first=Richard A. |date=October 4, 2023 |title=The Prosecutor's Fallacy Framed as a Sample Space Substitution |journal=OSF Preprints |language=en |doi=10.31219/osf.io/cs248}}</ref>