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Propensities and Second Order Uncertainty: A Modified Taxi Cab Problem

Stephen H. Dewitt, Norman E. Fenton, Alice Liefgreen, David A. Lagnado

Frontiers in Psychology, Volume: 11

Swansea University Author: Alice Liefgreen

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Abstract

The study of people’s ability to engage in causal probabilistic reasoning has typically used fixed-point estimates for key figures. For example, in the classic taxi-cab problem, where a witness provides evidence on which of two cab companies (the more common ‘green’/less common ‘blue’) were responsi...

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Published in: Frontiers in Psychology
ISSN: 1664-1078
Published: Frontiers Media SA 2020
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URI: https://cronfa.swan.ac.uk/Record/cronfa60563
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spelling 2022-08-19T11:23:13.6474975 v2 60563 2022-07-20 Propensities and Second Order Uncertainty: A Modified Taxi Cab Problem 5a11aaeb0cd68f36ec54c5534dc541bd Alice Liefgreen Alice Liefgreen true false 2022-07-20 LAWD The study of people’s ability to engage in causal probabilistic reasoning has typically used fixed-point estimates for key figures. For example, in the classic taxi-cab problem, where a witness provides evidence on which of two cab companies (the more common ‘green’/less common ‘blue’) were responsible for a hit and run incident, solvers are told the witness’s ability to judge cab color is 80%. In reality, there is likely to be some uncertainty around this estimate (perhaps we tested the witness and they were correct 4/5 times), known as second-order uncertainty, producing a distribution rather than a fixed probability. While generally more closely matching real world reasoning, a further important ramification of this is that our best estimate of the witness’ accuracy can and should change when the witness makes the claim that the cab was blue. We present a Bayesian Network model of this problem, and show that, while the witness’s report does increase our probability of the cab being blue, it simultaneously decreases our estimate of their future accuracy (because blue cabs are less common). We presented this version of the problem to 131 participants, requiring them to update their estimates of both the probability the cab involved was blue, as well as the witness’s accuracy, after they claim it was blue. We also required participants to explain their reasoning process and provided follow up questions to probe various aspects of their reasoning. While some participants responded normatively, the majority self-reported ‘assuming’ one of the probabilities was a certainty. Around a quarter assumed the cab was green, and thus the witness was wrong, decreasing their estimate of their accuracy. Another quarter assumed the witness was correct and actually increased their estimate of their accuracy, showing a circular logic similar to that seen in the confirmation bias/belief polarization literature. Around half of participants refused to make any change, with convergent evidence suggesting that these participants do not see the relevance of the witness’s report to their accuracy before we know for certain whether they are correct or incorrect. Journal Article Frontiers in Psychology 11 Frontiers Media SA 1664-1078 causal Bayesian networks, second order uncertainty, propensity, uncertainty, confirmation bias 20 10 2020 2020-10-20 10.3389/fpsyg.2020.503233 COLLEGE NANME Law COLLEGE CODE LAWD Swansea University 2022-08-19T11:23:13.6474975 2022-07-20T14:17:44.0196352 Faculty of Humanities and Social Sciences Hilary Rodham Clinton School of Law Stephen H. Dewitt 1 Norman E. Fenton 2 Alice Liefgreen 3 David A. Lagnado 4 60563__24964__c0f6ab974a2341bd96b2e28e092fb61b.pdf 60563.pdf 2022-08-19T11:21:52.4735027 Output 1369960 application/pdf Version of Record true © 2020 Dewitt, Fenton, Liefgreen and Lagnado. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). true eng http://creativecommons.org/licenses/by/4.0/
title Propensities and Second Order Uncertainty: A Modified Taxi Cab Problem
spellingShingle Propensities and Second Order Uncertainty: A Modified Taxi Cab Problem
Alice Liefgreen
title_short Propensities and Second Order Uncertainty: A Modified Taxi Cab Problem
title_full Propensities and Second Order Uncertainty: A Modified Taxi Cab Problem
title_fullStr Propensities and Second Order Uncertainty: A Modified Taxi Cab Problem
title_full_unstemmed Propensities and Second Order Uncertainty: A Modified Taxi Cab Problem
title_sort Propensities and Second Order Uncertainty: A Modified Taxi Cab Problem
author_id_str_mv 5a11aaeb0cd68f36ec54c5534dc541bd
author_id_fullname_str_mv 5a11aaeb0cd68f36ec54c5534dc541bd_***_Alice Liefgreen
author Alice Liefgreen
author2 Stephen H. Dewitt
Norman E. Fenton
Alice Liefgreen
David A. Lagnado
format Journal article
container_title Frontiers in Psychology
container_volume 11
publishDate 2020
institution Swansea University
issn 1664-1078
doi_str_mv 10.3389/fpsyg.2020.503233
publisher Frontiers Media SA
college_str Faculty of Humanities and Social Sciences
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hierarchy_top_title Faculty of Humanities and Social Sciences
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hierarchy_parent_title Faculty of Humanities and Social Sciences
department_str Hilary Rodham Clinton School of Law{{{_:::_}}}Faculty of Humanities and Social Sciences{{{_:::_}}}Hilary Rodham Clinton School of Law
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description The study of people’s ability to engage in causal probabilistic reasoning has typically used fixed-point estimates for key figures. For example, in the classic taxi-cab problem, where a witness provides evidence on which of two cab companies (the more common ‘green’/less common ‘blue’) were responsible for a hit and run incident, solvers are told the witness’s ability to judge cab color is 80%. In reality, there is likely to be some uncertainty around this estimate (perhaps we tested the witness and they were correct 4/5 times), known as second-order uncertainty, producing a distribution rather than a fixed probability. While generally more closely matching real world reasoning, a further important ramification of this is that our best estimate of the witness’ accuracy can and should change when the witness makes the claim that the cab was blue. We present a Bayesian Network model of this problem, and show that, while the witness’s report does increase our probability of the cab being blue, it simultaneously decreases our estimate of their future accuracy (because blue cabs are less common). We presented this version of the problem to 131 participants, requiring them to update their estimates of both the probability the cab involved was blue, as well as the witness’s accuracy, after they claim it was blue. We also required participants to explain their reasoning process and provided follow up questions to probe various aspects of their reasoning. While some participants responded normatively, the majority self-reported ‘assuming’ one of the probabilities was a certainty. Around a quarter assumed the cab was green, and thus the witness was wrong, decreasing their estimate of their accuracy. Another quarter assumed the witness was correct and actually increased their estimate of their accuracy, showing a circular logic similar to that seen in the confirmation bias/belief polarization literature. Around half of participants refused to make any change, with convergent evidence suggesting that these participants do not see the relevance of the witness’s report to their accuracy before we know for certain whether they are correct or incorrect.
published_date 2020-10-20T04:18:46Z
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