Propensities and Second Order Uncertainty: A Modified Taxi Cab Problem

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

doi:10.3389/fpsyg.2020.503233

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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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DOI (Published version): 10.3389/fpsyg.2020.503233

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
Online Access:	Check full text
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 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 COLLEGE CODE 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
hierarchy_parent_id	facultyofhumanitiesandsocialsciences
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	2020-10-20T05:17:17Z
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Propensities and Second Order Uncertainty: A Modified Taxi Cab Problem

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