Magnitude-sensitive reaction times reveal non-linear time costs in multi-alternative decision-making
Optimality analysis of value-based decisions in binary and multi-alternative choice settings predicts that reaction times should be sensitive only to differences in stimulus magnitudes, but not to overall absolute stimulus magnitude. Yet experimental work in the binary case has shown magnitude sensi...
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| Published in | PLoS computational biology Vol. 18; no. 10; p. e1010523 |
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| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
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| Abstract | Optimality analysis of value-based decisions in binary and multi-alternative choice settings predicts that reaction times should be sensitive only to differences in stimulus magnitudes, but not to overall absolute stimulus magnitude. Yet experimental work in the binary case has shown magnitude sensitive reaction times, and theory shows that this can be explained by switching from linear to multiplicative time costs, but also by nonlinear subjective utility. Thus disentangling explanations for observed magnitude sensitive reaction times is difficult. Here for the first time we extend the theoretical analysis of geometric time-discounting to ternary choices, and present novel experimental evidence for magnitude-sensitivity in such decisions, in both humans and slime moulds. We consider the optimal policies for all possible combinations of linear and geometric time costs, and linear and nonlinear utility; interestingly, geometric discounting emerges as the predominant explanation for magnitude sensitivity. |
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| AbstractList | Optimality analysis of value-based decisions in binary and multi-alternative choice settings predicts that reaction times should be sensitive only to differences in stimulus magnitudes, but not to overall absolute stimulus magnitude. Yet experimental work in the binary case has shown magnitude sensitive reaction times, and theory shows that this can be explained by switching from linear to multiplicative time costs, but also by nonlinear subjective utility. Thus disentangling explanations for observed magnitude sensitive reaction times is difficult. Here for the first time we extend the theoretical analysis of geometric time-discounting to ternary choices, and present novel experimental evidence for magnitude-sensitivity in such decisions, in both humans and slime moulds. We consider the optimal policies for all possible combinations of linear and geometric time costs, and linear and nonlinear utility; interestingly, geometric discounting emerges as the predominant explanation for magnitude sensitivity. Optimality analysis of value-based decisions in binary and multi-alternative choice settings predicts that reaction times should be sensitive only to differences in stimulus magnitudes, but not to overall absolute stimulus magnitude. Yet experimental work in the binary case has shown magnitude sensitive reaction times, and theory shows that this can be explained by switching from linear to multiplicative time costs, but also by nonlinear subjective utility. Thus disentangling explanations for observed magnitude sensitive reaction times is difficult. Here for the first time we extend the theoretical analysis of geometric time-discounting to ternary choices, and present novel experimental evidence for magnitude-sensitivity in such decisions, in both humans and slime moulds. We consider the optimal policies for all possible combinations of linear and geometric time costs, and linear and nonlinear utility; interestingly, geometric discounting emerges as the predominant explanation for magnitude sensitivity.Optimality analysis of value-based decisions in binary and multi-alternative choice settings predicts that reaction times should be sensitive only to differences in stimulus magnitudes, but not to overall absolute stimulus magnitude. Yet experimental work in the binary case has shown magnitude sensitive reaction times, and theory shows that this can be explained by switching from linear to multiplicative time costs, but also by nonlinear subjective utility. Thus disentangling explanations for observed magnitude sensitive reaction times is difficult. Here for the first time we extend the theoretical analysis of geometric time-discounting to ternary choices, and present novel experimental evidence for magnitude-sensitivity in such decisions, in both humans and slime moulds. We consider the optimal policies for all possible combinations of linear and geometric time costs, and linear and nonlinear utility; interestingly, geometric discounting emerges as the predominant explanation for magnitude sensitivity. Optimality analysis of value-based decisions in binary and multi-alternative choice settings predicts that reaction times should be sensitive only to differences in stimulus magnitudes, but not to overall absolute stimulus magnitude. Yet experimental work in the binary case has shown magnitude sensitive reaction times, and theory shows that this can be explained by switching from linear to multiplicative time costs, but also by nonlinear subjective utility. Thus disentangling explanations for observed magnitude sensitive reaction times is difficult. Here for the first time we extend the theoretical analysis of geometric time-discounting to ternary choices, and present novel experimental evidence for magnitude-sensitivity in such decisions, in both humans and slime moulds. We consider the optimal policies for all possible combinations of linear and geometric time costs, and linear and nonlinear utility; interestingly, geometric discounting emerges as the predominant explanation for magnitude sensitivity. Analysis of decisions based on option value ( e.g . which pile of coins would you like?) suggests that the optimal rules correspond to simple mechanisms also known to be optimal for perceptual decisions ( e.g . which light is brighter?) But, crucially, these analyses assume that the cost of time is linear—when the more usual assumption is made that time discounts multiplicatively ( e.g . ‘a bird in the hand is worth two in the bush (and so two in the hand are worth four in the bush)’) then optimal decision-making looks quite different—in particular, the theory predicts that decision-making should be sensitive to the absolute magnitude of the opportunities, such as coin pile sizes, under consideration, in a way that the optimal perceptual mechanisms are not. As well as the theory, we present novel experimental evidence from human decision-making experiments, and foraging slime mould, of precisely such magnitude-sensitivity. This is a rare example of theory in behaviour making a falsifiable prediction that is confirmed in two, highly divergent, species, one with a brain and one without. |
| Audience | Academic |
| Author | Dussutour, Audrey Marshall, James A. R. Reina, Andreagiovanni Pirrone, Angelo Hay, Célia |
| AuthorAffiliation | Ecole Normale Superieure, FRANCE 1 Department of Computer Science, University of Sheffield, Sheffield, United Kingdom 4 Research Centre for Animal Cognition (CRCA), Centre for Integrative Biology (CBI), Toulouse University, Toulouse, France 5 Centre for Philosophy of Natural and Social Science, London School of Economics and Political Science, London, United Kingdom 3 IRIDIA, Université Libre de Bruxelles, Brussels, Belgium 2 Opteran Technologies, Sheffield, United Kingdom |
| AuthorAffiliation_xml | – name: 4 Research Centre for Animal Cognition (CRCA), Centre for Integrative Biology (CBI), Toulouse University, Toulouse, France – name: 3 IRIDIA, Université Libre de Bruxelles, Brussels, Belgium – name: 2 Opteran Technologies, Sheffield, United Kingdom – name: 5 Centre for Philosophy of Natural and Social Science, London School of Economics and Political Science, London, United Kingdom – name: 1 Department of Computer Science, University of Sheffield, Sheffield, United Kingdom – name: Ecole Normale Superieure, FRANCE |
| Author_xml | – sequence: 1 givenname: James A. R. orcidid: 0000-0002-1506-167X surname: Marshall fullname: Marshall, James A. R. – sequence: 2 givenname: Andreagiovanni orcidid: 0000-0003-4745-992X surname: Reina fullname: Reina, Andreagiovanni – sequence: 3 givenname: Célia surname: Hay fullname: Hay, Célia – sequence: 4 givenname: Audrey orcidid: 0000-0002-1377-3550 surname: Dussutour fullname: Dussutour, Audrey – sequence: 5 givenname: Angelo orcidid: 0000-0001-5984-7853 surname: Pirrone fullname: Pirrone, Angelo |
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| Copyright | COPYRIGHT 2022 Public Library of Science 2022 Marshall et al. This is an open access article distributed under the terms of the Creative Commons Attribution License: http://creativecommons.org/licenses/by/4.0/ (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. Distributed under a Creative Commons Attribution 4.0 International License 2022 Marshall et al 2022 Marshall et al |
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| SubjectTerms | Analysis Biology and Life Sciences Choice Behavior Computer and Information Sciences Computer simulation Computer-generated environments Cost analysis Costs Costs and Cost Analysis Decision analysis Decision Making Experiments Food Foraging behavior Human subjects Humans Life Sciences Methods Neurosciences Optimization Physical Sciences Reaction Time Reward Sensitivity Slime molds Social Sciences Theoretical analysis |
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| Title | Magnitude-sensitive reaction times reveal non-linear time costs in multi-alternative decision-making |
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