Coherent Distorted Beliefs
Many models of economics assume that individuals distort objective probabilities. We propose a simple consistency condition on distortion functions, which we term distortion coherence, that ensures that the function commutes with conditioning on an event. We show that distortion coherence restricts...
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creator | Chambers, Christopher P Masatlioglu, Yusufcan Raymond, Collin |
description | Many models of economics assume that individuals distort objective
probabilities. We propose a simple consistency condition on distortion
functions, which we term distortion coherence, that ensures that the function
commutes with conditioning on an event. We show that distortion coherence
restricts belief distortions to have a particular function form: power-weighted
distortions, where distorted beliefs are proportional to the original beliefs
raised to a power and weighted by a state-specific value. We generalize our
findings to allow for distortions of the probabilities assigned to both states
and signals, which nests the functional forms widely used in studying
probabilistic biases (e.g., Grether, 1980 and Benjamin, 2019). We show how
coherent distorted beliefs are tightly related to several extant models of
motivated beliefs: they are the outcome of maximizing anticipated expected
utility subject to a generalized Kullback-Liebler cost of distortion. Moreover,
in the domain of lottery choice, we link coherent distortions to explanations
of non-expected utility like the Allais paradox: individuals who maximize
subjective expected utility maximizers conditional on coherent distorted
beliefs are equivalent to the weighted utility maximizers studied by Chew
[1983]. |
doi_str_mv | 10.48550/arxiv.2310.09879 |
format | Article |
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probabilities. We propose a simple consistency condition on distortion
functions, which we term distortion coherence, that ensures that the function
commutes with conditioning on an event. We show that distortion coherence
restricts belief distortions to have a particular function form: power-weighted
distortions, where distorted beliefs are proportional to the original beliefs
raised to a power and weighted by a state-specific value. We generalize our
findings to allow for distortions of the probabilities assigned to both states
and signals, which nests the functional forms widely used in studying
probabilistic biases (e.g., Grether, 1980 and Benjamin, 2019). We show how
coherent distorted beliefs are tightly related to several extant models of
motivated beliefs: they are the outcome of maximizing anticipated expected
utility subject to a generalized Kullback-Liebler cost of distortion. Moreover,
in the domain of lottery choice, we link coherent distortions to explanations
of non-expected utility like the Allais paradox: individuals who maximize
subjective expected utility maximizers conditional on coherent distorted
beliefs are equivalent to the weighted utility maximizers studied by Chew
[1983].</description><identifier>DOI: 10.48550/arxiv.2310.09879</identifier><language>eng</language><creationdate>2023-10</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2310.09879$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2310.09879$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Chambers, Christopher P</creatorcontrib><creatorcontrib>Masatlioglu, Yusufcan</creatorcontrib><creatorcontrib>Raymond, Collin</creatorcontrib><title>Coherent Distorted Beliefs</title><description>Many models of economics assume that individuals distort objective
probabilities. We propose a simple consistency condition on distortion
functions, which we term distortion coherence, that ensures that the function
commutes with conditioning on an event. We show that distortion coherence
restricts belief distortions to have a particular function form: power-weighted
distortions, where distorted beliefs are proportional to the original beliefs
raised to a power and weighted by a state-specific value. We generalize our
findings to allow for distortions of the probabilities assigned to both states
and signals, which nests the functional forms widely used in studying
probabilistic biases (e.g., Grether, 1980 and Benjamin, 2019). We show how
coherent distorted beliefs are tightly related to several extant models of
motivated beliefs: they are the outcome of maximizing anticipated expected
utility subject to a generalized Kullback-Liebler cost of distortion. Moreover,
in the domain of lottery choice, we link coherent distortions to explanations
of non-expected utility like the Allais paradox: individuals who maximize
subjective expected utility maximizers conditional on coherent distorted
beliefs are equivalent to the weighted utility maximizers studied by Chew
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probabilities. We propose a simple consistency condition on distortion
functions, which we term distortion coherence, that ensures that the function
commutes with conditioning on an event. We show that distortion coherence
restricts belief distortions to have a particular function form: power-weighted
distortions, where distorted beliefs are proportional to the original beliefs
raised to a power and weighted by a state-specific value. We generalize our
findings to allow for distortions of the probabilities assigned to both states
and signals, which nests the functional forms widely used in studying
probabilistic biases (e.g., Grether, 1980 and Benjamin, 2019). We show how
coherent distorted beliefs are tightly related to several extant models of
motivated beliefs: they are the outcome of maximizing anticipated expected
utility subject to a generalized Kullback-Liebler cost of distortion. Moreover,
in the domain of lottery choice, we link coherent distortions to explanations
of non-expected utility like the Allais paradox: individuals who maximize
subjective expected utility maximizers conditional on coherent distorted
beliefs are equivalent to the weighted utility maximizers studied by Chew
[1983].</abstract><doi>10.48550/arxiv.2310.09879</doi><oa>free_for_read</oa></addata></record> |
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title | Coherent Distorted Beliefs |
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