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The two faces of independence: betweenness and homotheticity


Burghart, Daniel R; Epper, Thomas; Fehr, Ernst (2014). The two faces of independence: betweenness and homotheticity. Working paper series / Department of Economics 179, University of Zurich.

Abstract

Many studies document failures of expected utility’s key assumption, the independence axiom. Here, we show that independence can be decomposed into two distinct axioms – betweenness and homotheticity – and that these two axioms are necessary and sufficient for independence. Thus, independence can fail because homotheticity, betweenness, or both are violated. Most research has focused on models that assume subjects will violate both axioms or models that assume subjects will satisfy betweenness but violate homotheticity. Our decomposition of independence into betweenness and homotheticity allows us to show, however, that a significant share of subjects obey homotheticity but violate betweenness. Using data from a revealed preference experiment, and without making any parametric assumptions, we show that 1/3 of participants belong in the neglected class of preferences that violate independence but satisfy homotheticity, indicating that betweenness is violated. Another 1/3 of participants satisfy independence. The remaining 1/3 fail both independence and homotheticity and may also fail betweenness. Our results provide useful constraints on future modeling attempts by highlighting, in a non-parametric way, an empirically relevant class of preferences.

Abstract

Many studies document failures of expected utility’s key assumption, the independence axiom. Here, we show that independence can be decomposed into two distinct axioms – betweenness and homotheticity – and that these two axioms are necessary and sufficient for independence. Thus, independence can fail because homotheticity, betweenness, or both are violated. Most research has focused on models that assume subjects will violate both axioms or models that assume subjects will satisfy betweenness but violate homotheticity. Our decomposition of independence into betweenness and homotheticity allows us to show, however, that a significant share of subjects obey homotheticity but violate betweenness. Using data from a revealed preference experiment, and without making any parametric assumptions, we show that 1/3 of participants belong in the neglected class of preferences that violate independence but satisfy homotheticity, indicating that betweenness is violated. Another 1/3 of participants satisfy independence. The remaining 1/3 fail both independence and homotheticity and may also fail betweenness. Our results provide useful constraints on future modeling attempts by highlighting, in a non-parametric way, an empirically relevant class of preferences.

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Additional indexing

Item Type:Working Paper
Communities & Collections:03 Faculty of Economics > Department of Economics
Working Paper Series > Department of Economics
Dewey Decimal Classification:330 Economics
JEL Classification:C91, D11, D12, D83
Uncontrolled Keywords:Revealed preferences, risk preferences, expected utility, independence axiom, betweenness, homotheticity, consumer choice, aggregation
Language:English
Date:November 2014
Deposited On:12 Nov 2014 16:09
Last Modified:15 Aug 2017 18:51
Series Name:Working paper series / Department of Economics
Number of Pages:60
ISSN:1664-7041
Official URL:http://www.econ.uzh.ch/static/wp/econwp179.pdf
Related URLs:http://www.econ.uzh.ch/static/workingpapers.php

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