# 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.

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.

Detailed statistics

Item Type: Working Paper 03 Faculty of Economics > Department of Economics Working Paper Series > Department of Economics 330 Economics C91, D11, D12, D83 Revealed preferences, risk preferences, expected utility, independence axiom, betweenness, homotheticity, consumer choice, aggregation English November 2014 12 Nov 2014 16:09 05 Apr 2016 18:30 Working paper series / Department of Economics 60 1664-7041 http://www.econ.uzh.ch/static/wp/econwp179.pdf http://www.econ.uzh.ch/static/workingpapers.php
Permanent URL: https://doi.org/10.5167/uzh-100725