Decomposition properties of dual choice functionals |
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Authors: | S David Promislow Virginia R Young |
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Institution: | (1) York University, Department of Mathematics and Statistics, 4700 Keele Street, Toronto, Ontario, Canada M3J 1P3, CA;(2) University of Wisconsin-Madison, School of Business, 975 University Avenue, Madison, WI 53706-1323, USA (e-mail: vyoung@bus.wisc.edu), US |
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Abstract: | The Gini coefficient is a well-known measure of inequality, and it satisfies a non-overlapping additive decomposition property
(Ebert 1988b). The Gini coefficient is related to the dual theory of choice, as developed by Yaari (1987, 1988). We determine
which other dual choice functionals satisfy a non-overlapping additive decomposition property that is weaker than the additive
one suggested in Ebert (1988b). It turns out that the only functionals that do are those that arise from the Lebesgue measure,
the measure associated with the Gini coefficient, and degenerate delta functions.
Received: 8 January 2001/Accepted: 22 February 2002
We thank the Actuarial Education and Research Fund for financial support of this project. We also thank anonymous referees
for helpful comments. |
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