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(U,V) ordering and a duality theorem for risk aversion and Lorenz type orderings

Giovagnoli, Alessandra and Wynn, Henry P. (2012) (U,V) ordering and a duality theorem for risk aversion and Lorenz type orderings. LSE Philosophy Papers. Centre for Philosophy of Natural and Social Science, London, UK.

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Abstract

There is a duality theory connecting certain stochastic orderings between cumulative distribution functions F1 , F2 and stochastic orderings between their inverses F −1 , F −1. This underlies some theories of utility in the case of the cdf and deprivation indices in the case of the inverse. Under certain conditions there is an equivalence between the two theories. An example is the equivalence between second order stochastic dominance and the Lorenz ordering. This duality is generalised to include the case where there is “distortion” of the cdf of the form v(F ) and also of the inverse. A comprehensive duality theorem is presented in a form which includes the distortions and links the duality to the parallel theories of risk and deprivation indices. It is shown that some well-known examples are special cases of the results, including some from the Yaari social welfare theory and the theory of majorization.

Item Type: Monograph (Report)
Official URL: http://www.lse.ac.uk/CPNSS/home.aspx
Additional Information: © 2012 The Authors
Divisions: Centre for Analysis of Time Series
Subjects: H Social Sciences > HA Statistics
Sets: Research centres and groups > Centre for the Analysis of Time Series (CATS)
Research centres and groups > Decision Support and Risk Group (DSRG)
Date Deposited: 25 Feb 2014 11:59
Last Modified: 01 May 2019 23:09
URI: http://eprints.lse.ac.uk/id/eprint/55856

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