Ordinal Aggregation Results via Karlin's Variation Diminishing Property

13 Pages Posted: 5 Sep 2014 Last revised: 26 Jan 2017

See all articles by Michael Choi

Michael Choi

University of California, Irvine

Lones Smith

University of Wisconsin at Madison - Department of Economics

Date Written: November 15, 2016

Abstract

When is the weighted sum of quasi-concave functions quasi-concave? We answer this, extending an analogous preservation of the single-crossing property in QS: Quah and Strulovici (2012). Our approach develops a general preservation of n-crossing properties, applying the variation diminishing property in Karlin (1956). The QS premise is equivalent to Karlin’s total positivity of order two, while our premise uses total positivity of order three: The weighted sum of quasi-concave functions is quasi-concave if each has an increasing portion more risk averse than any decreasing portion.

Keywords: single-crossing property, quasi-concavity, variation diminishing property, logsupermodularity, signed-ratio monotonicity

JEL Classification: C60

Suggested Citation

Choi, Michael and Smith, Lones, Ordinal Aggregation Results via Karlin's Variation Diminishing Property (November 15, 2016). Available at SSRN: https://ssrn.com/abstract=2491021 or http://dx.doi.org/10.2139/ssrn.2491021

Michael Choi (Contact Author)

University of California, Irvine ( email )

3151 Social Science Plaza
Irvine, CA 92697-5100
United States

Lones Smith

University of Wisconsin at Madison - Department of Economics ( email )

1180 Observatory Drive
Madison, WI 53706-1393
United States
608-263-3871 (Phone)
608-262-2033 (Fax)

HOME PAGE: http://www.lonessmith.com

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