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Reference: James E. Foster, Mark McGillivray and Suman Seth, (2012). Rank robustness of composite indices : dominance and ambiguity.Citable link to this page:


Rank robustness of composite indices : dominance and ambiguity Subtitle: OPHI working paper no. 26b

Abstract: Many structures in economics – from development indices to expected utility – take theform of a linear composite index, which aggregates linearly across multiple dimensions usinga vector of weights. Judgments rendered by composite indices are often given greatimportance, yet by definition are contingent on an initial vector of weights. A comparisonmade with one weighting vector could be robust to variations in the weights or, alternatively,it may be reversed at some other plausible vector. This paper presents criteria to discernbetween these two cases. A general robustness quasi-ordering is defined that requiresdominance or unanimous comparisons for a set of weighting vectors, and methods from the Bewley model of Knightian uncertainty are invoked to characterize it. We focus on aparticular set of weighting vectors suggested by the epsilon-contamination model ofambiguity, which allows the degree of confidence in the initial weighting vector to play arole. We provide a practical vector-valued representation of the resulting epsilon-robustnessquasi-ordering and propose a numerical measure to gauge the robustness of a givencomparison. An empirical illustration reports on the robustness of Human DevelopmentIndex country rankings. We extend our methods to certain nonlinear composite indices andexplore the links with decision theory, partial comparability in social choice, and themeasurement of the freedom of choice.

Publication status:PublishedPeer Review status:Reviewed (other)Version:Publisher's version Funder: Economic and Social Research Council   Funder: Robertson Foundation   Funder: UNICEF   Funder: Praus   Funder: Georg-August-Universität Göttingen   Funder: International Food Policy Research Institute   Funder: John Fell Fund   Funder: German Federal Ministry for Economic Cooperation and Development   Funder: United Nations Development Programme (UNDP)   Funder: International Development Research Council   Funder: Canadian International Development Agency   Funder: Department for International Development   Funder: AusAID   Notes:Copyright © Oxford Poverty & Human Development Initiative 2012. This publication is copyright, however it may be reproduced without fee for teaching or non-profit purposes, but not for resale. Formal permission is required for all such uses, and will normally be granted immediately. For copying in any other circumstances, or for re-use in other publications, or for translation or adaptation, prior written permission must be obtained from OPHI and may be subject to a fee.

Bibliographic Details

Publisher: Oxford Poverty & Human Development Initiative (OPHI)

Publisher Website: http://www.ophi.org.uk/

Issue Date: 2012

Copyright Date: 2012 Identifiers

Issn: 2040-8188

Isbn: 978-1-907194-43-6

Urn: uuid:5c247b0e-9e98-4c7c-95f0-2a8d09056434 Item Description

Type: Working/Discussion paper;

Language: en

Version: Publisher's versionKeywords: Composite index robust comparisons dominance ambiguity epsiloncontamination Knightian uncertainty Human Development Index ophi Tiny URL: ora:9416


Author: James E. Foster - institutionUniversity of Oxford facultySSD, Queen Elizabeth House, Department of International Development rese

Source: https://ora.ox.ac.uk/objects/uuid:5c247b0e-9e98-4c7c-95f0-2a8d09056434


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