Athanassoglou, Stergios (2013): Multidimensional welfare rankings.

PDF
MPRA_paper_51642.pdf Download (740kB)  Preview 
Abstract
Social wellbeing is intrinsically multidimensional. Welfare indices attempting to reduce this complexity to a unique measure abound in many areas of economics and public policy. Ranking alternatives based on such measures depends, sometimes critically, on how the different dimensions of welfare are weighted. In this paper, a theoretical framework is presented that yields a set of consensus rankings in the presence of such weight imprecision. The main idea is to consider a vector of weights as an imaginary voter submitting preferences over alternatives in the form of an ordered list. With this voting construct in mind, a rule for aggregating the preferences of many plausible choices of weights, suitably weighted by the importance attached to them, is proposed. An axiomatic characterization of the rule is provided, and its computational implementation is developed. An analytic solution is derived for an interesting special case of the model corresponding to generalized weighted means and the $\epsilon$contamination framework of Bayesian statistics. The model is applied to the Academic Ranking of World Universities index of Shanghai University, a popular composite index measuring academic excellence.
Item Type:  MPRA Paper 

Original Title:  Multidimensional welfare rankings 
Language:  English 
Keywords:  multidimensional welfare, social choice, voting, Kemeny's rule, graph theory, $\epsilon$contamination 
Subjects:  C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61  Optimization Techniques ; Programming Models ; Dynamic Analysis D  Microeconomics > D7  Analysis of Collective DecisionMaking > D71  Social Choice ; Clubs ; Committees ; Associations D  Microeconomics > D7  Analysis of Collective DecisionMaking > D72  Political Processes: RentSeeking, Lobbying, Elections, Legislatures, and Voting Behavior I  Health, Education, and Welfare > I3  Welfare, WellBeing, and Poverty > I31  General Welfare, WellBeing 
Item ID:  51642 
Depositing User:  Stergios Athanassoglou 
Date Deposited:  22 Nov 2013 05:54 
Last Modified:  07 Oct 2016 05:35 
References:  N. Ailon (2007), ``Aggregation of Partial Rankings, $p$Ratings and Top$m$ Lists,'' {\em Proc 18th Annual Sympos. Discrete Algorithms (SODA '07)}, 415424. S. Alkire and J.E. Foster (2011), ``Counting and Multidimensional Poverty Measurement,'' {\em Journal of Public Economics}, 95, 476487. S. Anand and A.K. Sen (1997). ``Concepts of Human Development and Poverty: a Multidimensional Perspective,'' UNDP. New York. G. Anderson, I. Crawford, and A. Leicester (2011), ``Welfare Rankings from Multivariate Data, a Nonparametric Approach,'' {\em Journal of Public Economics}, 95, 247252. A. Atkinson (2003), ``Multidimensional Deprivation: Contrasting Social Welfare and Counting Approaches,'' {\em Journal of Economic Inequality}, 1, 5165. D. Bertsimas and J. Tsitsiklis, {\em Introduction to Linear Optimization}, Athena Scientific, Belmont, MA, USA, 1997. J. Bartholdi III, C. A. Tovey, and M. A. Trick (1989), ``Voting schemes for which it can be difficult to tell who won the election", {\em Social Choice and Welfare}, 6, 157–165. J. Berger and L. Berliner (1986), ``Robust Bayes and empirical Bayes analysis with $\epsilon$contaminated priors,'' {\em Annals of Statistics}, 14, 461486. B. Bueler, A. Enge, and K. Fukuda (2000), ``Exact volume computation for convex polytopes: A practical study,'' In G. Kalai and G. M. Ziegler, editors, {\em Polytopes  Combinatorics and Computation}, DMV Seminar Volume 29, 131154. F. Bourguignon and S.R. Chakravarty (2003), ``The Measurement of Multidimensional Poverty,'' {\em Journal of Economic Inequality}, 1, 2549. V. Conitzer (2012), ``Should Social Network Structure be Taken Into Account in Elections?'' {\em Mathematical Social Sciences}, 64, 100102. K. Decancq and M.A. Lugo (2013), ``Weights in Multidimensional Indices of wellbeing: An Overview,'' {\em Econometric Reviews}, 32, 734. J.Y. Duclos, D. E. Sahn, and S.D. Younger (2006), ``Robust Multidimensional Poverty Comparisons,'' {\em Economic Journal}, 116, 943968. J.Y. Duclos, D. E. Sahn, and S.D. Younger (2011), ``Partial Multidimensional Inequality Orderings,'' {\em Journal of Public Economics}, 95, 225238. C. Dwork, R. Kumar, M. Naor, and D. Sivakumar (2001), ``Rank Aggregation Methods for the Web,'' {\em Proceedings of 10th International World Wide Web Conference}, 613622. J.E. Foster, M. McGillivray, and S. Seth (2013), ``Composite Indices: Rank Robustness, Statistical Association, and Redundancy,'' {\em Econometric Reviews}, 32, 3556. J.E. Foster and A.K. Sen. {\em On Economic Inequality. After a Quarter Century}. Annexe to the Expanded Edition of {\em On Economic Inequality} by A.K. Sen., Clarendon Press, Oxford, 1997. Gilboa, I. and M. Marinacci (2013), ``Ambiguity and the Bayesian Paradigm,'' in {\em Advances in Economics and Econometrics, Tenth World Congress of the Econometric Society: Economic Theory}, Volume I, Eds. D. Acemoglu, M. Arellano, E. Dekel, Cambridge University Press. David F. Gleich (2009). http://www.mathworks.it/matlabcentral/fileexchange/24134gaimcgraphalgorithmsinmatlabcode/content/gaimc/scomponents.m . Copyright, Stanford University, 20082009. J.G. Kemeny (1959), ``Mathematics without Numbers,'' {\em Daedalus}, 88, 575591. P. Klibanoff, M. Marinacci, and S. Mukerji (2005), ``A Smooth Model of Decision Making Under Ambiguity,'' \emph{Econometrica}, 73, 18491892. I. Kopylov (2009), ``Choice deferral and ambiguity aversion,'' {\em Theoretical Economics}, 4, 199225. S. Lang, {\em Linear Algebra}, Springer 3rd Edition, New Haven, CT, USA, 1987. J. Lawrence (1991), ``Polytope Volume Computation,'' {\em Mathematics of Computation}, 57, 259271. H. Moulin, {\em Axioms of Cooperative Decision Making}, Econometric Society Monographs, Cambridge University Press, Cambridge, 1988. K.G. Nishimura and H. Ozaki (2004), ``Search and Knightian uncertainty,'' {\em Journal of Economic Theory}, 119, 299333. K.G. Nishimura and H. Ozaki (2006) ``An axiomatic approach to $\epsilon$contamination,'' {\em Economic Theory}, 27, 333340. K.G. Nishimura and H. Ozaki (2007), ``Irreversible investment and Knightian uncertainty,''{\em Journal of Economic Theory}, 136, 668694. OECD and European Commission JRC, {\em Handbook on Constructing Composite Indicators}, OECD Publications, Paris, France, 2008. M. Pinar, T. Stengos, and N. Topaloglou (2013), ``Measuring Human Development: A Stochastic Dominance Approach,'' {\em Journal of Economic Growth}, 18, 69108. M. Ravallion (2012), ``Troubling Tradeoffs in the Human Development Index,'' {\em Journal of Development Economics}, 99, 201209. M. Ravallion (2012), ``Mashup Indices of Development,'' {\em World Bank Research Observer,} 27, 132. M. Saisana, A. Saltelli, and S. Tarantola (2005), ``Uncertainty and Sensitivity Analysis as Tools for the Quality of Composite Indicators,'' {\em Journal of the Royal Statistical Society A}, 168, 117. M. Saisana, B. D'Hombres, and A. Saltelli (2011), ``Rickety Numbers: Volatility of University Rankings and Policy Implications,'' {\em Research Policy}, 40, 165177. A.K. Sen, {\em Commodities and Capabilities}. Elsevier, Amsterdam; New York. NorthHolland press, 1985. A.K. Sen (1993), ``Capability and WellBeing,'' in: Nussbaum, M., Sen, A.K. (Eds). Quality of Life, Clarendon Press, Oxford, 3053. R. Tarjan (1972), ``Depthfirst Search and Linear Graph Algorithms,'' {\em SIAM Journal on Computing}, 1, 146160. K. Tsui (1995), ``Multidimensional Generalizations of the Relative and Absolute Inequality Indices: The AtkinsonKolmSen Approach,'' {\em Journal of Economic Theory}, 67, 251266. United Nations Development Programme, {\em 2013 Human Development Report. The Rise of the South: Human Progress in a Diverse World}, New York, NY, 2013. H. P. Young (1974), ``An Axiomatization of Borda's Rule,'' {\em Journal of Economic Theory}, 9, 4352. H. P. Young (1988), ``Condorcet's Theory of Voting," {\em American Political Science Review}, 82, 12311244 H. P. Young (1995), ``Optimal Voting Rules,'' {\em Journal of Economic Perspectives}, 9, 5164. H. P. Young and A. Levenglick (1978), ``A Consistent Extension of Condorcet's election principle,'' {\em SIAM Journal on Applied Mathematics}, 35, 285300. A. van Zuylen and D. Williamson (2009), ``Deterministic Pivoting Algorithms for Constrained Ranking and Clustering Problems,'' {\em Mathematics of Operations Research}, 34, 594620. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/51642 