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Intensity of preference and related uncertainty in non-compensatory aggregation rules

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  • Giuseppe Munda

Abstract

Non-compensatory aggregation rules are applied in a variety of problems such as voting theory, multi-criteria analysis, composite indicators, web ranking algorithms and so on. A major open problem is the fact that non-compensability implies the analytical cost of loosing all available information about intensity of preference, i.e. if some variables are measured on interval or ratio scales, they have to be treated as measured on an ordinal scale. Here this problem has been tackled in its most general formulation, that is when mixed measurement scales (interval, ratio and ordinal) are used and both stochastic and fuzzy uncertainties are present. Objectives of this article are first to present a comprehensive review of useful solutions already proposed in the literature and second to advance the state of the art mainly in the theoretical guarantee that weights have the meaning of importance coefficients and they can be summarized in a voting matrix. This is a key result for using non-compensatory Condorcet consistent rules. A proof on the probability of existence of ties in the voting matrix is also developed. Copyright Springer Science+Business Media New York 2012

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  • Giuseppe Munda, 2012. "Intensity of preference and related uncertainty in non-compensatory aggregation rules," Theory and Decision, Springer, vol. 73(4), pages 649-669, October.
    • Handle: RePEc:kap:theord:v:73:y:2012:i:4:p:649-669
    DOI: 10.1007/s11238-012-9317-4
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    12. Giuseppe Munda, 2012. "Choosing Aggregation Rules for Composite Indicators," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 109(3), pages 337-354, December.
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    Cited by:

    1. Tommaso Agasisti & Giuseppe Munda & Ralph Hippe, 2019. "Measuring the efficiency of European education systems by combining Data Envelopment Analysis and Multiple-Criteria Evaluation," Journal of Productivity Analysis, Springer, vol. 51(2), pages 105-124, June.
    2. Fusco, Elisa, 2015. "Enhancing non-compensatory composite indicators: A directional proposal," European Journal of Operational Research, Elsevier, vol. 242(2), pages 620-630.
    3. Giuseppe Munda, 2014. "On the Use of Shadow Prices for Sustainable Well-Being Measurement," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 118(2), pages 911-918, September.
    4. Patrícia Bernardes & Petr Iakovlevitch Ekel & Sérgio Fernando Loureiro Rezende & Joel Gomes Pereira Júnior & Angélica Cidália Gouveia Santos & Maurício Andrade Rodrigues Costa & Rafael Lopes Carvalhai, 2022. "Cost of doing business index in Latin America," Quality & Quantity: International Journal of Methodology, Springer, vol. 56(4), pages 2233-2252, August.
    5. Yu, Shiwei & Duan, Haoran & Cheng, Jinhua, 2021. "An evaluation of the supply risk for China's strategic metallic mineral resources," Resources Policy, Elsevier, vol. 70(C).
    6. L. Haak & K. Pagilla, 2020. "The Water-Economy Nexus: a Composite Index Approach to Evaluate Urban Water Vulnerability," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 34(1), pages 409-423, January.
    7. Azzini, Ivano & Munda, Giuseppe, 2020. "A new approach for identifying the Kemeny median ranking," European Journal of Operational Research, Elsevier, vol. 281(2), pages 388-401.
    8. Giuseppe Munda, 2022. "Qualitative reasoning or quantitative aggregation rules for impact assessment of policy options? A multiple criteria framework," Quality & Quantity: International Journal of Methodology, Springer, vol. 56(5), pages 3259-3277, October.
    9. Luzzati, T. & Gucciardi, G., 2015. "A non-simplistic approach to composite indicators and rankings: an illustration by comparing the sustainability of the EU Countries," Ecological Economics, Elsevier, vol. 113(C), pages 25-38.

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    More about this item

    Keywords

    Condorcet consistent rules; Composite indicators; Multi-criteria analysis; Fuzzy uncertainty; C43; C44; D71; D81;
    All these keywords.

    JEL classification:

    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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