IDEAS home Printed from https://ideas.repec.org/a/kap/theord/v73y2012i4p649-669.html

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

Author

Listed:
  • 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

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11238-012-9317-4
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11238-012-9317-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Munda, G. & Nijkamp, P. & Rietveld, P., 1992. "Comparison of fuzzy sets : a new semantic distance," Serie Research Memoranda 0055, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    2. Bouyssou, Denis, 1986. "Some remarks on the notion of compensation in MCDM," European Journal of Operational Research, Elsevier, vol. 26(1), pages 150-160, July.
    3. Giuseppe Munda & Michela Nardo, 2009. "Noncompensatory/nonlinear composite indicators for ranking countries: a defensible setting," Applied Economics, Taylor & Francis Journals, vol. 41(12), pages 1513-1523.
    4. Giuseppe Munda, 2003. "Social Multi-Criteria Evaluation (SMCE)," UHE Working papers 2003_04, Universitat Autònoma de Barcelona, Departament d'Economia i Història Econòmica, Unitat d'Història Econòmica.
    5. Kenneth J. Arrow & Herve Raynaud, 1986. "Social Choice and Multicriterion Decision-Making," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262511754, December.
    6. 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.
    7. Vansnick, Jean-Claude, 1986. "On the problem of weights in multiple criteria decision making (the noncompensatory approach)," European Journal of Operational Research, Elsevier, vol. 24(2), pages 288-294, February.
    8. Frank A. Cowell & Maria-Pia Victoria-Feser, 2002. "Welfare Rankings in the Presence of Contaminated Data," Econometrica, Econometric Society, vol. 70(3), pages 1221-1233, May.
    9. Denis Bouyssou & Jean-Claude Vansnick, 1986. "Noncompensatory and generalized noncompensatory preference structures," Post-Print hal-02920182, HAL.
    10. JosÉ Figueira & Salvatore Greco & Matthias Ehrogott, 2005. "Multiple Criteria Decision Analysis: State of the Art Surveys," International Series in Operations Research and Management Science, Springer, number 978-0-387-23081-8, December.
    11. Munda, Giuseppe, 2004. "Social multi-criteria evaluation: Methodological foundations and operational consequences," European Journal of Operational Research, Elsevier, vol. 158(3), pages 662-677, November.
    12. Bertrand Mareschal & Jean Pierre Brans & Philippe Vincke, 1986. "How to select and how to rank projects: the Prométhée method," ULB Institutional Repository 2013/9307, ULB -- Universite Libre de Bruxelles.
    13. Mina Baliamoune-Lutz, 2004. "On the Measurement of Human Well-being: Fuzzy Set Theory and Sen's Capability Approach," WIDER Working Paper Series RP2004-16, World Institute for Development Economic Research (UNU-WIDER).
    14. Matarazzo, B. & Munda, G., 1996. "New Approaches for the Comparison of L-R Fuzzy Numbers : a Theoretical and Operational Analysis," UFAE and IAE Working Papers 346.96, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    15. Truchon, M., 1998. "Figure Skating and the Theory of Social Choice," Papers 9814, Laval - Recherche en Politique Economique.
    16. Brans, J. P. & Vincke, Ph. & Mareschal, B., 1986. "How to select and how to rank projects: The method," European Journal of Operational Research, Elsevier, vol. 24(2), pages 228-238, February.
    17. Podinovskii, Vladislav V., 1994. "Criteria importance theory," Mathematical Social Sciences, Elsevier, vol. 27(3), pages 237-252, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    5. 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.
    6. Matheus Pereira Libório & Alexandre Magno Alvez Diniz & Douglas Alexandre Gomes Vieira & Petr Iakovlevitch Ekel, 2024. "Subjective–Objective Method of Maximizing the Average Variance Extracted From Sub-indicators in Composite Indicators," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 175(2), pages 613-637, November.
    7. 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.
    8. 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).
    9. 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.
    10. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Giuseppe Munda, 2015. "Beyond Gdp: An Overview Of Measurement Issues In Redefining ‘Wealth’," Journal of Economic Surveys, Wiley Blackwell, vol. 29(3), pages 403-422, July.
    2. 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.
    3. Greco, Salvatore & Ishizaka, Alessio & Tasiou, Menelaos & Torrisi, Gianpiero, 2019. "The Ordinal Input for Cardinal Output Approach of Non-compensatory Composite Indicators: The PROMETHEE Scoring Method," MPRA Paper 95816, University Library of Munich, Germany.
    4. Greco, Salvatore & Ishizaka, Alessio & Tasiou, Menelaos & Torrisi, Gianpiero, 2021. "The ordinal input for cardinal output approach of non-compensatory composite indicators: the PROMETHEE scoring method," European Journal of Operational Research, Elsevier, vol. 288(1), pages 225-246.
    5. Munda, Giuseppe, 2009. "A conflict analysis approach for illuminating distributional issues in sustainability policy," European Journal of Operational Research, Elsevier, vol. 194(1), pages 307-322, April.
    6. 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.
    7. Hatami-Marbini, Adel & Tavana, Madjid, 2011. "An extension of the Electre I method for group decision-making under a fuzzy environment," Omega, Elsevier, vol. 39(4), pages 373-386, August.
    8. Salvatore Greco & Alessio Ishizaka & Menelaos Tasiou & Gianpiero Torrisi, 2019. "On the Methodological Framework of Composite Indices: A Review of the Issues of Weighting, Aggregation, and Robustness," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 141(1), pages 61-94, January.
    9. Fusco, Elisa, 2015. "Enhancing non-compensatory composite indicators: A directional proposal," European Journal of Operational Research, Elsevier, vol. 242(2), pages 620-630.
    10. 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.
    11. Angilella, Silvia & Giarlotta, Alfio & Lamantia, Fabio, 2010. "A linear implementation of PACMAN," European Journal of Operational Research, Elsevier, vol. 205(2), pages 401-411, September.
    12. Attardi, Raffaele & Cerreta, Maria & Sannicandro, Valentina & Torre, Carmelo Maria, 2018. "Non-compensatory composite indicators for the evaluation of urban planning policy: The Land-Use Policy Efficiency Index (LUPEI)," European Journal of Operational Research, Elsevier, vol. 264(2), pages 491-507.
    13. Tommaso Agasisti & Giuseppe Munda, 2017. "Efficiency of investment in compulsory education: An Overview of Methodological Approaches," JRC Research Reports JRC106681, Joint Research Centre.
    14. Vanessa Silva & Danielle Morais & Adiel Almeida, 2010. "A Multicriteria Group Decision Model to Support Watershed Committees in Brazil," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 24(14), pages 4075-4091, November.
    15. Shmelev, Stanislav E. & Rodríguez-Labajos, Beatriz, 2009. "Corrigendum to "Dynamic multidimensional assessment of sustainability at the macro level: The case of Austria" [Ecological Economics 68 (2009) 2560-2573]," Ecological Economics, Elsevier, vol. 69(1), pages 209-209, November.
    16. Szántó, Richárd, 2012. "Több szempontú részvételi döntések a fenntarthatósági értékelésekben. A legnépszerűbb módszerek összehasonlítása [Participatory multi-criteria decision analysis. A comparison of methodologies]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(12), pages 1336-1355.
    17. Marta Bottero & Chiara D’Alpaos & Alessandra Oppio, 2019. "Ranking of Adaptive Reuse Strategies for Abandoned Industrial Heritage in Vulnerable Contexts: A Multiple Criteria Decision Aiding Approach," Sustainability, MDPI, vol. 11(3), pages 1-18, February.
    18. Giuseppe Munda, 2004. "Métodos y procesos multicriterio para la evaluación social de las políticas públicas," Revista Iberoamericana de Economía Ecológica, Red Iberoamericana de Economía Ecológica, vol. 1, pages 31-45.
    19. Martin, D.M. & Mazzotta, M., 2018. "Non-monetary valuation using Multi-Criteria Decision Analysis: Using a strength-of-evidence approach to inform choices among alternatives," Ecosystem Services, Elsevier, vol. 33(PB), pages 124-133.
    20. Lars Carlsen & Rainer Bruggemann, 2020. "Environmental perception in 33 European countries: an analysis based on partial order," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 22(3), pages 1873-1896, March.

    More about this item

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:theord:v:73:y:2012:i:4:p:649-669. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.