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The Possibility Of Group Welfare Functions

Author

Listed:
  • THOMAS L. SAATY

    (Katz Graduate School of Business, University of Pittsburgh, Pittsburgh, PA 15260, USA)

  • LUIS G. VARGAS

    (Katz Graduate School of Business, University of Pittsburgh, Pittsburgh, PA 15260, USA)

Abstract

This paper gives a brief overview of the well-known impossibility-possibility theorem in constructing a social welfare function from individual functions. The Analytic Hierarchy Process uses a fundamental scale of absolute numbers to represent judgments about dominance in paired comparisons. It is shown that it is possible to derive such a function in two ways. One is from the synthesized functions of the judgments of each of the individuals. The other is obtained by first combining corresponding pairwise comparison judgments made by all the individuals, thus obtaining a matrix of combined judgments for the group and then deriving a welfare function for the group. With consistency the four conditions imposed by Arrow are satisfied. With inconsistency, an additional condition is needed.

Suggested Citation

  • Thomas L. Saaty & Luis G. Vargas, 2005. "The Possibility Of Group Welfare Functions," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 4(02), pages 167-176.
    • Handle: RePEc:wsi:ijitdm:v:04:y:2005:i:02:n:s0219622005001453
    DOI: 10.1142/S0219622005001453
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    Citations

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    Cited by:

    1. Thomas L. Saaty, 2013. "The Modern Science of Multicriteria Decision Making and Its Practical Applications: The AHP/ANP Approach," Operations Research, INFORMS, vol. 61(5), pages 1101-1118, October.
    2. Juan Aguarón & María Teresa Escobar & José María Moreno-Jiménez, 2016. "The precise consistency consensus matrix in a local AHP-group decision making context," Annals of Operations Research, Springer, vol. 245(1), pages 245-259, October.
    3. Michail Nerantzidis, 2018. "The role of weighting in corporate governance ratings," Journal of Management & Governance, Springer;Accademia Italiana di Economia Aziendale (AIDEA), vol. 22(3), pages 589-628, September.
    4. Wolfgang Ossadnik & Stefanie Schinke & Ralf H. Kaspar, 2016. "Group Aggregation Techniques for Analytic Hierarchy Process and Analytic Network Process: A Comparative Analysis," Group Decision and Negotiation, Springer, vol. 25(2), pages 421-457, March.
    5. Florentino Morales & Walter Timo de Vries, 2021. "Establishment of Land Use Suitability Mapping Criteria Using Analytic Hierarchy Process (AHP) with Practitioners and Beneficiaries," Land, MDPI, vol. 10(3), pages 1-20, February.
    6. Saaty, Thomas L. & Shang, Jen S., 2007. "Group decision-making: Head-count versus intensity of preference," Socio-Economic Planning Sciences, Elsevier, vol. 41(1), pages 22-37, March.
    7. Dong-Fei XUE & Shi-Jie ZHAO & De-Peng ZHANG, 2014. "Comparison of CRM Programs Basing on Improving Customer Profitability: Using the AHP Method," International Review of Management and Marketing, Econjournals, vol. 4(2), pages 167-174.

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