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On the denominator rule and a theorem by Janos Aczél

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  • Färe, Rolf
  • Karagiannis, Giannis

Abstract

In this note we compare and contrast arithmetic and geometric share-weighting aggregations of ratio expressions (i.e., relative scores) and we provide conditions under which they result in approximately the same value of the aggregate measure. We also provide some comparative empirical results about the differences among the suggested alternative aggregate measures.

Suggested Citation

  • Färe, Rolf & Karagiannis, Giannis, 2020. "On the denominator rule and a theorem by Janos Aczél," European Journal of Operational Research, Elsevier, vol. 282(1), pages 398-400.
    • Handle: RePEc:eee:ejores:v:282:y:2020:i:1:p:398-400
    DOI: 10.1016/j.ejor.2019.09.013
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    References listed on IDEAS

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    1. Rolf Fare & Valentin Zelenyuk, 2005. "On Farrell's Decomposition and Aggregation," International Journal of Business and Economics, School of Management Development, Feng Chia University, Taichung, Taiwan, vol. 4(2), pages 167-171, August.
    2. Aczel, J. & Alsina, C., 1986. "On synthesis of judgements," Socio-Economic Planning Sciences, Elsevier, vol. 20(6), pages 333-339.
    3. Färe, Rolf & Karagiannis, Giannis, 2017. "The denominator rule for share-weighting aggregation," European Journal of Operational Research, Elsevier, vol. 260(3), pages 1175-1180.
    4. Benton F. Massell, 1961. "A Disaggregated View of Technical Change," Journal of Political Economy, University of Chicago Press, vol. 69(6), pages 547-547.
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    Cited by:

    1. Rolf Färe & Giannis Karagiannis, 2022. "Aggregation and decomposition of Farrell efficiencies," Operational Research, Springer, vol. 22(5), pages 5675-5683, November.
    2. Karagiannis, Giannis, 2023. "Decomposition and aggregation of tone efficiencies," Omega, Elsevier, vol. 119(C).
    3. Rolf Färe & Giannis Karagiannis, 2024. "The denominator rule with unit ratio difference," Journal of Productivity Analysis, Springer, vol. 61(2), pages 183-190, April.
    4. Karagiannis, Giannis, 2023. "Aggregating faculty members’ research effectiveness to the department or university level: Exact versus approximate solutions," Socio-Economic Planning Sciences, Elsevier, vol. 90(C).

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