IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2409.02087.html
   My bibliography  Save this paper

Objective Weights for Scoring: The Automatic Democratic Method

Author

Listed:
  • Chris Tofallis

Abstract

When comparing performance (of products, services, entities, etc.), multiple attributes are involved. This paper deals with a way of weighting these attributes when one is seeking an overall score. It presents an objective approach to generating the weights in a scoring formula which avoids personal judgement. The first step is to find the maximum possible score for each assessed entity. These upper bound scores are found using Data Envelopment Analysis. In the second step the weights in the scoring formula are found by regressing the unique DEA scores on the attribute data. Reasons for using least squares and avoiding other distance measures are given. The method is tested on data where the true scores and weights are known. The method enables the construction of an objective scoring formula which has been generated from the data arising from all assessed entities and is, in that sense, democratic.

Suggested Citation

  • Chris Tofallis, 2024. "Objective Weights for Scoring: The Automatic Democratic Method," Papers 2409.02087, arXiv.org.
    • Handle: RePEc:arx:papers:2409.02087
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2409.02087
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bruce Hollingsworth, 2008. "The measurement of efficiency and productivity of health care delivery," Health Economics, John Wiley & Sons, Ltd., vol. 17(10), pages 1107-1128, October.
    2. F. Hosseinzadeh Lotfi & G. R. Jahanshahloo & M. Khodabakhshi & M. Rostamy-Malkhlifeh & Z. Moghaddas & M. Vaez-Ghasemi, 2013. "A Review of Ranking Models in Data Envelopment Analysis," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-20, July.
    3. Koen Decancq & María Ana Lugo, 2013. "Weights in Multidimensional Indices of Wellbeing: An Overview," Econometric Reviews, Taylor & Francis Journals, vol. 32(1), pages 7-34, January.
    4. Chris Tofallis, 2013. "An automatic-democratic approach to weight setting for the new human development index," Journal of Population Economics, Springer;European Society for Population Economics, vol. 26(4), pages 1325-1345, October.
    5. Adler, Nicole & Friedman, Lea & Sinuany-Stern, Zilla, 2002. "Review of ranking methods in the data envelopment analysis context," European Journal of Operational Research, Elsevier, vol. 140(2), pages 249-265, July.
    6. I. Contreras & S. Lozano & M. A. Hinojosa, 2021. "A DEA cross-efficiency approach based on bargaining theory," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 72(5), pages 1156-1167, May.
    7. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    8. Ali, Agha Iqbal, 1993. "Streamlined computation for data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 64(1), pages 61-67, January.
    9. B. J. Gajewski & R. Lee & M. Bott & U. Piamjariyakul & R. L. Taunton, 2009. "On estimating the distribution of data envelopment analysis efficiency scores: an application to nursing homes' care planning process," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(9), pages 933-944.
    10. C Kao & H-T Hung, 2005. "Data envelopment analysis with common weights: the compromise solution approach," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(10), pages 1196-1203, October.
    11. Cook, Wade D. & Zhu, Joe, 2007. "Within-group common weights in DEA: An analysis of power plant efficiency," European Journal of Operational Research, Elsevier, vol. 178(1), pages 207-216, April.
    12. D K Despotis, 2002. "Improving the discriminating power of DEA: focus on globally efficient units," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(3), pages 314-323, March.
    13. M Zohrehbandian & A Makui & A Alinezhad, 2010. "A compromise solution approach for finding common weights in DEA: an improvement to Kao and Hung's approach," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(4), pages 604-610, April.
    14. K. M. Matawie & A. Assaf, 2010. "Bayesian and DEA efficiency modelling: an application to hospital foodservice operations," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(6), pages 945-953.
    15. D K Despotis, 2005. "A reassessment of the human development index via data envelopment analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(8), pages 969-980, August.
    16. Akram Dehnokhalaji & Behjat Hallaji & Narges Soltani & Jafar Sadeghi, 2017. "Convex cone-based ranking of decision-making units in DEA," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(3), pages 861-880, July.
    Full references (including those not matched with items on IDEAS)

    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. Marianela Carrillo & Jesús M. Jorge, 2017. "DEA-Like Efficiency Ranking of Regional Health Systems in Spain," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 133(3), pages 1133-1149, September.
    2. Afsharian, Mohsen & Ahn, Heinz & Harms, Sören Guntram, 2021. "A review of DEA approaches applying a common set of weights: The perspective of centralized management," European Journal of Operational Research, Elsevier, vol. 294(1), pages 3-15.
    3. Ruiz, José L. & Sirvent, Inmaculada, 2016. "Common benchmarking and ranking of units with DEA," Omega, Elsevier, vol. 65(C), pages 1-9.
    4. Mariano, Enzo Barberio & Sobreiro, Vinicius Amorim & Rebelatto, Daisy Aparecida do Nascimento, 2015. "Human development and data envelopment analysis: A structured literature review," Omega, Elsevier, vol. 54(C), pages 33-49.
    5. Cristina Bernini & Andrea Guizzardi & Giovanni Angelini, 2013. "DEA-Like Model and Common Weights Approach for the Construction of a Subjective Community Well-Being Indicator," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 114(2), pages 405-424, November.
    6. Helmi Hammami & Thanh Ngo & David Tripe & Dinh-Tri Vo, 2022. "Ranking with a Euclidean common set of weights in data envelopment analysis: with application to the Eurozone banking sector," Annals of Operations Research, Springer, vol. 311(2), pages 675-694, April.
    7. Jesús Peiró-Palomino & Andrés J. Picazo-Tadeo, 2018. "Assessing well-being in European regions. Does government quality matter?," Working Papers 2018/06, Economics Department, Universitat Jaume I, Castellón (Spain).
    8. Jorge Guardiola & Andrés J. Picazo-Tadeo, 2013. "Weighting life domains with Data Envelopment Analysis," Working Papers 1311, Department of Applied Economics II, Universidad de Valencia.
    9. 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.
    10. Ernest Reig, 2012. "Building an Enlarged Human Development Indicator: Europe and the Southern Mediterranean Basin," Working Papers 1203, Department of Applied Economics II, Universidad de Valencia.
    11. Ernest Reig-Martínez, 2013. "Social and Economic Wellbeing in Europe and the Mediterranean Basin: Building an Enlarged Human Development Indicator," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 111(2), pages 527-547, April.
    12. Jesús Peiró‐Palomino & Andrés J. Picazo‐Tadeo & Vicente Rios, 2020. "Well‐being in European regions: Does government quality matter?," Papers in Regional Science, Wiley Blackwell, vol. 99(3), pages 555-582, June.
    13. Jorge Guardiola & Andrés Picazo-Tadeo, 2014. "Building Weighted-Domain Composite Indices of Life Satisfaction with Data Envelopment Analysis," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 117(1), pages 257-274, May.
    14. Oliveira, Renata & Zanella, Andreia & Camanho, Ana S., 2019. "The assessment of corporate social responsibility: The construction of an industry ranking and identification of potential for improvement," European Journal of Operational Research, Elsevier, vol. 278(2), pages 498-513.
    15. Omrani, Hashem & Valipour, Mahsa & Jafari Mamakani, Saeid, 2019. "Construct a composite indicator based on integrating Common Weight Data Envelopment Analysis and principal component analysis models: An application for finding development degree of provinces in Iran," Socio-Economic Planning Sciences, Elsevier, vol. 68(C).
    16. Sebastián Lozano & Narges Soltani & Akram Dehnokhalaji, 2020. "A compromise programming approach for target setting in DEA," Annals of Operations Research, Springer, vol. 288(1), pages 363-390, May.
    17. Ramón, Nuria & Ruiz, José L. & Sirvent, Inmaculada, 2011. "Reducing differences between profiles of weights: A "peer-restricted" cross-efficiency evaluation," Omega, Elsevier, vol. 39(6), pages 634-641, December.
    18. Jie Wu & Junfei Chu & Qingyuan Zhu & Pengzhen Yin & Liang Liang, 2016. "DEA cross-efficiency evaluation based on satisfaction degree: an application to technology selection," International Journal of Production Research, Taylor & Francis Journals, vol. 54(20), pages 5990-6007, October.
    19. Hussein Sayed & Ramadan Hamed & Samaa Hazem Hosny & Alyaa Hegazy Abdelhamid, 2018. "Avoiding Ranking Contradictions in Human Development Index Using Goal Programming," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 138(2), pages 405-442, July.
    20. Jesús Peiró-Palomino & Andrés J. Picazo-Tadeo, 2018. "OECD: One or Many? Ranking Countries with a Composite Well-Being Indicator," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 139(3), pages 847-869, October.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:2409.02087. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.