Using Social Choice Function for Multi Criteria Decision Making Problems

Orakçı, Erhan; Özdemir, Ali

doi:https://doi.org/10.17093/alphanumeric.1426694

Using Social Choice Function for Multi Criteria Decision Making Problems

bib

Erhan Orakçı, Ph.D.

Ali Özdemir, Ph.D.

Abstract

This study comparatively examines the performance of social choice functions such as Borda, Copeland, Dodgson, and Kemeny in aggregating rankings in Multi-Criteria Decision Making (MCDM) problems. The analyses, conducted using a total of 500,000 datasets, observed that the aggregation results of different social choice functions were generally similar. Although the Borda and Copeland techniques are advantageous in terms of ease of application, they were found to be insufficient in obtaining a complete ranking, especially as the number of alternatives increases. This situation is also valid for the Dodgson and Kemeny techniques. The findings of the study indicate that these techniques provide consensus in the aggregation of rankings but fail to achieve a complete ranking. In 78% of the ranking aggregations using the techniques considered, a complete ranking could not be obtained. Additionally, it was determined that the average rate of achieving a complete ranking was higher in datasets with an even number of rankings compared to those with an odd number of rankings, specifically for the Copeland and Dodgson techniques. This study evaluates the effectiveness of social choice functions in aggregating MCDM problems and provides significant insights for future research.

Keywords: Aggregation Techniques, Borda, Copeland, Dodgson, Kemeny, Multi Criteria Decision Making, Social Choice Function

Jel Classification: C61, C72, G11

Suggested citation

Orakçı, E. & Özdemir, A. (2024). Using Social Choice Function for Multi Criteria Decision Making Problems. Alphanumeric Journal, 12(1), 21-38. https://doi.org/10.17093/alphanumeric.1426694

References

Albulescu, A.-C., Grozavu, A., Larion, D., & Burghiu, G. (2022). Assessing the earthquake systemic vulnerability of the urban centres in the South-East region of Romania. The tale of Galați and Brăila Cities, Romania. Geomatics, Natural Hazards and Risk, 13(1), 1106–1133. https://doi.org/10.1080/19475705.2022.2065219
Almutairi, K., Mostafaeipour, A., Jahanshahi, E., Jooyandeh, E., Himri, Y., Jahangiri, M., Issakhov, A., Chowdhury, S., Hosseini Dehshiri, S., Hosseini Dehshiri, S., & Techato, K. (2021). Ranking Locations for Hydrogen Production Using Hybrid Wind-Solar: A Case Study. Sustainability, 13(8), 4524–4525. https://doi.org/10.3390/su13084524
Arrow, K. J. (1951). Social choice and individual values. Yale University Press.
Aytekin, A., & Orakçı, E. (2020). Spor Kulüplerinin Performanslarının Çok Kriterli Karar Verme ve Toplulaştırma Teknikleriyle İncelenmesi. Ekonomi, Politika & Finans Araştırmaları Dergisi, 435–470. https://doi.org/10.30784/epfad.752483
Azadfallah, M. (2016). A Supplier Selection Using a Group Decision Making Under Multiple Criteria by Considering Individual Criteria Set. Journal of Supply Chain Management Systems, 5(2). https://doi.org/10.21863/jscms/2016.5.2.029
Banihabib, M. E., Hashemi, F., & Shabestari, M. H. (2016). A Framework for Sustainable Strategic Planning of Water Demand and Supply in Arid Regions. Sustainable Development, 25(3), 254–266. https://doi.org/10.1002/sd.1650
Barak, S., & Mokfi, T. (2019). Evaluation and selection of clustering methods using a hybrid group MCDM. Expert Systems with Applications, 138, 112817–112818. https://doi.org/10.1016/j.eswa.2019.07.034
Bartholdi, J., Tovey, C. A., & Trick, M. A. (1989). Voting schemes for which it can be difficult to tell who won the election. Social Choice and Welfare, 6(2), 157–165. https://doi.org/10.1007/bf00303169
Black, D. (1948). On the Rationale of Group Decision-making. Journal of Political Economy, 56(1), 23–34. https://doi.org/10.1086/256633
Boehmer, N., & Schaar, N. (2023). Collecting, classifying, analyzing, and using real-world ranking data. Proceedings of the 2023 International Conference on Autonomous Agents and Multiagent Systems, 1706–1715.
Çakır, E., & Özdemir, M. (2018). Alti Sigma Projelerinin Bulanik Copras Yöntemiyle Değerlendirilmesi: Bir Üretim İşletmesi Örneği. Verimlilik Dergisi, 1, 7–39.
Copeland, A. H. (1951). A reasonable social welfare function.
Dodgson, C. (1876). A method of taking votes on more than two issues. The Theory of Committees and Elections.
Donyaii, A., Sarraf, A., & Ahmadi, H. (2020). Water Reservoir Multiobjective Optimal Operation Using Grey Wolf Optimizer. Shock and Vibration, 2020, 1–10. https://doi.org/10.1155/2020/8870464
Dortaj, A., Maghsoudy, S., Doulati Ardejani, F., & Eskandari, Z. (2020). A hybrid multi-criteria decision making method for site selection of subsurface dams in semi-arid region of Iran. Groundwater for Sustainable Development, 10, 100284–100285. https://doi.org/10.1016/j.gsd.2019.100284
Duleba, S., & Moslem, S. (2018). Sustainable Urban Transport Development with Stakeholder Participation, an AHP-Kendall Model: A Case Study for Mersin. Sustainability, 10(10), 3647–3648. https://doi.org/10.3390/su10103647
Ecer, F. (2021). A consolidated MCDM framework for performance assessment of battery electric vehicles based on ranking strategies. Renewable and Sustainable Energy Reviews, 143, 110916–110917. https://doi.org/10.1016/j.rser.2021.110916
Firouzi, S., Allahyari, M. S., Isazadeh, M., Nikkhah, A., & Van Haute, S. (2021). Hybrid multi-criteria decision-making approach to select appropriate biomass resources for biofuel production. Science of the Total Environment, 770, 144449–144450. https://doi.org/10.1016/j.scitotenv.2020.144449
Gaertner, W. (2006). A primer in social choice theory. Oxford University Press.
Gök Kısa, A. C., & Perçin, S. (2020). Bulanık Çok Kriterli Karar Verme Yaklaşimi İle Türkiye İmalat Sanayii'nde Performans Ölçümü. Uluslararası İktisadi Ve İdari İncelemeler Dergisi, 31–56. https://doi.org/10.18092/ulikidince.522799
Heckelman, J. C., & Miller, N. R. (2015). Introduction: issues in social choice and voting. In Handbook of Social Choice and Voting. Edward Elgar Publishing. https://doi.org/10.4337/9781783470730.00005
Honarmande Azimi, M., Taghizadeh, H., Fegh-hi Farahmand, N., & Pourmahmoud, J. (2014). Selection of industrial robots using the Polygons area method. International Journal of Industrial Engineering Computations, 5(4), 631–646. https://doi.org/10.5267/j.ijiec.2014.6.001
Kemeny, J. G. (1959). Mathematics without numbers. Daedalus, 88(4), 577–591.
Kendall, M. G., & Smith, B. B. (1939). The problem of m rankings. The Annals of Mathematical Statistics, 10(3), 275–287.
Kiani, M., Bagheri, M., Ebrahimi, A., & Alimohammadlou, M. (2019). A model for prioritizing outsourceable activities in universities through an integrated fuzzy-MCDM method. International Journal of Construction Management, 22(5), 784–800. https://doi.org/10.1080/15623599.2019.1645264
Li, X., Wang, X., & Xiao, G. (2017). A comparative study of rank aggregation methods for partial and top ranked lists in genomic applications. Briefings in Bioinformatics, 20(1), 178–189. https://doi.org/10.1093/bib/bbx101
May, K. O. (1952). A Set of Independent Necessary and Sufficient Conditions for Simple Majority Decision. Econometrica, 20(4), 680–681. https://doi.org/10.2307/1907651
Moghimi, M., & Taghizadeh Yazdi, M. (2017). Applying Multi-Criteria Decision-Making (MCDM) Methods for Economic Ranking of Tehran-22 Districts to Establish Financial and Commercial Centers (Case: City of Tehran). Journal of Urban Economics and Management, 5(20), 39–51. https://doi.org/10.29252/iueam.5.20.39
Mostafaeipour, A., & Jooyandeh, E. (2017). Prioritizing the locations for hydrogen production using a hybrid wind-solar system: A case study. Advances in Energy Research, 5(2), 107–108.
Nanson, E. J. (1883). Methods of election. Royal Society of Victoria.
Ömürbek, N., & Akçakaya, E. (2018). Forbes 2000 Listesinde Yeralan Havacilik Sektöründeki Şirketlerin Entropi, MAUT, COPRAS ve SAW Yöntemleri İle Analizi. Süleyman Demirel Üniversitesi İktisadi Ve İdari Bilimler Fakültesi Dergisi, 23(1), 257–278.
Penn, E. M. (2015). Arrow's Theorem and its descendants. In Handbook of Social Choice and Voting. Edward Elgar Publishing. https://doi.org/10.4337/9781783470730.00022
Rossi, F., Venable, K. B., & Walsh, T. (2011). A Short Introduction to Preferences: Between Artificial Intelligence and Social Choice. Synthesis Lectures on Artificial Intelligence and Machine Learning, 5(4), 1–102. https://doi.org/10.2200/s00372ed1v01y201107aim014
Şahin, M. (2021). A comprehensive analysis of weighting and multicriteria methods in the context of sustainable energy. International Journal of Environmental Science and Technology, 18(6), 1591–1616. https://doi.org/10.1007/s13762-020-02922-7
Sen, A. (1970). Collective choice and social welfare. Holden-Day.
Sidney, S. (1957). Nonparametric statistics for the behavioral sciences. The Journal of Nervous and Mental Disease, 125(3), 497–498.
Supçiller, A. A., & Deligöz, K. (2018). Tedarikçi Seçimi Probleminin Çok Kriterli Karar Verme Yöntemleriyle Uzlaşık Çözümü. Uluslararası İktisadi Ve İdari İncelemeler Dergisi, 355–368. https://doi.org/10.18092/ulikidince.352742
Tavana, M., Shaabani, A., & Valaei, N. (2020). An integrated fuzzy framework for analyzing barriers to the implementation of continuous improvement in manufacturing. International Journal of Quality & Reliability Management, 38(1), 116–146. https://doi.org/10.1108/ijqrm-06-2019-0196
Tuş Işık, A., & Aytaç Adalı, E. (2016). A new integrated decision making approach based on SWARA and OCRA methods for the hotel selection problem. International Journal of Advanced Operations Management, 8(2), 140–151. https://doi.org/10.1504/IJAOM.2016.079681
Ustinovichius, L., Zavadskas, E. K., & Podvezko, V. (2007). Application of a quantitative multiple criteria decision making (MCDM-1) approach to the analysis of investments in construction. Control and Cybernetics, 36(1), 251–268.
Voogd, J. H. (1982). Multicriteria Evaluation for Urban and Regional Planning.
Wang, J.-J., Jing, Y.-Y., Zhang, C.-F., & Zhao, J.-H. (2009). Review on multi-criteria decision analysis aid in sustainable energy decision-making. Renewable and Sustainable Energy Reviews, 13(9), 2263–2278. https://doi.org/10.1016/j.rser.2009.06.021
Yakut, E. (2020). OECD ülkelerinin bilgi ve iletişim teknolojileri gelişmişliklerinin MOORA ve WASPAS yöntemiyle değerlendirilerek kullanılan yöntemlerin Copeland yöntemiyle karşılaştırılması. Atatürk Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, 24(3), 1275–1294.
Zanakis, S. H., Solomon, A., Wishart, N., & Dublish, S. (1998). Multi-attribute decision making: A simulation comparison of select methods. European Journal of Operational Research, 107(3), 507–529. https://doi.org/10.1016/s0377-2217(97)00147-1
Zavadskas, E., Cavallaro, F., Podvezko, V., Ubarte, I., & Kaklauskas, A. (2017). MCDM Assessment of a Healthy and Safe Built Environment According to Sustainable Development Principles: A Practical Neighborhood Approach in Vilnius. Sustainability, 9(5), 702–703. https://doi.org/10.3390/su9050702

2024.12.01.OR.03

alphanumeric journal

Volume 12, Issue 1, 2024

Pages 21-38

Received: Jan. 24, 2024

Accepted: June 22, 2024

Published: July 20, 2024

Full Text [755.9 KB]

2024 Orakçı, E., Özdemir, A.

This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence, which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.

scan QR code to access this article from your mobile device

alphanumeric journal

The Journal of Operations Research, Statistics, Econometrics and Management Information Systems

Using Social Choice Function for Multi Criteria Decision Making Problems

Contact Us

alphanumeric journal