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An Integrated Approach to Preferential Voting Models with Variable Weights for Rank Positions

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Abstract

In a ranked voting system, voters select a subset of candidates and rank them from most to least preferred. Data envelopment analysis (DEA)-based voting models, among others, are used to determine the rank-position weights most favorable for each candidate, with the goal of achieving the highest aggregate score. However, concerns have been raised about the weights assigned to each rank position, as well as the potential for rank reversal of some candidates resulting from changes in votes earned by other candidates. To address these issues, some authors have developed two improved models. These models aim to incorporate the constraints of candidates that are not being evaluated into a single restriction, preventing inefficient candidates from influencing the order of efficient candidates. Moreover, these models treat the parameters used to make the distance between successive ranks as variable weights, and calculate average efficiency scores of candidates while considering the entire range of parameters. In this study, we revisit the two improved models and explore an alternative approach based on results from linear algebra and convex analysis, which is more intuitive and easier to understand. Furthermore, we provide closed-form optimal solutions for DEA-based voting models that share the common goal of maximizing the distance between successive ranks while considering both efficiency-related and weight constraints. The analysis of these four models offers a better understanding of their similarities and differences.

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Notes

  1. See Sect. 3 for the range of ε that ensures the feasibility of the set.

  2. We have omitted the detailed formulation of the OPA model to prevent the paper from becoming overly lengthy.

References

  • Ahn BS (2017) Approximate weighting method for multiattribute decision problems with imprecise parameters. Omega 72:87–95

    Article  Google Scholar 

  • Angiz MZ, Tajaddini A, Mustafa A, Kamali MJ (2012) Ranking alternatives in a preferential voting system using fuzzy concepts and data envelopment analysis. Comput Ind Eng 63:784–790

    Article  Google Scholar 

  • Ataei Y, Mahmoudi A, Feylizadeh MR, Li DF (2020) Ordinal priority approach (OPA) in multiple attribute decision-making. Appl Soft Comput 86:105893

    Article  Google Scholar 

  • Baranwal G, Vidyarthi DP (2016) A cloud service selection model using improved ranked voting method. Concurr Comput Pract Exp 28:3540–3567

    Article  Google Scholar 

  • Bazaraa M, Jarvis J, Sherali H (1990) Linear programming and network flows. John Wiley and Sons, New York

    Google Scholar 

  • Berman A, Plemmons RJ (1994) Nonnegative matrices in the mathematical sciences. Society for Industrial and Applied Mathematics (SIAM), Philadelphia

    Book  Google Scholar 

  • Contreras I (2010) A distance-based consensus model with flexible choice of rank-position weights. Group Decis Negot 19:441–456

    Article  Google Scholar 

  • Contreras I, Hinojosa MA, Mármol AM (2005) A class of flexible weight indices for ranking alternatives. IMA J Manag Math 16:71–85

    Google Scholar 

  • Cook WD, Kress M (1990) A data envelopment model for aggregating preference rankings. Manag Sci 36:1302–1310

    Article  Google Scholar 

  • Csatό L (2023) A comparative study of scoring systems by simulations. J Sports Econ 24:526–545

    Article  Google Scholar 

  • Ebrahimnejad A (2012) A new approach for ranking of candidates in voting systems. Opsearch 49:103–115

    Article  Google Scholar 

  • Ebrahimnejad A, Tavana M, Santos-Arteaga FJ (2016) An integrated data envelopment analysis and simulation method for group consensus ranking. Math Comput Simul 119:1–17

    Article  Google Scholar 

  • Fishburn PC (1981) Inverted orders for monotone scoring rules. Discrete Appl Math 3:27–36

    Article  Google Scholar 

  • Foroughi AA, Aouni B (2012) New approaches for determining a common set of weights for a voting system. Int Trans Oper Res 19:521–530

    Article  Google Scholar 

  • Foroughi AA, Tamiz M (2005) An effective total ranking model for a ranked voting system. Omega 33:491–496

    Article  Google Scholar 

  • Green RH, Doyle JR, Cook WD (1996) Preference voting and project ranking using DEA and cross evaluation. Eur J Oper Res 90:461–472

    Article  Google Scholar 

  • Hadi-Vencheh A (2014) Two effective total ranking models for preference voting and aggregation. Math Sci 8:115

    Article  Google Scholar 

  • Hadi-Vencheh A, Niazi-Motlagh M (2011) An improved voting analytic hierarchy process-data envelopment analysis methodology for suppliers selection. Int J Comput Integr Manuf 24:189–197

    Article  Google Scholar 

  • Hashimoto A (1997) A ranked voting system using a DEA/AR exclusion model: a note. Eur J Oper Res 97:600–604

    Article  Google Scholar 

  • Hatefi MA (2023) A new method for weighting decision making attributes: an application in high-tech selection in oil and gas industry. Soft Comput. https://doi.org/10.1007/s00500-023-09282-7

    Article  Google Scholar 

  • Hatefi MA, Razavi SA, Abiri V (2023) A novel multi-attribute model to select appropriate weighting method in decision making, an empirical application in petroleum industry. Group Decis Negot. https://doi.org/10.1007/s10726-023-09846-w

    Article  Google Scholar 

  • Izadikhah M, Saen RF (2019) Solving voting system by data envelopment analysis for assessing sustainability of suppliers. Group Decis Negot 28:641–669

    Article  Google Scholar 

  • Izadikhah M, Saen RF, Zare R, Shamsi M, Hezaveh MK (2022) Assessing the stability of suppliers using a multi-objective fuzzy voting data envelopment analysis model. Environ Dev Sustain. https://doi.org/10.1007/s10668-022-02376-6

    Article  Google Scholar 

  • Khodabakhshi M, Aryavash K (2015) Aggregating preference rankings using an optimistic-pessimistic approach. Comput Ind Eng 85:13–16

    Article  Google Scholar 

  • Kim JH, Ahn BS (2022) Volume-based ranking method for a ranked voting system. Int Trans Oper Res 29:3758–3777

    Article  Google Scholar 

  • Kondratev AY, Ianovski E, Nesterov AS (2023) How should we score athletes and candidates: geometric scoring rules. Oper Res. https://doi.org/10.1287/opre.2023.2473

    Article  Google Scholar 

  • Llamazares B (2016) Ranking candidates through convex sequences of variable weights. Group Decis Negot 25:567–584

    Article  Google Scholar 

  • Llamazares B (2017) Aggregating preference rankings using an optimistic-pessimistic approach: closed-form expressions. Comput Ind Eng 110:109–111

    Article  Google Scholar 

  • Llamazares B, Peña T (2009) Preference aggregation and DEA: an analysis of the methods proposed to discriminate efficient candidates. Eur J Oper Res 197:714–721

    Article  Google Scholar 

  • Llamazares B, Peña T (2013) Aggregating preferences rankings with variable weights. Eur J Oper Res 230:348–355

    Article  Google Scholar 

  • Mahmoudi A, Javed SA (2022) Probabilistic approach to multi-stage supplier evaluation: confidence level measurement in ordinal priority approach. Group Decis Negot 31:1051–1096

    Article  Google Scholar 

  • Mahmoudi A, Javed SA (2023) Uncertainty analysis in group decisions through interval ordinal priority approach. Group Decis Negot 32:807–833

    Article  Google Scholar 

  • Mahmoudi A, Abbasi M, Deng X (2022a) Evaluating the performance of the suppliers using hybrid DEA-OPA model: a sustainable development perspective. Group Decis Negot 31:335–362

    Article  Google Scholar 

  • Mahmoudi A, Abbasi M, Deng X (2022b) A novel project portfolio selection framework towards organizational resilience: robust ordinal priority approach. Expert Syst Appl 188:116067

    Article  Google Scholar 

  • Noguchi H, Ogawa M, Ishii H (2002) The appropriate total ranking method using DEA for multiple categorized purposes. J Comput Appl Math 146:155–166

    Article  Google Scholar 

  • Obata T, Ishii H (2003) A method for discriminating efficient candidates with ranked voting data. Eur J Oper Res 151:233–237

    Article  Google Scholar 

  • Pishchulov G, Trautrims A, Chesney T, Gold S, Schwab L (2019) The voting analytic hierarchy process revisited: a revised method with application to sustainable supplier selection. Int J Prod Econ 211:166–179

    Article  Google Scholar 

  • Sharafi H, Soltanifar M, Lotfi FH (2022) Selecting a green supplier utilizing the new fuzzy voting model and the fuzzy combinative distance-based assessment method. EURO J Decis Process 10:100010

    Article  Google Scholar 

  • Sitarz S (2013) The medal points’ incenter for rankings in sport. Appl Math Lett 26:408–412

    Article  Google Scholar 

  • Soltanifar M, Shahghobadi S (2013) Selecting a benevolent secondary goal model in data envelopment analysis cross-efficiency evaluation by a voting model. Socio-Econ Plann Sci 47:65–74

    Article  Google Scholar 

  • Soltanifar M, Sharafi H, Lotfi FH, Pedrycz W, Allahviranloo T (2023) Preferential voting and applications: Approaches based on data envelopment analysis. Studies in systems, decision and control, vol 471. Springer, Cham

    Google Scholar 

  • Stein WE, Mizzi PJ, Pfaffenberger RC (1994) A stochastic dominance analysis of ranked voting systems with scoring. Eur J Oper Res 74:78–85

    Article  Google Scholar 

  • Wang YM, Chin KS (2007) Discriminating DEA efficient candidates by considering their east relative total scores. J Comput Appl Math 206:209–215

    Article  Google Scholar 

  • Wang YM, Chin KS (2011) The use of OWA operator weights for cross-efficiency aggregation. Omega 39:493–503

    Article  Google Scholar 

  • Wang YM, Chin KS, Yang JB (2007) Three new models for preference voting and aggregation. J Oper Res Soc 58:1389–1393

    Article  Google Scholar 

  • Wang NS, Yi RH, Liu D (2008) A solution method to the problem proposed by Wang in voting systems. J Comput Appl Math 221:106–113

    Article  Google Scholar 

Download references

Acknowledgements

The author expresses gratitude to two anonymous reviewers for their thorough reviews and valuable suggestions, which have significantly improved the presentation and quality of this paper. The author is also grateful to Ahn ES and Kwak YS for their valuable assistance.

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  1. College of Business and Economics, Chung-Ang University, 221 Heukseok, Dongjak, Seoul, 156-756, South Korea

    Byeong Seok Ahn

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Ahn, B.S. An Integrated Approach to Preferential Voting Models with Variable Weights for Rank Positions. Group Decis Negot (2024). https://doi.org/10.1007/s10726-024-09874-0

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