Operations research methods in political decisions: a case study on the European Parliament composition



In this paper, we show that operations research methods can be successfully applied to support decision-making in politics on the case study of the apportionment of seats in the European Parliament. The related political constraints and assumptions are quantitatively described and the optimization problem is formulated. On this basis, it is revealed that the current composition of the European Parliament as well as some intuitive propositions do not respect degressive proportionality as far as it was assumed. Nevertheless, our algorithm allows us to find better solutions, and among them, there is only one best allocation, which respects degressive proportionality as far as possible, according to the well known and often applied measures. Namely, over 9 thousands allocations consistent with the political requirement “nobody gains and nobody loses more than one” are referred to over 5.4 millions degressively proportional solutions, and only one allocation is revealed to be the best for all defined criteria under given populations of countries.


Decision support systems OR methods Allocation Degressive proportionality Government European Parliament 



We are grateful to the Editor and the Referees for their valuable comments on an earlier version of our paper. The results presented in this paper have been supported by the Polish National Science Centre under Grant No. DEC-2013/09/B/HS4/02702.


  1. Avery G (2014) Independentis and the Europran Union. Europan Policy Centre, BrusselsGoogle Scholar
  2. Baliński M, Young H (1977) On Huntington methods for apportionment. SIAM J Appl Math 33:607–618CrossRefGoogle Scholar
  3. Birkhoff G (1976) House monotone apportionment schemes. Proc Natl Acad Sci 37:684–686CrossRefGoogle Scholar
  4. Dniestrzański P (2014) Proposal for measure of degressive proportionality. Proc Soc Behav Sci 110:140–147CrossRefGoogle Scholar
  5. Eckert D, Klamler C, Mitlöhner J, Schlötterer C (2006) A distance-based comparison of basic voting rules. Cent Eur J Oper Res 14:377–386CrossRefGoogle Scholar
  6. European Union (2007) Treaty of Lisbon. Off J Eur Union, vol 50(C 306/1)Google Scholar
  7. Florek J (2012) A numerical method to determine a degressive proportional distribution of seats in the European Parliament. Math Soc Sci 63:121–129CrossRefGoogle Scholar
  8. Fores S, Krarup J (2013) On the origins of OR and its institutions. Cent Eur J Oper Res 21:265–275CrossRefGoogle Scholar
  9. Gallagher M (1991) Proportionality, disproportionality and electoral systems. Elect Stud 10:33–51CrossRefGoogle Scholar
  10. Gambarelli G, Uristani A (2009) Multicameral voting cohesion games. Cent Eur J Oper Res 17:433–460CrossRefGoogle Scholar
  11. Grimmett G, Laslier JF, Pukelsheim F, Ramírez González V, Rose R, Słomczyński W, Zachariasen M, Życzkowski K (2011) The allocation between the EU Member States of the seats in the European Parliament. European Parliament Studies PE 432.760. Accessed 14 June 2012
  12. Grimmett GR (2012) European apportionment via the Cambridge Compromise. Math Soc Sci 63:68–73CrossRefGoogle Scholar
  13. Gualtieri R, Trzaskowski R (2013) Report on the composition of the European Parliament with a view to the 2014 elections (2012/2309(INI)) 8–9Google Scholar
  14. Gunasekarana A, Ngaib E (2012) The future of operations management: an outlook and analysis. Int J Prod Econ 135:687–701Google Scholar
  15. Hong L (2012) An improved lns algorithm for real-time vehicle routing problem with time windows. Comput Oper Res 39:151–163CrossRefGoogle Scholar
  16. Jaber MY, Zanoni S, Zavanella LE (2014) A consignment stock coordination scheme for the production, remanufacturing and waste disposal problem. Int J Prod Res 52:50–65CrossRefGoogle Scholar
  17. Jawad H, Jaber MY, Bonney M, Rosen MA (2016) Deriving an exergetic economic production quantity model for better sustainability. Appl Math Model 40:6026–6039CrossRefGoogle Scholar
  18. Khasraghi MM, Sefidkouhi MAG, Valipour M (2015) Simulation of open- and closed-end border irrigation systems using sirmod. Arch Agron Soil Sci 61:929–941CrossRefGoogle Scholar
  19. Lamassoure A, Severin A (2007) European Parliament Resolution on “Proposal to amend the Treaty provisions concerning the composition of the European Parliament”. Accessed 11 Oct 2007 (INI/2007/2169)
  20. Lauwers L, Van Puyenbroeck T (2006) The Hamilton apportionment method is between the Adams method and the Jefferson method. Math Oper Res 31:390–397CrossRefGoogle Scholar
  21. Lee WC, Chuang MC, Yeh WC (2012) Uniform parallel-machine scheduling to minimize makespan with position-based learning curves. Comput Ind Eng 63:813–818CrossRefGoogle Scholar
  22. Łyko J, Rudek R (2013) A fast exact algorithm for the allocation of seats for the EU Parliament. Exp Syst Appl 40:5284–5291CrossRefGoogle Scholar
  23. McMullen PR, Clark M, Albritton D, Bell J (2003) A correlation and heuristic approach for obtaining production sequences requiring a minimum of tool replacements. Comput Oper Res 30:443–462CrossRefGoogle Scholar
  24. Nurmi H (2014) Some remarks on the concept of proportionality. Ann Oper Res 215:231–244CrossRefGoogle Scholar
  25. Prodhon C, Prins C (2014) A survey of recent research on location-routing problems. Eur J Oper Res 238:1–17CrossRefGoogle Scholar
  26. Pukelsheim F (2014) Proportional representation: apportionment methods and their applications. Springer, ChamCrossRefGoogle Scholar
  27. Ramírez-González V, Martínez-Aroza J, Márquez-García A (2012) Spline methods for degressive proportionality in the composition of the European Parliament. Math Soc Sci 63:114–120CrossRefGoogle Scholar
  28. Serafini P (2012) Allocation of the EU Parliament seats via integer linear programming and revised quotas. Math Soc Sci 63:107–113CrossRefGoogle Scholar
  29. Słomczyński JW, Życzkowski K (2012) Mathematical aspects of degressive proportionality. Math Soc Sci 63:94–101CrossRefGoogle Scholar
  30. Valipour M (2012) Comparison of surface irrigation simulation models: full hydrodynamic, zero inertia, kinematic wave. J Agric Sci 4:68–74Google Scholar
  31. Valipour M (2012) Sprinkle and trickle irrigation system design using tapered pipes for pressure loss adjusting. J Agric Sci 4:125–133Google Scholar
  32. Valipour M (2016) Optimization of neural networks for precipitation analysis in a humid region to detect drought and wet year alarms. Meteorol Appl 23:91–100CrossRefGoogle Scholar
  33. Valipour M, Sefidkouhi MAG, Eslamian S (2015) Surface irrigation simulation models: a review. Int J Hydrol Sci Technol 5:51–70CrossRefGoogle Scholar
  34. Yang D-L, Cheng TCE, Yang S-J, Hsu C-J (2012) Unrelated parallel-machine scheduling with aging effects and multi-maintenance activities. Comput Oper Res 39:1458–1464CrossRefGoogle Scholar
  35. Yannopoulos SI, Lyberatos G, Theodossiou N, Li W, Valipour M, Tamburrino A, Angelakis AN (2015) Evolution of water lifting devices (pumps) over the centuries worldwide. Water 7:5031–5060CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Wrocław University of EconomicsWrocławPoland

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