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Beyond the Cambridge Compromise algorithm towards degressively proportional allocations

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Abstract

Although proportional allocation methods are well-known and widely used in the parliamentary tradition, they cannot be applied in a wide variety of cases. Such problems occur in the European Parliament, where a constitutional principle is to assure that less populous countries will not be dominated by the others, which implies that allocations have to be degressively proportional. However, under this assumption an exhaustive search of the solution space is intractable. To solve the problem, the Cambridge Compromise algorithm was proposed, which is durable, transparent, impartial to politics and unambiguous, but the allocations obtained are not degressively proportional. Therefore, we propose an allocation algorithm derived from operations research that inherits the transparency of the Cambridge Compromise and produces an unambiguous degressively proportional allocation. Hence, the paper aims at testing our alternative allocation method and comparing its outcomes during computational analysis.

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Notes

  1. Note that Clara, from Latin Clarus, means clear, which in our case is interpreted as a method that is transparent and impartial to politics.

References

  • Avery G (2014) Independentis and the Europran Union. Europan Policy Centre, Brussels

    Google Scholar 

  • Bautista J, Companys R, Corominas A (2001) Solving the generalized apportionment problem through the optimization of discrepancy functions. Eur J Oper Res 131:676–684

    Article  Google Scholar 

  • Dniestrzański P (2014) Proposal for measure of degressive proportionality. Procedia Soc Behav Sci 110:140–147

    Article  Google Scholar 

  • European Union (2007) Treaty of lisbon. Off J Eur Union 50(C 306/1)

  • European Union (2012) Consolidated version of the treaty on European union. Off J Eur Union 55(C 326/01)

  • Florek J (2012) A numerical method to determine a degressive proportional distribution of seats in the European Parliament. Math Soc Sci 63:121–129

    Article  Google Scholar 

  • Grimmett GR (2012) European apportionment via the Cambridge compromise. Math Soc Sci 63:68–73

    Article  Google Scholar 

  • Gualtieri R, Trzaskowski R (2013) Report on the composition of the European Parliament with a view to the 2014 elections (2012/2309(INI)), pp 8–9

  • Lamassoure A, Severin A (2007) European Parliament resolution on “proposal to amend the treaty provisions concerning the composition of the European Parliament”, 2007. adopted on 2007-10-11 (INI/2007/2169)

  • Lauwers L, Van Puyenbroeck T (2006) The Hamilton apportionment method is between the Adams method and the Jefferson method. Math Oper Res 31:390–397

    Article  Google Scholar 

  • Łyko J, Rudek R (2013) A fast exact algorithm for the allocation of seats for the EU Parliament. Expert Syst Appl 40:5284–5291

    Article  Google Scholar 

  • Marshall AW, Olkin I, Pukelsheim F (2002) A majorization comparison of apportionment methods in proportional representation. Soc Choice Welf 19:885–900

    Article  Google Scholar 

  • Martínez-Aroza J, Ramírez-González V (2008) Several methods for degressively proportional allotments. A case study. Math Comput Model 48:1439–1445

    Article  Google Scholar 

  • Pukelsheim F (2014) Proportional representation: apportionment methods and their applications. Springer, Cham

    Book  Google Scholar 

  • Serafini P (2012) Allocation of the EU Parliament seats via integer linear programming and revised quotas. Math Soc Sci 63:107–113

    Article  Google Scholar 

  • Słomczyński JW, Życzkowski K (2012) Mathematical aspects of degressive proportionality. Math Soc Sci 63:94–101

    Article  Google Scholar 

  • Te Riele HJJ (1978) The proportional representation problem in the second chamber: an approach via minimal distances. Stat Neerl 32:163–179

    Article  Google Scholar 

  • Young HP (1994) Equity: in theory and practice. Princeton University Press, Princeton

    Google Scholar 

Download references

Acknowledgements

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.

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Correspondence to Radosław Rudek.

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Cegiełka, K., Łyko, J. & Rudek, R. Beyond the Cambridge Compromise algorithm towards degressively proportional allocations. Oper Res Int J 19, 317–332 (2019). https://doi.org/10.1007/s12351-017-0292-y

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  • DOI: https://doi.org/10.1007/s12351-017-0292-y

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