Bi-proportional Apportionments

  • Mirko BezziEmail author
  • Gianfranco Gambarelli
  • Giuliana Angela Zibetti
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11890)


An apportionment method is proposed that generalises Hamilton’s method for matrices, optimising proportionality in both directions, both for rows and columns. The resulting matrix respects fixed totals for rows and columns even when such totals do not satisfy standard criteria (monotonicity, maximum or minimum Hare), for example following the allocation of majority prizes to parties or coalitions.

Optionally, if required, the result can also respect the minimum Hare quotae for rows and columns. The algorithm may easily be expressed on the basis of rules.


Bi-proportional Apportionment Electoral system Calculation software 



This paper is under the patronage of MIUR. The authors wish to thank Luciano Violante for his valuable comments on a previous version of this paper, and Angelo Uristani for useful discussions on a local level seat assignation method.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Management, Economics and Quantitative MethodsUniversity of BergamoBergamoItaly

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