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2019 | OriginalPaper | Chapter

Bi-proportional Apportionments

Authors : Mirko Bezzi, Gianfranco Gambarelli, Giuliana Angela Zibetti

Published in: Transactions on Computational Collective Intelligence XXXIV

Publisher: Springer Berlin Heidelberg

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Abstract

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.

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Appendix
Available only for authorised users
Footnotes
1
From Gambarelli and Palestini [3].
 
2
For more information about calculation methods used for these elections, please refer to the law in force at the time of the elections [11].
 
3
Hare 5.13 obtained by dividing the 388,046 district votes by the 7,332,134 national votes and multiplying by 97 total seats to be assigned to the party at a national level.
 
4
Hare 8.18 obtained by dividing the 658,475 district votes by the 8,691,406 national votes and multiplying by 108 total seats to be assigned to the party at a national level.
 
5
Hare 6.62 obtained by dividing the 532,699 district votes by the 8,691,406 national votes and multiplying by 108 total seats to be assigned to the party at a national level.
 
Literature
1.
go back to reference Demange, G.: On allocating seats to parties and districts: apportionments. In: Fragnelli, V., Gambarelli, G. (eds.) Open Problems in Applications of Cooperative Games - a Special Issue of International Game Theory Review, vol. 15, no. 3 (2013) Demange, G.: On allocating seats to parties and districts: apportionments. In: Fragnelli, V., Gambarelli, G. (eds.) Open Problems in Applications of Cooperative Games - a Special Issue of International Game Theory Review, vol. 15, no. 3 (2013)
2.
go back to reference Gambarelli, G.: Minimax apportionments. Group Decis. Negot. 8(6), 441–461 (1999)CrossRef Gambarelli, G.: Minimax apportionments. Group Decis. Negot. 8(6), 441–461 (1999)CrossRef
3.
go back to reference Gambarelli, G., Palestini, A.: Minimax multi-district apportionments. Homo Oecon. 24(3/4), 335–356 (2007)MATH Gambarelli, G., Palestini, A.: Minimax multi-district apportionments. Homo Oecon. 24(3/4), 335–356 (2007)MATH
4.
go back to reference Gambarelli, G., Stach, I.: Power indices in politics; some results and open problems. Essays in honor of Hannu Nurmi. Homo Oecon. 26(3/4), 417–441 (2009). ISBN 978–3-89265-072-0, ISSN 0943-0180 Gambarelli, G., Stach, I.: Power indices in politics; some results and open problems. Essays in honor of Hannu Nurmi. Homo Oecon. 26(3/4), 417–441 (2009). ISBN 978–3-89265-072-0, ISSN 0943-0180
5.
go back to reference Hamilton, A.: Proposal of apportionment approved by U.S.A. Congress (1791) Hamilton, A.: Proposal of apportionment approved by U.S.A. Congress (1791)
8.
go back to reference Pukelsheim, F., Ricca, F., Scozzari, A., Serafini, P., Simeone, B.: Network flow methods for electoral systems. Networks 59, 73–88 (2011). Special Issue on the INOC 2009 Conference, April 26–29, 2009, Pisa, ItalyMathSciNetCrossRef Pukelsheim, F., Ricca, F., Scozzari, A., Serafini, P., Simeone, B.: Network flow methods for electoral systems. Networks 59, 73–88 (2011). Special Issue on the INOC 2009 Conference, April 26–29, 2009, Pisa, ItalyMathSciNetCrossRef
11.
go back to reference Italian Law December 21, 2005, n. 270 Changes to the rules for the election of the Chamber of Deputies and the Senate of the Republic (2005) Italian Law December 21, 2005, n. 270 Changes to the rules for the election of the Chamber of Deputies and the Senate of the Republic (2005)
Metadata
Title
Bi-proportional Apportionments
Authors
Mirko Bezzi
Gianfranco Gambarelli
Giuliana Angela Zibetti
Copyright Year
2019
Publisher
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-662-60555-4_10