Geodesic
Fair majorities in proportional voting
Kybernetika, Tome 49 (2013) no. 3, pp. 498-505 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In parliaments elected by proportional systems the seats are allocated to the elected political parties roughly proportionally to the shares of votes for the party lists. Assuming that members of the parliament representing the same party are voting together, it has sense to require that distribution of the influence of the parties in parliamentary decision making is proportional to the distribution of seats. There exist measures (so called voting power indices) reflecting an ability of each party to influence outcome of voting. Power indices are functions of distribution of seats and voting quota (where voting quota means a minimal number of votes required to pass a proposal). By a fair voting rule we call such a quota that leads to proportionality of relative influence to relative representation. Usually simple majority is not a fair voting rule. That is the reason why so called qualified or constitutional majority is being used in voting about important issues requiring higher level of consensus. Qualified majority is usually fixed (60% or 66.67%) independently on the structure of political representation. In the paper we use game-theoretical model of voting to find a quota that defines the fair voting rule as a function of the structure of political representation. Such a quota we call a fair majority. Fair majorities can differ for different structures of the parliament. Concept of a fair majority is applied on the Lower House of the Czech Parliament elected in 2010.
In parliaments elected by proportional systems the seats are allocated to the elected political parties roughly proportionally to the shares of votes for the party lists. Assuming that members of the parliament representing the same party are voting together, it has sense to require that distribution of the influence of the parties in parliamentary decision making is proportional to the distribution of seats. There exist measures (so called voting power indices) reflecting an ability of each party to influence outcome of voting. Power indices are functions of distribution of seats and voting quota (where voting quota means a minimal number of votes required to pass a proposal). By a fair voting rule we call such a quota that leads to proportionality of relative influence to relative representation. Usually simple majority is not a fair voting rule. That is the reason why so called qualified or constitutional majority is being used in voting about important issues requiring higher level of consensus. Qualified majority is usually fixed (60% or 66.67%) independently on the structure of political representation. In the paper we use game-theoretical model of voting to find a quota that defines the fair voting rule as a function of the structure of political representation. Such a quota we call a fair majority. Fair majorities can differ for different structures of the parliament. Concept of a fair majority is applied on the Lower House of the Czech Parliament elected in 2010.
Classification : 05C65, 91A12, 91A40
Keywords: fair majority; power indices; quota interval of stable power; simple weighted committee; voting power 
@article{KYB_2013_49_3_a8,
     author = {Turnovec, Franti\v{s}ek},
     title = {Fair majorities in proportional voting},
     journal = {Kybernetika},
     pages = {498--505},
     year = {2013},
     volume = {49},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2013_49_3_a8/}
}
TY  - JOUR
AU  - Turnovec, František
TI  - Fair majorities in proportional voting
JO  - Kybernetika
PY  - 2013
SP  - 498
EP  - 505
VL  - 49
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/KYB_2013_49_3_a8/
LA  - en
ID  - KYB_2013_49_3_a8
ER  - 
%0 Journal Article
%A Turnovec, František
%T Fair majorities in proportional voting
%J Kybernetika
%D 2013
%P 498-505
%V 49
%N 3
%U http://geodesic.mathdoc.fr/item/KYB_2013_49_3_a8/
%G en
%F KYB_2013_49_3_a8
Turnovec, František. Fair majorities in proportional voting. Kybernetika, Tome 49 (2013) no. 3, pp. 498-505. http://geodesic.mathdoc.fr/item/KYB_2013_49_3_a8/

[1] Banzhaf, J. F.: Weighted voting doesn't work: A mathematical analysis. Rutgers Law Rev. 19 (1965), 317-343.

[2] Felsenthal, D. S., Machover, M.: The Measurement of Voting Power, Theory and Practice. Edward Elgar, Cheltenham 1998. | MR | Zbl

[3] Gallagher, M.: Proportionality, disproportionality and electoral systems. Electoral Stud. 10 (1991), 33-51. | DOI

[4] Loosemore, J., Hanby, V. J.: The theoretical limits of maximum distortion: Some analytical expressions for electoral systems. British J. Polit. Sci. 1 (1971), 467-477. | DOI

[5] Nurmi, H.: On power indices and minimal winning coalitions. Control Cybernet. 26 (1997), 609-611. | MR | Zbl

[6] Owen, G.: Multilinear extensions of games. Management Sci. 18 (1972), 64-79. | DOI | MR | Zbl

[7] Penrose, L. S.: The elementary statistics of majority voting. J. Royal Statist. Soc. 109 (1946), 53-57. | DOI

[8] Shapley, L. S., Shubik, M.: A method for evaluation the distribution of power in a committee system. Amer. Polit. Sci. Rev. 48 (1954), 787-792. | DOI

[9] Słomczyński, W., Życzkowski, K.: From a toy model to double square root system. Homo Oeconomicus 24 (2007), 381-400.

[10] Słomczyński, W., Życzkowski, K.: Penrose voting system and optimal quota. Acta Phys. Polon. B 37 (2006), 3133-3143.

[11] Turnovec, F.: Fair voting rules in committees, strict proportional power and optimal quota. Homo Oeconomicus 27 (2011), 4, 463-479.

[12] Turnovec, F.: Power, power indices and intuition. Control Cybernet. 26 (1997), 613-615. | MR | Zbl