Fair majorities in proportional voting

František Turnovec

Kybernetika (2013)

  • Volume: 49, Issue: 3, page 498-505
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Turnovec, František. "Fair majorities in proportional voting." Kybernetika 49.3 (2013): 498-505. <http://eudml.org/doc/260613>.

@article{Turnovec2013,
abstract = {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.},
author = {Turnovec, František},
journal = {Kybernetika},
keywords = {fair majority; power indices; quota interval of stable power; simple weighted committee; voting power; fair majority; power indices; quota interval of stable power; simple weighted committee; voting power},
language = {eng},
number = {3},
pages = {498-505},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Fair majorities in proportional voting},
url = {http://eudml.org/doc/260613},
volume = {49},
year = {2013},
}

TY - JOUR
AU - Turnovec, František
TI - Fair majorities in proportional voting
JO - Kybernetika
PY - 2013
PB - Institute of Information Theory and Automation AS CR
VL - 49
IS - 3
SP - 498
EP - 505
AB - 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.
LA - eng
KW - fair majority; power indices; quota interval of stable power; simple weighted committee; voting power; fair majority; power indices; quota interval of stable power; simple weighted committee; voting power
UR - http://eudml.org/doc/260613
ER -

References

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  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. Zbl1054.91535MR1642828

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