Voting power and proportional representation of voters

Artyom Jelnov; Yair Tauman

doi:https://doi.org/10.1007/s00182-013-0400-z

Voting power and proportional representation of voters

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that for the proportional representative election system if parties’ sizes are uniformly distributed on the simplex, the expected ratio of a party size to its political power, measured by the Shapley–Shubik index, converges to 1, as the number n of parties increases indefinitely. The rate of convergence is high and it is of the magnitude of 1/n. Empirical evidence from the Netherlands elections supports our result. A comparison with the Banzhaf index is provided.

Original language	English
Pages (from-to)	747-766
Number of pages	20
Journal	International Journal of Game Theory
Volume	43
Issue number	4
DOIs	https://doi.org/10.1007/s00182-013-0400-z
State	Published - 3 Dec 2013
Externally published	Yes

Keywords

Banzhaf index
Proportional representation
Shapley-Shubik index
Voting power
Voting systems

All Science Journal Classification (ASJC) codes

Statistics and Probability
Mathematics (miscellaneous)
Social Sciences (miscellaneous)
Economics and Econometrics
Statistics, Probability and Uncertainty

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https://doi.org/10.1007/s00182-013-0400-z

Cite this

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title = "Voting power and proportional representation of voters",

abstract = "We prove that for the proportional representative election system if parties{\textquoteright} sizes are uniformly distributed on the simplex, the expected ratio of a party size to its political power, measured by the Shapley–Shubik index, converges to 1, as the number n of parties increases indefinitely. The rate of convergence is high and it is of the magnitude of 1/n. Empirical evidence from the Netherlands elections supports our result. A comparison with the Banzhaf index is provided.",

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AU - Tauman, Yair

PY - 2013/12/3

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N2 - We prove that for the proportional representative election system if parties’ sizes are uniformly distributed on the simplex, the expected ratio of a party size to its political power, measured by the Shapley–Shubik index, converges to 1, as the number n of parties increases indefinitely. The rate of convergence is high and it is of the magnitude of 1/n. Empirical evidence from the Netherlands elections supports our result. A comparison with the Banzhaf index is provided.

AB - We prove that for the proportional representative election system if parties’ sizes are uniformly distributed on the simplex, the expected ratio of a party size to its political power, measured by the Shapley–Shubik index, converges to 1, as the number n of parties increases indefinitely. The rate of convergence is high and it is of the magnitude of 1/n. Empirical evidence from the Netherlands elections supports our result. A comparison with the Banzhaf index is provided.

KW - Banzhaf index

KW - Proportional representation

KW - Shapley-Shubik index

KW - Voting power

KW - Voting systems

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VL - 43

SP - 747

EP - 766

JO - International Journal of Game Theory

JF - International Journal of Game Theory

IS - 4

ER -

Voting power and proportional representation of voters

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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