TY - JOUR
T1 - Voting power and proportional representation of voters
AU - Jelnov, Artyom
AU - Tauman, Yair
N1 - Publisher Copyright:
© 2013, Springer-Verlag Berlin Heidelberg.
PY - 2013/12/3
Y1 - 2013/12/3
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
UR - http://www.scopus.com/inward/record.url?scp=84888331725&partnerID=8YFLogxK
U2 - 10.1007/s00182-013-0400-z
DO - 10.1007/s00182-013-0400-z
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AN - SCOPUS:84888331725
SN - 0020-7276
VL - 43
SP - 747
EP - 766
JO - International Journal of Game Theory
JF - International Journal of Game Theory
IS - 4
ER -