Jelnov, Artyom; Tauman, Yair - In: International Journal of Game Theory 43 (2014) 4, pp. 747-766
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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$1$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mn>1</mn> </mrow> </math> </EquationSource> </InlineEquation>, as the number <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$n$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>n</mi> </math> </EquationSource> </InlineEquation> of parties...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>