Shapley and Shubik in 1954 proposed an index to measure the relative voting power of members of a decision-making body, given their weights in the said body. In this article, we have tried to investigate whether one can ensure equal voting power for all the citizens in a democracy through their respective representatives in the state legislature. The article shows that if the citizens realise their voting power through legislators and the number of constituencies in a democracy are at most four, then there does not exist any weighted voting rule such that the citizens enjoy equal voting power.
AbizadehA. (2022). A recursive measure of voting power with partial decisiveness or efficacy. The Journal of Politics, 84(3), 1652–1666.
2.
AbizadehA., & VettaA. (2023). The blocker postulates for measures of voting power. Social Choice and Welfare, 60, 595–623.
3.
Alonso- MeijideJ. M., Casas-MéndezB., & Fiestras -JaneiroM. G. (2015). Computing Banzhaf –Coleman and Shapley– Shubik power indices with incompatible players. Applied Mathematics and Computation, 252, 377–387.
4.
BanzhafJ. F.III (1964). Weighted voting doesn’t work: A mathematical analysis. Rutgers Law Review, 19, 317.
5.
BramsS. J., & AffusoP. J. (1976). Power and size: A new paradox. Theory and Decision, 7(1–2), 29–56.
6.
ColemanJ. S. (1971). Control of collectivities and the power of a collectivity to act. In LiebermanB. (Ed.), Social choice (pp. 269–300). Gordon and Breach.
7.
CourtinS., NganmeniZ., & TchantchoB. (2016). The Shapley– Shubik power index for dichotomous mu l ti-type games. Theory and Decision, 81(3), 413–426.
8.
DeeganJ., & PackelE. W. (1978). A new index of power for simple n-person games. International Journal of Game Theory, 7(2), 113–123.
9.
DreyerJ. S., & SchotterA. (1980). Power relationships in the international monetary fund: The consequences of quota changes. The Review of Economics and Statistics, 62, 97–106.
10.
FelsenthalD. S., & MachoverM. (1997). Ternary voting games. International Journal of Game Theory, 26(3), 335–351.
11.
FischerD., & SchotterA. (1978). The inevitability of the ‘paradox of redistribution’ in the allocation of voting weights. Public Choice, 33(2), 49–67.
12.
GáborJ. (2020). Impact of Brexit on voting power in Council of the European Union. Open Political Science, 3(1), 192–197.
13.
GelmanA., KatzJ. N., & BafumiJ. (2004). Standard voting power indexes do not work: An empirical analysis. British Journal of Political Science, 34(4), 657–674.
14.
HollerM. J. (1982). Forming coalitions and measuring voting power. Political Studies, 30(2), 262–271.
15.
KirschW., & LangnerJ. (2010). Power indices and minimal winning coalitions. Social Choice and Welfare, 34(1), 33–46.
16.
LaruelleA., & ValencianoF. (2002). Assessment of voting situations: The probabilistic foundations. Universidad del País Vasco, Departamento de Economía Aplicada IV.
17.
LaruelleA., & ValencianoF. (2012). Quaternary dichotomous voting rules. Social Choice and Welfare, 38(3), 431–454.
18.
MaskinE., & TiroleJ. (2004). The politician and the judge: Accountability in government. American Economic Review, 94(4), 1034–1054.
19.
ShapleyL. S., & ShubikM. (1954). A method for evaluating the distribution of power in a committee system. American Political Science Review, 48(3), 787–792.
20.
TolleJ. (2003). Power distribution in four-player weighted voting systems. Mathematics Magazine, 76(1), 33–39.
