Minimizing the threat of a positive majority deficit in two-tier voting systems with equipopulous units
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The mean majority deficit in a two-tier voting system is a function of the partition of the population. We derive a new square-root rule: For odd-numbered population sizes and equipopulous units the mean majority deficit is maximal when the member size of the units in the partition is close to the square root of the population size. Furthermore, within the partitions into roughly equipopulous units, partitions with small even numbers of units or small even-sized units yield high mean majority deficits. We discuss the implications for the winner-takes-all system in the US Electoral College.
KeywordsTwo-tier voting system Mean majority deficit Voting power Electoral College Sensitivity Majoritarianism
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- Banzhaf, J. F. (1965). Weighted voting doesn’t work: a mathematical analysis. Rutgers Law Review, 19, 317–334. Google Scholar
- Edwards III, G. C. (2004). Why the electoral college is bad for America. New Haven: Yale University Press. Google Scholar
- Felsenthal, D. S., & Machover, M. (1998). The measurement of voting power: theory and practice, problems and paradoxes. Cheltenham: Edward Elgar. Google Scholar
- Felsenthal, D. S., & Machover, M. (2000). Enlargement of the EU and weighted voting in its Council of Ministers. Voting Power report 01/00, London. London School of Economics and Political Science, Centre for Philosophy of Natural and Social Science, downloadable from http://eprints.lse.ac.uk/archive/00000407 (checked May 2011).
- Havil, J. (2003). Gamma: exploring Euler’s constant. Princeton: Princeton University Press. Google Scholar
- Miller, N. R. (2009). A priori voting power and the U.S. Electoral College. Homo Oeconomicus, 26(3–4), 341–380 (special issue: Holler, M. J., & Widgrén, eds., Essays in Honour of Hannu Nurmi). Google Scholar
- Morse, P. M., & Feshbach, H. (1953). Methods of theoretical physics. Part I. New York: McGraw-Hill. Google Scholar
- Žyczkowski, K., & Słomczyński, W. (2004). Voting in the European Union: the square root system of Penrose and a critical point. Mimeo. http://arxiv.org/ftp/cond-mat/papers/0405/0405396.pdf (checked May 2011).