Article
MSC:
91B12
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Summary:
V textu představíme tzv. Banzhafův index, který umožňuje kvantifikovat sílu voliče v předepsaném hlasovacím systému. Definice indexu je zcela elementární, podrobnější zkoumání jeho vlastností však vede k zajímavé a hlubší matematice. Výklad je ilustrován řadou konkrétních příkladů ze světa politiky; uvidíme, že díky Banzhafovu indexu se matematika dostala i na stránky novin.
References:
[1] Banzhaf, J. F.: Weighted voting doesn’t work: a mathematical analysis. Rutgers Law Rev. 19 (1965), 317–343.
[2] Bilbao, J. M., Fernández, J. R., Jiménez, N., López, J. J.: Voting power in the European Union enlargement. European J. Oper. Res. 143 (2002), 181–196. MR 1922625 | Zbl 1073.91539
[3] Brams, S. J.: Game theory and politics. Dover Publications, 2004. MR 2098546 | Zbl 1129.91001
[4] Deegan, J., Packel, E. W.: A new index of power for simple $n$-person games. Internat. J. Game Theory 7 (1978), 113–123. MR 0507589 | Zbl 0389.90093
[5] Fischer, D., Schotter, A.: The inevitability of the paradox of redistribution in the allocation of voting weights. Public Choice 33 (1978), 49–67. DOI 10.1007/BF00118357
[6] Hykšová, M.: Počátky teorie kooperativních her. In: Bečvář, J., Bečvářová, M. (ed.), Sborník 37. mezinárodní konference Historie matematiky, MatfyzPress, Praha, 2016.
[7] Johnston, R. J.: On the measurement of power: Some reactions to laver. Environ. Plan. 10 (1978), 907–914.
[8] de Keijzer, B.: A survey on the computation of power indices. Technical report. Delft University of Technology, 2008, http://homepages.cwi.nl/~keijzer/powerindexsurvey.pdf
[9] Kirsch, W.: A mathematical view on voting and power. In: König, W. (ed.), Mathematics and Society, European Mathematical Society, 2016, 251–279. MR 3497597 | Zbl 1354.91004
[10] Laruelle, A., Widgrén, M.: Is the allocation of voting power among EU states fair?. Public Choice 94 (1998), 317–339. DOI 10.1023/A:1004965310450
[11] Leech, D.: Computation of power indices. Warwick Economic Research Papers, no. 644, The University of Warwick, 2002, http://www.warwick.ac.uk/fac/soc/economics/research/workingpapers/2008/twerp644.pdf
[12] Leech, D., Leech, R.: Computer algorithms for voting power analysis. http://homepages.warwick.ac.uk/~ecaae/
[13] Matsui, T., Matsui, Y.: A survey of algorithms for calculating power indices of weighted majority games. J. Oper. Res. Soc. Japan 43 (2000), 71–86. MR 1768387 | Zbl 1028.91511
[14] Matsui, Y., Matsui, T.: NP-completeness for calculating power indices of weighted majority games. Theoret. Comput. Sci. 263 (2001), 305–310. MR 1846937 | Zbl 0991.91006
[15] Münchau, W.: Multiple answers to Europe’s maths problem. Financial Times, 18th June 2007, https://goo.gl/X3p7zA
[16] Owen, G.: Game theory. 3rd edition, Academic Press, San Diego, 1995. MR 1355082 | Zbl 1284.91004
[17] Penrose, L. S.: The elementary statistics of majority voting. J. R. Stat. Soc. 109 (1946), 53–57.
[18] Rachman, G.: Square root of the EU’s problems. Financial Times, 11th June 2007, https://goo.gl/hfyZvu
[19] Shapley, L. S., Shubik, M.: A method for evaluating the distribution of power in a committee system. Amer. Political Sci. Rev. 48 (1954), 787–792. MR 0989821
[20] Zavadil, P.: O druhé odmocnině z Polska. Lidové noviny, 19. června 2007, https://goo.gl/XidrPJ
Search
Partner of
