| Title:
|
Banzhafův index a dvoustupňové hlasovací systémy (Czech) |
| Title:
|
Banzhaf power index and two-tier voting systems (English) |
| Author:
|
Slavík, Antonín |
| Language:
|
Czech |
| Journal:
|
Pokroky matematiky, fyziky a astronomie |
| ISSN:
|
0032-2423 |
| Volume:
|
62 |
| Issue:
|
3 |
| Year:
|
2017 |
| Pages:
|
213-228 |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| 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. (Czech) |
| MSC:
|
91B12 |
| . |
| Date available:
|
2017-11-06T15:41:24Z |
| Last updated:
|
2022-08-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146926 |
| . |
| Reference:
|
[1] Banzhaf, J. F.: Weighted voting doesn’t work: a mathematical analysis.. Rutgers Law Rev. 19 (1965), 317–343. |
| Reference:
|
[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. Zbl 1073.91539, MR 1922625 |
| Reference:
|
[3] Brams, S. J.: Game theory and politics.. Dover Publications, 2004. Zbl 1129.91001, MR 2098546 |
| Reference:
|
[4] Deegan, J., Packel, E. W.: A new index of power for simple $n$-person games.. Internat. J. Game Theory 7 (1978), 113–123. Zbl 0389.90093, MR 0507589 |
| Reference:
|
[5] Fischer, D., Schotter, A.: The inevitability of the paradox of redistribution in the allocation of voting weights.. Public Choice 33 (1978), 49–67. 10.1007/BF00118357 |
| Reference:
|
[6] Hykšová, M.: Počátky teorie kooperativních her.. In: Bečvář, J., Bečvářová, M. (ed.), Sborník 37. mezinárodní konference Historie matematiky, MatfyzPress, Praha, 2016. |
| Reference:
|
[7] Johnston, R. J.: On the measurement of power: Some reactions to laver.. Environ. Plan. 10 (1978), 907–914. |
| Reference:
|
[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 |
| Reference:
|
[9] Kirsch, W.: A mathematical view on voting and power.. In: König, W. (ed.), Mathematics and Society, European Mathematical Society, 2016, 251–279. Zbl 1354.91004, MR 3497597 |
| Reference:
|
[10] Laruelle, A., Widgrén, M.: Is the allocation of voting power among EU states fair?. Public Choice 94 (1998), 317–339. 10.1023/A:1004965310450 |
| Reference:
|
[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 |
| Reference:
|
[12] Leech, D., Leech, R.: Computer algorithms for voting power analysis.http://homepages.warwick.ac.uk/~ecaae/ |
| Reference:
|
[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. Zbl 1028.91511, MR 1768387 |
| Reference:
|
[14] Matsui, Y., Matsui, T.: NP-completeness for calculating power indices of weighted majority games.. Theoret. Comput. Sci. 263 (2001), 305–310. Zbl 0991.91006, MR 1846937 |
| Reference:
|
[15] Münchau, W.: Multiple answers to Europe’s maths problem.. Financial Times, 18th June 2007, https://goo.gl/X3p7zA |
| Reference:
|
[16] Owen, G.: Game theory.. 3rd edition, Academic Press, San Diego, 1995. Zbl 1284.91004, MR 1355082 |
| Reference:
|
[17] Penrose, L. S.: The elementary statistics of majority voting.. J. R. Stat. Soc. 109 (1946), 53–57. |
| Reference:
|
[18] Rachman, G.: Square root of the EU’s problems.. Financial Times, 11th June 2007, https://goo.gl/hfyZvu |
| Reference:
|
[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 |
| Reference:
|
[20] Zavadil, P.: O druhé odmocnině z Polska.. Lidové noviny, 19. června 2007, https://goo.gl/XidrPJ |
| . |
