Partial Homogeneity Structure And Its Impact On Players’ Power. Hybrid Power Indices

Bożykowski, Marek; Jasiński, Mikołaj

Abstract

: The paper presents the probabilistic interpretation of ShapleyShubik index and Banzhaf value and the concept of partial homogeneity structure. Probabilities of being critical can be calculated based on this structure. These probabilities constitute the basis for calculating hybrid power indices, ShapleyShubik index and Banzhaf index being the extreme cases. The paper presents the idea of reconstruction of partial homogeneity structure based on maximum likelihood estimation. This method is based on the same assumptions as hybrid power indices. The method is illustrated by simple heuristic examples and results of analysis of clubs’ voting in 7th term of Sejm – the lower house of the Polish parliament.

Keywords

simple game (2)power index (2)Shapley-Shubik index (1)Banzhaf value (1)critical player (1)partial homogeneity structure (2)maximum likelihood estimation (1)

References

Dubey, P. 1975. On the Uniqueness of the Shapley Value. „International Journal of Game Theory” 4(3): 131-139. [Google Scholar]
Dubey, P. i L. S. Shapley. 1979. Mathematical Properties of the Banhaf Power Index. „Mathematics of Operations Research” 4: 99-131. [Google Scholar]
Ekes, M. 2006. Two types of the Banzhaf-Coleman index in games with a priori unions. „Roczniki Kolegium Analiz Ekonomicznych SGH” 15: 31-45. [Google Scholar]
Falsenthal, D.S. i M. Machover. 1998. The Measurement of Voting Power. Cheltenham: Edward Elgar. [Google Scholar]
Feltkamp, V. 1995. Alternative axiomatic characterizations of the Shapley and Banzhaf values. „International Journal of Game Theory” 24.2: 179-186. [Google Scholar]
Grofman, B., G. Owen, N. Noviello, G. Glazer. 1987. Stability and centrality of legislative choice in the spatial context. „American Political Science Review” 81: 539-552. [Google Scholar]
Jasiński, M. 2003. Stanowisko ideologiczne a znaczenie uczestnika zgromadzenia decyzyjnego. „Studia Socjologiczne” 1: 139-174. [Google Scholar]
Jasiński, M. 2012. Przestrzeń ideologiczna oparta na politycznych faktach. „Decyzje” 17: 5-28. [Google Scholar]
Jasiński, M. 2013. Przestrzenna generalizacja wartości Shapleya dla gier prostych jako mocny punkt w chaosie ideologii. „Decyzje” 20: 49-65. [Google Scholar]
Laruelle, A. i F. Valenciano. 2001. Shapley-Shubik and Banzhaf indices revisited. „Mathematics of Operations Research” 26.1: 89-104. [Google Scholar]
Lehrer, E. 1988. An axiomatization of the Banzhaf value. „International Journal of Game Theory” 17: 89-99. [Google Scholar]
Lissowski, G., J. Haman, M. Jasiński. 2008. Podstawy statystyki dla socjologów. Warszawa: WN Scholar. [Google Scholar]
Mercik, J.W. 1999. Modelowanie zachowań parlamentarnych – Sejm RP II kadencji. w: H. Sosnowska (red.) „Grupowe podejmowanie decyzji” Warszawa: WN Scholar: 81-102. [Google Scholar]
Napel, S. i M. Widgrén. 2002. Power measurement as sensitivity analysis a unified approach. „Journal of Theoretical Politics” 16.4: 517-538. [Google Scholar]
Owen, G. 1971. Political games. „Naval Research Logistics Quarterly” 18: 345-355. [Google Scholar]
Owen, G. 1977. Values of games with a priori unions. w: R. Henn i O. Moeschlin (red.) „Mathematical economics and game theory”. Berlin: 76-88. [Google Scholar]
Owen, G. 1981. Modifi cation of the Banzhaf – Coleman Index for games with a priori unions. w: M. Holler (red.) „Power, Voting and Voting Power”, Wurzburg: 355-358. [Google Scholar]
Rapoport, A. i E. Golan. 1985. Assessment of political power in the Israeli Knesset. American Political Science Review” 79: 673-692. [Google Scholar]
Shapley, L.S. 1977. A comparison of power indices and a non-symmetric generalization. RAND Paper P-5872. Rand Corporation. Santa Monica. [Google Scholar]
Shapley, L.S. i M. Shubik. 1954. A method of evaluating the distribution of power in a committee system. „American Political Science Review” 48: 787-792. [Google Scholar]
Silvey, S.D. 1978. Wnioskowanie statystyczne. R. Zieliński (tłum.)Warszawa: PWN. [Google Scholar]
Straffi n, P.D. 1977. Homogeneity, independence, and power indices. „Public Choice” 30: 107-118. [Google Scholar]

Full metadata record

Cite this record

APA style

Bożykowski, Marek & Jasiński, Mikołaj (2014). Partial Homogeneity Structure And Its Impact On Players’ Power. Hybrid Power Indices. (2014). Partial Homogeneity Structure And Its Impact On Players’ Power. Hybrid Power Indices. Decyzje, (21), 5-29. https://doi.org/10.7206/DEC.1733-0092.20 (Original work published 6/2014AD)

MLA style

Bożykowski, Marek and Jasiński, Mikołaj. “Partial Homogeneity Structure And Its Impact On Players’ Power. Hybrid Power Indices”. 6/2014AD. Decyzje, no. 21, 2014, pp. 5-29.

Chicago style

Bożykowski, Marek and Jasiński, Mikołaj. “Partial Homogeneity Structure And Its Impact On Players’ Power. Hybrid Power Indices”. Decyzje, Decyzje, no. 21 (2014): 5-29. doi:10.7206/DEC.1733-0092.20.

Copyright info

CC-BY

[1] Dubey, P. 1975. On the Uniqueness of the Shapley Value. „International Journal of Game Theory” 4(3): 131-139. [Google Scholar]

[2] Dubey, P. i L. S. Shapley. 1979. Mathematical Properties of the Banhaf Power Index. „Mathematics of Operations Research” 4: 99-131. [Google Scholar]

[3] Ekes, M. 2006. Two types of the Banzhaf-Coleman index in games with a priori unions. „Roczniki Kolegium Analiz Ekonomicznych SGH” 15: 31-45. [Google Scholar]

[4] Falsenthal, D.S. i M. Machover. 1998. The Measurement of Voting Power. Cheltenham: Edward Elgar. [Google Scholar]

[5] Feltkamp, V. 1995. Alternative axiomatic characterizations of the Shapley and Banzhaf values. „International Journal of Game Theory” 24.2: 179-186. [Google Scholar]

[6] Grofman, B., G. Owen, N. Noviello, G. Glazer. 1987. Stability and centrality of legislative choice in the spatial context. „American Political Science Review” 81: 539-552. [Google Scholar]

[7] Jasiński, M. 2003. Stanowisko ideologiczne a znaczenie uczestnika zgromadzenia decyzyjnego. „Studia Socjologiczne” 1: 139-174. [Google Scholar]

[8] Jasiński, M. 2012. Przestrzeń ideologiczna oparta na politycznych faktach. „Decyzje” 17: 5-28. [Google Scholar]

[9] Jasiński, M. 2013. Przestrzenna generalizacja wartości Shapleya dla gier prostych jako mocny punkt w chaosie ideologii. „Decyzje” 20: 49-65. [Google Scholar]

[10] Laruelle, A. i F. Valenciano. 2001. Shapley-Shubik and Banzhaf indices revisited. „Mathematics of Operations Research” 26.1: 89-104. [Google Scholar]

[11] Lehrer, E. 1988. An axiomatization of the Banzhaf value. „International Journal of Game Theory” 17: 89-99. [Google Scholar]

[12] Lissowski, G., J. Haman, M. Jasiński. 2008. Podstawy statystyki dla socjologów. Warszawa: WN Scholar. [Google Scholar]

[13] Mercik, J.W. 1999. Modelowanie zachowań parlamentarnych – Sejm RP II kadencji. w: H. Sosnowska (red.) „Grupowe podejmowanie decyzji” Warszawa: WN Scholar: 81-102. [Google Scholar]

[14] Napel, S. i M. Widgrén. 2002. Power measurement as sensitivity analysis a unified approach. „Journal of Theoretical Politics” 16.4: 517-538. [Google Scholar]

[15] Owen, G. 1971. Political games. „Naval Research Logistics Quarterly” 18: 345-355. [Google Scholar]

[16] Owen, G. 1977. Values of games with a priori unions. w: R. Henn i O. Moeschlin (red.) „Mathematical economics and game theory”. Berlin: 76-88. [Google Scholar]

[17] Owen, G. 1981. Modifi cation of the Banzhaf – Coleman Index for games with a priori unions. w: M. Holler (red.) „Power, Voting and Voting Power”, Wurzburg: 355-358. [Google Scholar]

[18] Rapoport, A. i E. Golan. 1985. Assessment of political power in the Israeli Knesset. American Political Science Review” 79: 673-692. [Google Scholar]

[19] Shapley, L.S. 1977. A comparison of power indices and a non-symmetric generalization. RAND Paper P-5872. Rand Corporation. Santa Monica. [Google Scholar]

[20] Shapley, L.S. i M. Shubik. 1954. A method of evaluating the distribution of power in a committee system. „American Political Science Review” 48: 787-792. [Google Scholar]

[21] Silvey, S.D. 1978. Wnioskowanie statystyczne. R. Zieliński (tłum.)Warszawa: PWN. [Google Scholar]

[22] Straffi n, P.D. 1977. Homogeneity, independence, and power indices. „Public Choice” 30: 107-118. [Google Scholar]

Decyzje