The exact bias of the Banzhaf measure of power when votes are neither equiprobable nor independent

Social Choice and Welfare

Volumn 31, Issue 2, 2008, Pages 281-300

  Kaniovski, Serguei ^a  

^a AUSTRIAN INSTITUTE OF ECONOMIC RESEARCH WIFO   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 47849120237     PISSN: 01761714     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00355-007-0280-x     Document Type: Article

References (32)

1. Banzhaf JF (1965). Weighted voting does not work: a mathematical analysis. Rutgers Law Rev 19: 317-343
2. Barbera S and Jackson MO (2006). On the weights of nations: assigning voting weights in a heterogeneous union. J Polit Econ 114: 317-339
3. Berg S (1985). Paradox of voting under an urn-model: the effect of homogeneity. Pub Choice 47: 377-387
4. Berg S (1993). Condorcet's jury theorem, dependency among jurors. Social Choice and Welfare 10: 87-95
5. Boland PJ (1989). Majority systems and the Condorcet jury theorem. Statistician 38: 181-189
6. Braham M and Holler M (2005). The impossibility of a preference-based power index. J Theor Polit 17: 137-157
7. Braham M and Holler M (2005). Power and preferences again. A reply to Napel and Widgrén. J Theor Polit 17: 389-395
8. Chamberlain G and Rothschild M (1981). A note on the probability of casting a decisive vote. J Econ Theory 25: 152-162
9. Everitt BS (1992). The analysis of contingency tables. Chapman & Hall, London
10. Felsenthal DS, Machover M (1998) The measurement of voting power: theory and practice, problems and paradoxes. Edward Elgar
11. Garrett G and Tsebelis G (2001). Even more reasons to resist the temptation of power indices in the European Union. J Theor Polit 13: 99-105
12. Gelman A, Katz JN and Bafumi J (2004). Standard voting power indices don't work: an empirical analysis. Br J Polit Sci 34: 657-674
13. Gelman A, Katz JN and Tuerlinckx F (2002). The mathematics and statistics of voting power. Stat Sci 17: 420-435
14. Good I and Mayer L (1975). Estimating the efficacy of a vote. Behav Sci 20: 25-33
15. Grofman B (1981). Fair apportionment and the Banzhaf index. Am Math Mont 88: 1-5
16. Hall AR (2005). Generalized method of moments. Advanced texts in econometrics. Oxford University Press, Oxford
17. Kaniovski YM and Pflug GC (2007). Risk assessment for credit portfolios: a coupled Markov chain model. J Bank Finance 31: 2303-2323
18. Kirman A, Widgrén M (1995) European economic decision-making policy: progress or paralysis? Econ Policy 10:423-460
19. Leech D and Leech R (2006). Voting power and voting blocs. Pub Choice 127: 285-303
20. Maaser N and Napel S (2007). Equal representation in two-tier voting systems. Soc Choice Welf 28: 401-420
21. Merrill III S and Grofman B (1999). A unified theory of voting: directional and proximity spatial models. Cambridge University Press, Cambridge
22. Napel S and Widgrén M (2004). Power measurement as sensitivity analysis: a unified approach. J Theor Polit 16: 517-538
23. Napel S and Widgrén M (2005). The possibility of a preference-based power index. J Theor Polit 17: 377-387
24. Owen G (1972). Multilinear extensions of games. Manage Sci 18: 64-79
25. Page SE (2006). Path dependence. Q J Polit Sci 1: 87-115
26. Penrose LS (1946). The elementary statistics of majority voting. J R Stat Soc 109: 53-57
27. Shapley LS and Shubik M (1954). A method of evaluating the distribution of power in a committee system. Am Polit Sci Rev 48: 787-792
28. Steunenberg B, Schmidtchen D and Koboldt C (1999). Strategic power in the European Union: evaluating the distribution of power in policy games. J Theor Polit 11: 339-366
29. Straffin PD (1977). Homogeneity, independence and power indices. Pub Choice 30: 107-118
30. Straffin PD (1994). Power and stability in politics. In: Aumann, RJ and Hart, S (eds) Handbook of game theory, Vol 2, chap 32, pp. Elsevier, Amsterdam
31. Tsebelis G (1995). Decision making in political systems: veto players in presidentialism, parliamentarism, multicameralism and multipartyism. Br J Polit Sci 25: 289-325
32. Widgrén M (1995). Probabilistic voting power in the EU Council: the cases of trade policy and social regulation. Scand J Econ 97: 345-356