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

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  • Serguei Kaniovski

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  • Serguei Kaniovski, 2008. "The exact bias of the Banzhaf measure of power when votes are neither equiprobable nor independent," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(2), pages 281-300, August.
    • Handle: RePEc:spr:sochwe:v:31:y:2008:i:2:p:281-300
    DOI: 10.1007/s00355-007-0280-x
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    References listed on IDEAS

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    1. Dennis Leech & Robert Leech, 2006. "Voting power and voting blocs," Public Choice, Springer, vol. 127(3), pages 285-303, June.
    2. Stefan Napel & Mika Widgrén, 2005. "The Possibility of a Preference-Based Power Index," Journal of Theoretical Politics, , vol. 17(3), pages 377-387, July.
    3. Page, Scott E., 2006. "Path Dependence," Quarterly Journal of Political Science, now publishers, vol. 1(1), pages 87-115, January.
    4. Salvador Barbera & Matthew O. Jackson, 2006. "On the Weights of Nations: Assigning Voting Weights in a Heterogeneous Union," Journal of Political Economy, University of Chicago Press, vol. 114(2), pages 317-339, April.
    5. Sven Berg, 1985. "Paradox of voting under an urn model: The effect of homogeneity," Public Choice, Springer, vol. 47(2), pages 377-387, January.
    6. Nicola Maaser & Stefan Napel, 2007. "Equal representation in two-tier voting systems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(3), pages 401-420, April.
    7. Guillermo Owen, 1972. "Multilinear Extensions of Games," Management Science, INFORMS, vol. 18(5-Part-2), pages 64-79, January.
    8. Philip Straffin, 1977. "Homogeneity, independence, and power indices," Public Choice, Springer, vol. 30(1), pages 107-118, June.
    9. Bernard Steunenberg & Dieter Schmidtchen & Christian Koboldt, 1999. "Strategic Power in the European Union," Journal of Theoretical Politics, , vol. 11(3), pages 339-366, July.
    10. Dan S. Felsenthal & Moshé Machover, 1998. "The Measurement of Voting Power," Books, Edward Elgar Publishing, number 1489.
    11. Straffin, Philip Jr., 1994. "Power and stability in politics," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 32, pages 1127-1151, Elsevier.
    12. Tsebelis, George, 1995. "Decision Making in Political Systems: Veto Players in Presidentialism, Parliamentarism, Multicameralism and Multipartyism," British Journal of Political Science, Cambridge University Press, vol. 25(3), pages 289-325, July.
    13. Stefan Napel & Mika Widgren, 2004. "Power Measurement as Sensitivity Analysis," Journal of Theoretical Politics, , vol. 16(4), pages 517-538, October.
    14. Napel, Stefan & Widgrén, Mika, 2017. "Power measurement as sensitivity analysis: a unified approach," Center for Mathematical Economics Working Papers 345, Center for Mathematical Economics, Bielefeld University.
    15. Chamberlain, Gary & Rothschild, Michael, 1981. "A note on the probability of casting a decisive vote," Journal of Economic Theory, Elsevier, vol. 25(1), pages 152-162, August.
    16. Widgren, Mika, 1995. " Probabilistic Voting Power in the EU Council: The Cases of Trade Policy and Social Regulation," Scandinavian Journal of Economics, Wiley Blackwell, vol. 97(2), pages 345-356, June.
    17. Kaniovski, Y.M. & Pflug, G.Ch., 2007. "Risk assessment for credit portfolios: A coupled Markov chain model," Journal of Banking & Finance, Elsevier, vol. 31(8), pages 2303-2323, August.
    18. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
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    Cited by:

    1. Michel Le Breton & Dominique Lepelley, 2014. "Une analyse de la loi électorale du 29 juin 1820," Revue économique, Presses de Sciences-Po, vol. 65(3), pages 469-518.
    2. Maaser, Nicola & Napel, Stefan, 2012. "A note on the direct democracy deficit in two-tier voting," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 174-180.
    3. Artyom Jelnov & Pavel Jelnov, 2019. "Success, Survival and Probabilistic Voting: The Case of a ruling Party," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 36(3), pages 209-226, December.
    4. Serguei Kaniovski, 2010. "Aggregation of correlated votes and Condorcet’s Jury Theorem," Theory and Decision, Springer, vol. 69(3), pages 453-468, September.
    5. Kurz, Sascha & Maaser, Nicola & Napel, Stefan, 2018. "Fair representation and a linear Shapley rule," Games and Economic Behavior, Elsevier, vol. 108(C), pages 152-161.
    6. Serguei Kaniovski & Sreejith Das, 2015. "Measuring voting power in games with correlated votes using Bahadur’s parametrisation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(2), pages 349-367, February.
    7. Alexander Zaigraev & Serguei Kaniovski, 2012. "Bounds on the competence of a homogeneous jury," Theory and Decision, Springer, vol. 72(1), pages 89-112, January.
    8. Sascha Kurz & Stefan Napel, 2014. "Heuristic and exact solutions to the inverse power index problem for small voting bodies," Annals of Operations Research, Springer, vol. 215(1), pages 137-163, April.
    9. Madeleine O. Hosli & Běla Plechanovová & Serguei Kaniovski, 2018. "Vote Probabilities, Thresholds and Actor Preferences: Decision Capacity and the Council of the European Union," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 35(1), pages 31-52, June.
    10. Kaniovski, Serguei, 2009. "An invariance result for homogeneous juries with correlated votes," Mathematical Social Sciences, Elsevier, vol. 57(2), pages 213-222, March.
    11. Sascha Kurz, 2014. "Measuring Voting Power in Convex Policy Spaces," Economies, MDPI, vol. 2(1), pages 1-33, March.
    12. Madeleine Hosli & Rebecca Moody & Bryan O’Donovan & Serguei Kaniovski & Anna Little, 2011. "Squaring the circle? Collective and distributive effects of United Nations Security Council reform," The Review of International Organizations, Springer, vol. 6(2), pages 163-187, July.
    13. Matthias Weber, 2014. "Choosing Voting Systems behind the Veil of Ignorance: A Two-Tier Voting Experiment," Tinbergen Institute Discussion Papers 14-042/I, Tinbergen Institute.
    14. Sascha Kurz & Nicola Maaser & Stefan Napel & Matthias Weber, 2014. "Mostly Sunny: A Forecast of Tomorrow's Power Index Research," Tinbergen Institute Discussion Papers 14-058/I, Tinbergen Institute.

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