Abstract
The voting power of a voter—the extent to which she can affect the outcome of a collective decision—is often quantified in terms of the probability that she is critical. This measure is extended to a series of power measures of different ranks. The measures quantify the extent to which a voter can be part of a group that can jointly make a difference as to whether a bill passes or not. It is argued that the series of these measures allow for a more appropriate assessment of voting power, particularly of a posteriori voting power in case the votes are stochastically dependent. Also, the new measures discriminate between voting games that cannot be distinguished in terms of the probability of only criticality.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Banzhaf J.F. (1968) One man, 3.312 votes, a mathematical analysis of the electoral college. Villanova Law Review 13: 304–332
Beisbart, C. (2008). One political agent, several separate votes, working paper.
Beisbart C., Bovens L. (2008) A power measure analysis of amendment 36 in Colorado. Public Choice 134: 231–246
Bovens, L., & Beisbart, C. (2009). Measuring influence for dependent voters: A generalisation of the Banzhaf measure. Texts in Logic and Games (to appear).
Chamberlain G., Rothschild M. (1981) A note on the probability of casting a decisive vote. Journal of Economic Theory 25: 152–162
Coleman J.S. (1971). Control of collectivities and the power of a collectivity to act. In: Lieberman B. (eds) Social choice. New York, Gordon and Breach, pp 269–300
Dubey P., Shapley L.S. (1979) Mathematical properties of the Banzhaf power index. Mathematics of Operations Research 4: 99–131
Edelman P.H. (2004) Voting power and at-large representation. Mathematical Social Sciences 47: 219–232
Felsenthal D.S., Machover M. (1998) The measurement of voting power: Theory and practice, problems and paradoxes. Edward Elgar, Cheltenham
Felsenthal, D. S., & Machover, M. (2000). Enlargement of the EU and weighted voting in its Council of Ministers. http://eprints.lse.ac.uk/407/
Felsenthal D.S., Machover M. (2002) Annexions and alliances: When are blocs advantageous a priori? Social Choice and Welfare 19: 295–312
Gelman A., Katz J.N., Bafumi J. (2004) Standard voting power indexes don’t work: An empirical analysis. British Journal of Political Science 34: 657–674
Good I.J., Mayer L.S. (1975) Estimating the efficacy of a vote. Behavioral Science 20: 25–33
Kaniovski, S., & Leech, D. (2008). A behavioural power index, mimeo.http://serguei.kaniovski.wifo.ac.at/fileadmin/files_kaniovski/pdf/bpower.pdf
Laruelle A., Valenciano F. (2005) Assessing success and decisiveness in voting situations. Social Choice and Welfare 24: 171–197
Leech D., Leech R. (2006) Voting power and voting blocs. Public Choice 127: 293–311
Machover, M. (2007). Discussion topic: Voting power when voters’ independence is not assumed, mimeo. http://eprints.lse.ac.uk/2966/
Morriss, P. (1987). Power: A philosophical analysis. Manchester: Manchester University Press (second edition 2002).
Penrose L.S. (1946) The elementary statistics of majority voting. Journal of the Royal Statistical Society 109: 53–57
Raz J. (1999) Engaging reason. Oxford University Press, Oxford
Shapley L.S., Shubik M. (1954) A method for evaluating the distribution of power in a committee system. American Political Science Review 48: 787–792
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Beisbart, C. Groups can make a difference: voting power measures extended. Theory Decis 69, 469–488 (2010). https://doi.org/10.1007/s11238-009-9131-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11238-009-9131-9