Abstract
We defineternary voting games (TVGs), a generalization ofsimple voting games (SVGs). In a play of an SVG each voter has just two options: voting ‘yes’ or ‘no’. In a TVG a third option is added: abstention. Every SVG can be regarded as a (somewhat degenerate) TVG; but the converse is false. We define appropriate generalizations of the Shapley-Shubik and Banzhaf indices for TVGs. We define also theresponsiveness (ordegree of democratic participation) of a TVG and determine, for eachn, the most responsive TVGs withn voters. We show that these maximally responsive TVGs are more responsive than the corresponding SVGs.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Banzhaf JF (1965) Weighted voting doesn't work: a mathematical analysis. Rutgers Law Review 19: 317–343
Brams SJ (1975) Game theory and politics. Free Press, New York
Brams SJ, Affuso PJ, Kilgour DM (1989) Presidential power: a game-theoretic analysis. In Brace P, Harrington CB, King G (eds.) The presidency in American politics. New York University Press, New York, pp. 55–72
Coleman JS (1986) Individual interests and collective action: Selected essays. Cambridge University Press, Cambridge
Dubey P, Shapley LS (1979) Mathematical properties of the Banzhaf power index. Mathematics of Operations Research 4: 99–131
Felsenthal DS (1991) Averting the quorum paradox. Behavioral Science 36: 57–63
Felsenthal DS, Machover M (1995) Postulates and paradoxes of relative voting power: a critical re-appraisal. Theory and Decision 38: 195–229
Felsenthal DS, Machover M (1996) Alternative forms of the Shapley value and the Shapley-Shubik index. Public Choice 87: 315–318
Felsenthal DS, Machover M, Zwicker W (1997) The bicameral postulates and indices of a priori relative voting power. Theory and Decision (forthcoming)
Fishburn PC (1973) The theory of social choice. Princeton University Press, Princeton
Lambert JP (1988) Voting games, power indices and presidential elections. UMAP Journal 9: 216–277
Lucas WF (1982) Measuring power in weighted voting systems. In: Brams SJ, Lucas WF, Straffin PD (eds.) Political and related models, models in applied mathematics. Springer-Verlag, New York: 183–255
Rae DW (1969) Decision rules and individual values in constitutional choice. American Political Science Review 63: 40–56
Rapoport A (1970) N-person game theory: Concepts and applications. University of Michigan Press, Ann Arbor
Riker WH (1982) Liberalism against populism: A confrontation between the theory of democracy and the theory of social choice. WH Freeman and Company, San Francisco
Roth AE (ed.) (1988) The Shapley value: Eassys in honor of Lloyd S. Shapley. Cambridge University Press, Cambridge
Shapley LS (1962) Simple games: An outline of the descriptive theory. Behavioral Science 7: 59–66
Shapley LS, Shubik M (1954) A method for evaluating the distribution of power in a committee system. American Political Science Review 48: 787–792
Simma B (ed.) (1994) The charter of the United Nations-A commentary. Oxford University Press, New York
Straffin PD (1982) Power indices in politics. In Brams SJ, Lucas WF, Straffin PD (eds.) Political and related models, models in applied mathematics. Springer-Verlag, New York: 256–321
Taylor A (1995) Mathematics and politics: Strategy, voting, power and proof. Springer-Verlag, New York
Author information
Authors and Affiliations
Additional information
We wish to thank Robert Aumann and an anonymous referee for their helpful comments, and Ralph Amelan and Hazem Ghobarah for the information they provided us regarding voting rules in the US Congress.
Rights and permissions
About this article
Cite this article
Felsenthal, D.S., Machover, M. Ternary voting games. Int J Game Theory 26, 335–351 (1997). https://doi.org/10.1007/BF01263275
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01263275