Abstract
We discuss two inter-related puzzling features of the literature on a priori voting power. First, the mathematical model used in virtually all this literature does not recognize abstention as an option distinct from both a ‘yes’ and a ‘no’ vote. Second, real-life decision rules of voting bodies — in particular the US legislature and the UN Security Council — are misrepresented as though they did not allow abstention as a tertium quid. We suggest that these misrepresentations may be examples of what philosophers of science call ‘theory-laden observation’.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Banzhaf, J.F. (1965), “ Weighted voting doesn’t work: a mathematical analysis”, Rutgers Law Review, 19, 317–343.
Bolger, E.M. (1993), “A value for games with n players and r alternatives”, International Journal of Game Theory, 22, 319–334.
Brams, S.J. (1975), Game Theory and Politics, New York: Free Press.
Brams, S.J., P.J. Affuso, and D.M. Kilgour (1989), “Presidential power: a game-theoretic analysis”, in: P. Brace, C.B. Harrington, and G. King (eds.), The Presi-dency in American Politics, New York: New York University Press, 55–72.
Brams, S.J., and P.C. Fishburn (1983), Approval Voting, Boston: Birkhäuser.
Coleman, J.S. (1971), “Control of collectivities and the power of a collectivity to act”, in: B. Lieberman (ed.), Social Choice, New York: Gordon and Breach Science Publishers, 269–300.
Dubey, P., and L.S. Shapley (1979), “Mathematical properties of the Banzhaf power index”, Mathematics of Operations Research, 4, 99–131.
Felsenthal, D.S., and M. Machover (1995), “Postulates and paradoxes of relative vot-ing power: a critical re-appraisal”, Theory and Decision, 38, 195–229.
Felsenthal, D.S., and M. Machover (1996), “Alternative forms of the Shapley value and the Shapley-Shubik index”, Public Choice, 87, 315–318.
Felsenthal, D.S., and M. Machover (1997), “Ternary voting games”, International Journal of Game Theory, 26, 335–351.
Felsenthal, D.S., and M. Machover (1998), The Measurement of Voting Power: The-ory and Practice, Problems and Paradoxes, Cheltenham: Edward Elgar.
Felsenthal, D.S., and M. Machover (2000), Misreporting Rules,mimeographed.
Felsenthal, D.S., M. Machover, and W. Zwicker (1998), “The bicameral postulates and indices of a priori voting power”, Theory and Decision, 44, 83–116.
Fishburn, P.C. (1973), The Theory of Social Choice, Princeton: Princeton University Press.
Gillies, D. (1993), Philosophy of Science in the Twentieth Century: Four Central Themes, Blackwell: Oxford.
Hanson, N. (1958), Patterns of Discovery, Cambridge: Cambridge University Press. Kuhn, T. (1962), The Structure of Scientific Revolutions, Chicago: University of Chicago Press.
Lambert, J.P. (1988), “Voting games, power indices, and presidential elections”, UMAP Journal, 9, 216–277.
Laver, M., and N. Schofield (1990), Multiparty Government: the Politics of Coalition in Europe, Oxford: Oxford University Press.
Lucas, W.F. (1982), “Measuring power in weighted voting systems”, in: S.J. Brams, W.F. Lucas, and P.D. Straffin (eds.), Political and Related Methods, New York: Springer, 183–238.
Mann, I., and L.S. Shapley (1964), “The a priori voting strength of the electoral college”, in: M. Shubik (ed.) Game Theory and Related aApproaches to Social Behavior, New York: John Wiley, 151–164.
Morriss, P. (1987), Power - a Philosophical Analysis, Manchester: Manchester University Press.
Penrose, L.S. (1946), “The elementary statistics of majority voting”, Journal of the Royal Statistical Society, 109, 53–57.
Rapoport, A. (1970), N-Person Game Theory: Concepts and Applications, Ann Arbor: University of Michigan Press.
Riker, W.H. (1982), Liberalism Against Populism: a Confrontation Between the The-ory of Democracy and the Theory of Social Choice, San Francisco: WH Freeman.
Shapley, L.S. (1953), “A value for n-person games”, in: H.W. Kuhn, and A.W. Tucker (eds.), Contributions to the Theory of Games, Princeton: Princeton Uni-versity Press, 307–317.
Shapley, L.S. (1962), “Simple games: an outline of the descriptive theory”, Behavioral Science, 7, 59–66.
Shapley, L.S., and M. Shubik (1954), “A method for evaluating the distribution of power in a committee system”, American Political Science Review, 48, 787–792.
Simma, B. (ed.) (1982), The Charter of the United Nations - a Commentary, New York: Oxford University Press.
Straffin, P.D. (1982), “Power indices in politics”, in: S.J. Brams,W.F. Lucas, and P.D. Straffin (eds.), Political and Related Methods, Springer, New York, 256–321. The Supreme Court Reporter, vol. 39 (1920), St Paul: West Publishing Co.
Taylor, A.D. (1995), Mathematics and Politics: Strategy, Voting, Power and Proof, New York: Springer.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media New York
About this chapter
Cite this chapter
Felsenthal, D.S., Machover, M. (2001). Models and Reality: The Curious Case of the Absent Abstention. In: Holler, M.J., Owen, G. (eds) Power Indices and Coalition Formation. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6221-1_6
Download citation
DOI: https://doi.org/10.1007/978-1-4757-6221-1_6
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-4893-9
Online ISBN: 978-1-4757-6221-1
eBook Packages: Springer Book Archive