The Mathematics and Statistics of Voting Power

Statistical Science

Volumn 17, Issue 4, 2002, Pages 420-435

  Gelman, Andrew ^a   Katz, Jonathan N ^b   Tuerlinckx, Francis ^c  

^a Och Spine at New York Presbyterian Hospitals   (United States)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^c NONE

Author keywords

Banzhaf index; Decisive vote; Elections; Electoral college; Ising model; Political science; Random walk; Trees

Indexed keywords

EID: 0042919001     PISSN: 08834237     EISSN: None     Source Type: Journal    
DOI: 10.1214/ss/1049993201     Document Type: Article

References (52)

1. ALDRICH, J. H. (1993). Rational choice and turnout. American Journal of Political Science 37 246-278.
2. BANZHAF, J. F. (1965). Weighted voting doesn't work: A mathematical analysis. Rutgers Law Review 19 317-343.
3. BANZHAF, J. F. (1968). One man. 3.312 votes: A mathematical analysis of the Electoral College. Villanova Law Review 13 304-332.
4. BECK, N. (1975). A note on the probability of a tied election. Public Choice 23 75-79.
5. BEITZ, C. R. (1989). Political Equality: An Essay in Democratic Theory. Princeton Univ. Press.
6. BLEHER, P. M., RUIZ, J. and ZAGREBNOV, V. A. (1995). On the purity of the limiting Gibbs state for the Ising model on the Bethe lattice. J. Statist. Phys. 79 473-482.
7. BRAMS, S. J. and DAVIS, M. D. (1974). The 3/2's rule in presidential campaigning. American Political Science Review 68 113-134.
8. BRAMS, S. J. and DAVIS, M. D. (1975). Comment on "Campaign resource allocations under the electoral college," by C. S. Colantoni, T. J. Levesque and P. C. Ordeshook. American Political Science Review 69 155-156.
9. CHAMBERLAIN, G. and ROTHSCHILD, M. (1981). A note on the probability of casting a decisive vote. J. Econom. Theory 25 152-162.
10. CLEVELAND, W. S. (1979). Robust locally weighted regression and smoothing scatterplots. J. Amer. Statist. Assoc. 74 829-836.
11. COLANTONI, C. S., LEVESQUE, T. J. and ORDESHOOK, P. C. (1975). Campaign resource allocations under the electoral college (with discussion). American Political Science Review 69 141-161.
12. EDLIN, A., GELMAN, A. and KAPLAN, N. (2002). Rational voters vote for Social good. Technical report, Dept. Statistics, Columbia Univ.
13. EVANS, W., KENYON, C., PERES. Y. and SCHULMAN, L. J. (2000). Broadcasting on trees and the Ising model. Ann. Appl. Probab. 10 410-433.
14. FELSENTHAL, D. S. and MACHOVER, M. (1998). The Measurement of Voting Power. Elgar, Cheltenham, UK.
15. FELSENTHAL, D. S. and MACHOVER, M. (2000). Enlargement of the EU and weighted voting in its council of ministers. Report VPP 01/00, Centre for Philosophy of Natural and Social Science, London School of Economics and Political Science.
16. FELSENTHAL, D. S., MAOZ, Z. and RAPOPORT, A. (1993). An empirical evaluation of six voting procedures: Do they really make any difference? British Journal of Political Science 23 1-27.
17. FEREJOHN, J. and FIORINA, M. (1974). The paradox of not voting: A decision theoretic analysis. American Political Science Review 68 525-536.
18. FRIEDGUT, E. and KALAI, G. (1996). Every monotone graph property has a sharp threshold. Proc. Amer. Math. Soc. 124 2993-3002.
19. GARRETT, G. and TSEBELIS, G. (1999). Why resist the temptation to apply power indices to the European Union? Journal of Theoretical Politics 11 291-308.
20. GELMAN, A. (2002). Voting, fairness, and political representation (with discussion). Chance. 15(3) 22-26.
21. GELMAN, A., KATZ, J. N. and BAFUMI, J. (2002). Why standard voting power indexes don't work. An empirical analysis. Technical report, Dept. Statistics, Columbia Univ.
22. GELMAN, A. and KING, G. (1993). Why are American presidential election campaign polls so variable when votes are so predictable? British Journal of Political Science 23 409-451.
23. GELMAN, A. and KING, G. (1994). A unified method of evaluating electoral systems and redistricting plans. American Journal of Political Science 38 514-554.
24. GELMAN, A., KING, G. and BOSCARDIN, W. J. (1998). Estimating the probability of events that have never occurred: When is your vote decisive? J. Amer. Statist. Assoc. 93 1-9.
25. GOOD, I. J. and MAYER, L. S. (1975). Estimating the efficacy of a vote. Behavioral Science 20 25-33.
26. HEARD, A. D. and SWARTZ, T. B. (1999). Extended voting measures. Canad. J. Statist. 27 173-182.
27. KATZ, J. N., GELMAN, A. and KING, G. (2002). Empirically evaluating the electoral college. In Rethinking the Vote: The Politics and Prospects of American Election Reform (A. N. Crigler, M. R. Just and E. J. McCaffery, eds.). Oxford Univ. Press.
28. LEECH, D. (2002). An empirical comparison of the performance of classical (voting) power indices. Political Studies 50 1-22.
29. LUCE, R. D. and RAIFFA, H. (1957). Games and Decisions: Introduction and Critical Survey, Chap. 12. Wiley, New York.
30. MANN, I. and SHAPLEY, L. S. (1960). The a priori voting strength of the electoral college. Memo, RAND. Reprinted (1964) in Game Theory and Related Approaches to Social Behavior: Selections (M. Shubik, ed.). Wiley, New York.
31. MARGOLIS, H. (1977). Probability of a tie election. Public Choice 31 135-138.
32. MARGOLIS, H. (1983). The Banzhaf fallacy. American Journal of Political Science 27 321-326.
33. MERRILL, S., III (1978). Citizen voting power under the Electoral College: A stochastic model based on state voting patterns. SIAM J. Appl. Math. 34 376-390.
34. MULLIGAN, C. B. and HUNTER, C. G. (2001). The empirical frequency of a pivotal vote. Working Paper 8590, National Bureau of Economic Research.
35. NATAPOFF, A. (1996). A mathematical one-man one-vote rationale for Madisonian Presidential voting based on maximum individual voting power. Public Choice 88 259-273.
36. NOAH, T. (2000). Faithless elector watch: Gimme "equal protection." Slate, Dec. 13 (slate.msn.com/?id=1006680).
37. OWEN, G. (1975). Evaluation of a presidential election game. American Political Science Review 69 947-953.
38. PAGE, B. I. and SHAPIRO, R. Y. (1992). The Rational Public: Fifty Years of Trends in Americans ' Policy Preferences. Univ. Chicago Press.
39. PENROSE, L. S. (1946). The elementary statistics of majority voting. J. Roy. Statist. Soc. 109 53-57.
40. POOLE, K. T. and ROSENTHAL, H. (1997). Congress: A Political-Economic History of Roll Call Voting. Oxford Univ. Press.
41. RABINOWITZ, G. and MACDONALD, S. E. (1986). The power of the states in U.S. Presidential elections. American Political Science Review 80 65-87.
42. RIKER, W. H. and ORDESHOOK, P. C. (1968). A theory of the calculus of voting. American Political Science Review 62 25-42.
43. RIPLEY, B. D. (1981). Spatial Statistics. Wiley, New York.
44. SAARI, D. G. and SIEBERG, K. K. (1999). Some surprising properties of power indices. Discussion Paper 1271, Center of Mathematical Economics, Northwestern Univ.
45. SHAPLEY, L. S. (1953). A value for n-person games. In Contributions to the Theory of Games 2 (H. W. Kuhn and A. W. Tucker, eds.) 307-317. Princeton Univ. Press.
46. SHAPLEY, L. S. and SHUBIK, M. (1954). A method for evaluating the distribution of power in a committee system. American Political Science Review 48 787-792.
47. SNYDER, J. M., TING, M. M. and ANSOLABEHERE, S. (2001). Legislative bargaining under weighted voting. Technical Report, Dept. Economics, MIT.
48. STRAFFIN, P. D. (1978). Probability models for power indices. In Game Theory and Political Science (P. Ordeshook, ed.) 477-510. New York Univ. Press.
49. STROMBERG, D. (2002). Optimal campaigning in Presidential elections: The probability of being Florida. Technical report, IIES, Stockholm Univ.
50. UHLANER, C. J. (1989). Rational turnout: The neglected role of groups. American Journal of Political Science 33 390-422.
51. WATTS, D. J., DODDS, P. S. and NEWMAN, M. E. J. (2002). Identity and search in social networks. Science 296 1302-1305.
52. WHITTLE, P. (1956). On the variation of yield variance with plot size. Biometrika 43 337-343.