Abstract
Other than standard election disruptions involving shenanigans, strategic voting, and so forth, it is reasonable to expect that elections are free from difficulties. But this is far from being true; even sincere election outcomes admit all sorts of counterintuitive conclusions.
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Borda, J. C. 1781,Mémoire sur les élections au scrutin, Histoire de l013E;Académie Royale des Sciences, Paris.
Condorcet, M. 1785.Essai sur l’application de l’analyse à la probabilité des décisions rendues à la pluralité des voix, Paris.
Copeland, A. H. 1951, A reasonable social welfare function.Mimeo, University of Michigan.
Gibbard, A., 1973, Manipulation of voting schemes: a general result.Econometrica 41, 587–601.
Kemeny J., 1959, Mathematics without numbers.Daedalus 88, 571–591.
Merlin, V., M. Tataru, and F. Valognes 2000, On the probability that all decision rules select the same winner,Journal of Mathematical Economics 33, 183–208.
Nanson, E. J., 1882, Methods of elections,Trans. Proc. R. Soc. Victoria 18, 197–240.
Nurmi, H., 1999,Voting Paradoxes and How to Deal with Them, Springer-Verlag, NY.
Nurmi, H., 2002,Voting Procedures under Uncertainty Springer Verlag, Heidelberg.
Ratliff, T. 2001, A comparison of Dodgson’s method and Kemeny’s rule,Social Choice & Welfare 18, 79–89.
Ratliff, T. 2002, A comparison of Dodgson’s Method and the Borda Count,Economic Theory 20, 357–372.
Ratliff, T. 2003, Some starting paradoxes when electing committees, to appearSocial Choice & Welfare
Riker, W. H., 1982,Liberalism Against Populism, W. H. Freeman, San Francisco.
Saari, D. G., 1992, Millions of election rankings from a single profile,Social Choice & Welfare (1992) 9, 277–306.
Saari, D. G. 1994,Geometry of Voting, Springer-Verlag, New York.
Saari, D. G. 1995,Basic Geometry of Voting, Springer-Verlag, New York.
Saari, D. G. 1999, Explaining all three-alternative voting outcomes,Journal of Economic Theory 87, 313–355.
Saari, D. G. 2000a, Mathematical structure of voting paradoxes 1 ; pairwise vote,Economic Theory 15, 1–53.
Saari, D. G. 2000b, Mathematical structure of voting paradoxes 2: positional voting.Economic Theory 15, 55–101.
Saari, D. G. 2001,Chaotic Electionsl A Mathematician Looks at Voting, American Mathematical Society, Providence, RI.
Saari, D. G., and V. Merlin 2000, A geometric examination of Kemeny’s rule,Social Choice & Welfare 17, 403–438.
Saari, D. G., and J. Van Newenhizen, 1988, Is Approval Voting an “unmitigated evil?”Public Choice 59, 133–147.
Saari, D. G. and M. Tataru 1999, The likelihood of dubious election outcomes,Economic Theory 13, 345–363.
Satterthwaite, M., 1975, Strategyproofness and Arrow’s conditions,Jour. Econ. Theory 10, 187–217.
Tabarrok, A., 2001, Fundamentals of voting theory illustrated with the 1992 election, or could Perot have won in 1992?Public Choice 106, 275–297.
Tabarrok, A. and L. Spector 1999, Would the Borda Count have avoided the Civil War?Journal of Theoretical Politics 11, 261–288.
Tataru, M., and V. Merlin 1997, On the relationships of the Condorcet winner and positional voting rules,Mathematical Social Sciences 34, 81–90.
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Saari, D.G., Barney, S. Consequences of reversing preferences. The Mathematical Intelligencer 25, 17–31 (2003). https://doi.org/10.1007/BF02984858
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DOI: https://doi.org/10.1007/BF02984858