Condorcet's theory of voting

H. P. Young

Mathématiques et Sciences Humaines (1990)

  • Volume: 111, page 45-59
  • ISSN: 0987-6936

Abstract

top
Condorcet believed that the purpose of voting is to make a choice that is “best” for society. According to his view, there is one choice that is objectively best, another that is second-best, and so forth. Unfortunately, voters sometimes make mistakes ; they misperceive what is best. In designing a voting rule, therefore, the objective should be to choose the alternative that is most likely to be best. Condorcet solved this problem using a form of maximum likelihood estimation. The procedure that he derives can also be justified from a modern axiomatic perspective. It is the unique social welfare function that satisfies a variant of independant of irrelevant alternatives together with several other standard properties.

How to cite

top

Young, H. P.. "Condorcet's theory of voting." Mathématiques et Sciences Humaines 111 (1990): 45-59. <http://eudml.org/doc/94396>.

@article{Young1990,
abstract = {Condorcet believed that the purpose of voting is to make a choice that is “best” for society. According to his view, there is one choice that is objectively best, another that is second-best, and so forth. Unfortunately, voters sometimes make mistakes ; they misperceive what is best. In designing a voting rule, therefore, the objective should be to choose the alternative that is most likely to be best. Condorcet solved this problem using a form of maximum likelihood estimation. The procedure that he derives can also be justified from a modern axiomatic perspective. It is the unique social welfare function that satisfies a variant of independant of irrelevant alternatives together with several other standard properties.},
author = {Young, H. P.},
journal = {Mathématiques et Sciences Humaines},
keywords = {decision},
language = {eng},
pages = {45-59},
publisher = {Ecole des hautes-études en sciences sociales},
title = {Condorcet's theory of voting},
url = {http://eudml.org/doc/94396},
volume = {111},
year = {1990},
}

TY - JOUR
AU - Young, H. P.
TI - Condorcet's theory of voting
JO - Mathématiques et Sciences Humaines
PY - 1990
PB - Ecole des hautes-études en sciences sociales
VL - 111
SP - 45
EP - 59
AB - Condorcet believed that the purpose of voting is to make a choice that is “best” for society. According to his view, there is one choice that is objectively best, another that is second-best, and so forth. Unfortunately, voters sometimes make mistakes ; they misperceive what is best. In designing a voting rule, therefore, the objective should be to choose the alternative that is most likely to be best. Condorcet solved this problem using a form of maximum likelihood estimation. The procedure that he derives can also be justified from a modern axiomatic perspective. It is the unique social welfare function that satisfies a variant of independant of irrelevant alternatives together with several other standard properties.
LA - eng
KW - decision
UR - http://eudml.org/doc/94396
ER -

References

top
  1. Arrow, K.J., 1963, Social Choice and Individual Values, 2d ed., New York, John Wiley. Baker, K.M., 1975, Condorcet, Chicago, University of Chicago Press. Zbl0984.91513MR39976
  2. Barthélemy, J.P., and McMorris, F.R., 1986, "The Median Procedure for n-Trees", Journal of Classification, 3, 329-334. Zbl0617.62066MR874243
  3. Barthélemy, J.P., and Monjardet, B., 1981, "The Median Procedure in Cluster Analysis and Social Choice Theory", Mathematical Social Sciences, 1, 235-267. Zbl0486.62057MR616379
  4. Batchelder, W., and Bershad, N.J., 1979, "The Statistical Analysis of a Thurstonian Model for Rating Chess Players", Journal of Mathematical Psychology, 19, 39-60. Zbl0411.62082MR529035
  5. Black, D., 1958, The Theory of Committees and Elections, Cambridge, Cambridge University Press. Zbl0091.15706
  6. Borda, Jean-Charles (de), 1784, "Mémoire sur les Élections au Scrutin", in Histoire de l'Académie Royale des Sciences. 
  7. Condorcet, Marquis de, 1785, Essai sur l'application de l'analyse à la probabilité des décisions rendues à la probabilité des voix, Paris, de l'imprimerie royale. 
  8. Fishburn, P.C., 1973, The Theory of Social Choice, Princeton, Princeton University Press. Zbl0253.92006MR386742
  9. Gelfand, A., and Solomon, H., 1973, "A Study of Poisson's Models for Jury Verdicts in Criminal and Civil Trials", Journal of the American Statistical Association, 68, 271-278. 
  10. Good, I.J., 1955, "On the Marking of Chess Payers", The Mathematical Gazette, 39, 292-296. Zbl0065.11603MR73553
  11. Grofman, B., 1981, "When is the Condorcet Winner the Condorcet Winner ?", University of California, Irvine, typescript. 
  12. Grofman, B., and Feld S., 1988, "Rousseau's General Will : A Condorcetian Perspective ", American Political Science Review, 82, 567-576. 
  13. GROFMAN, B., and OWEN G., eds., 1986, Information Pooling and Group Decision Making, Greenwich, CT, JAI Press. 
  14. HENRY, C., eds., 1833, Correspondance Inédite de Condorcet et de Turgot 1770-1779, Paris, Charavay Frères. 
  15. Jacquet-Lagreze, E., 1969, "L'agrégation des opinions individuelles", in Informatique et Sciences humaines, vol.4. 
  16. Jech, T., 1983, "The ranking of Incomplete Tournaments : a Mathematician's Guide to Popular Sports", American Mathematical Monthly, 90, 246-266. Zbl0519.05034MR700265
  17. Kemeny, J., 1959, "Mathematics without Numbers", Daedalus, 88, 571-591. 
  18. Kemeny, J., and Snell L., 1960, Mathematical Models in the Social Sciences, Boston, Ginn. Zbl0256.92003
  19. Kramer, G., 1977, "A Dynamical Model of Political Equilibrium", Journal of Economic Theory, 16, 310-334. Zbl0404.90005MR524414
  20. Mascart, J., 1919, La vie et les travaux du Chevalier Jean-Charles de Borda, Paris, Rey. Zbl47.0867.02JFM47.0867.02
  21. Michaud, P., 1985, "Hommage à Condorcet (version intégrale pour le bicentenaire de l'Essai de Condorcet)", Etude F-084, Centre scientifique-IBM France, Paris. 
  22. Michaud, P., and Marcotorchino, J.F., 1978, "Optimization in Ordinal Data Analysis", étude F-001, Centre scientifique-IBM France, Paris. 
  23. Nash, J., 1950, "The Bargaining Problem", Econometrica, 18, 155-162. Zbl1202.91122MR35977
  24. Nitzan, S., and Paroush, J., 1982, "Optimal Decision Rules in Uncertain Dichotomous Situations ", International Economic Review, 23, 289-297. Zbl0489.90011MR668597
  25. Poisson, Siméon-Denis, 1837, Recherches sur la probabilité des jugements en matière criminale et en matière civile, précédées des règles générales du calcul des probabilités, Paris, Bachelier. 
  26. Rousseau, J.J., 1762, The Social Contract, Harmondsworth, England, Penguin (1968). 
  27. Shapley, L.S., and Grofman, B., 1984, "Optimizing Group Judgmental Accuracy in the Presence of Interdependencies", Public Choice, 43, 329-343. 
  28. Todhunter, I., 1949, A History of the Mathematical Theory of Probability, New York, Chelsea. 
  29. Urken, A.B., and Traflet, S., 1984, "Optimal Jury Design", Jurimetrics, 24, 218-235. 
  30. Young, H.P., 1974, "An Axiomatization of Borda's Rule", Journal of Economic Theory, 9, 43-52. MR496492
  31. Young, H.P., 1986, "Optimal Ranking and Choice from Pariwise Comparisons ", in Information Pooling and Group Decision Making, ed., B. Grofman and G. Owen, Greenwich, CT, JAI Press. 
  32. Young, H.P., and Levenglick, A., 1978, "A Consistent Extension of Condorcet's Election Principle ", SIAM Journal on Applied Mathematics, 35, 285-300. Zbl0385.90010MR504073

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.