Note sur le calcul de la probabilité des paradoxes du vote

Sven Berg; Dominique Lepelley

Mathématiques et Sciences Humaines (1992)

  • Volume: 120, page 33-48
  • ISSN: 0987-6936

Abstract

top
A number of papers have recently attempted to calculate the probability of the paradoxes or difficulties that social choice theory has discovered. We review in this note most of the probabilistic models which have been used in these papers. Furthermore, we apply one of these models to the computation of the probability of some well known voting paradoxes.

How to cite

top

Berg, Sven, and Lepelley, Dominique. "Note sur le calcul de la probabilité des paradoxes du vote." Mathématiques et Sciences Humaines 120 (1992): 33-48. <http://eudml.org/doc/94432>.

@article{Berg1992,
abstract = {De nombreux travaux se sont efforcés au cours des années récentes de calculer la probabilité des paradoxes ou des difficultés que la théorie des choix collectifs a mis en évidence. On passe en revue dans cette note les principaux modèles de calcul utilisés dans ces travaux. On applique en outre l'un des modèles présentés au calcul de la probabilité de quelques paradoxes bien connus de la théorie du vote.},
author = {Berg, Sven, Lepelley, Dominique},
journal = {Mathématiques et Sciences Humaines},
keywords = {social choice theory; voting paradoxes},
language = {fre},
pages = {33-48},
publisher = {Ecole des hautes-études en sciences sociales},
title = {Note sur le calcul de la probabilité des paradoxes du vote},
url = {http://eudml.org/doc/94432},
volume = {120},
year = {1992},
}

TY - JOUR
AU - Berg, Sven
AU - Lepelley, Dominique
TI - Note sur le calcul de la probabilité des paradoxes du vote
JO - Mathématiques et Sciences Humaines
PY - 1992
PB - Ecole des hautes-études en sciences sociales
VL - 120
SP - 33
EP - 48
AB - De nombreux travaux se sont efforcés au cours des années récentes de calculer la probabilité des paradoxes ou des difficultés que la théorie des choix collectifs a mis en évidence. On passe en revue dans cette note les principaux modèles de calcul utilisés dans ces travaux. On applique en outre l'un des modèles présentés au calcul de la probabilité de quelques paradoxes bien connus de la théorie du vote.
LA - fre
KW - social choice theory; voting paradoxes
UR - http://eudml.org/doc/94432
ER -

References

top
  1. Arrow K.J., Social choice and individual value, New York, Wiley, 1963. Zbl0984.91513
  2. Berg S., "Paradox of voting under an urn model : the effect of homogeneity", Public Choice, 47, (1985a), 377-387. 
  3. Berg S., "A note on plurality distorsion in large committees", European Journal of Political Economy, 1, (1985b), 271-284. 
  4. Berg S., "The probability of casting a decisive vote : the effects of a caucus", Public Choice, 64, (1990), 73-92. 
  5. Berg S. et B. Bjurulf, "A note on the paradox of voting : anonymous preference profiles and May's formula", Public Choice, 40, (1983), 307-316. 
  6. Berg S. et D. Lepelley, "Voting cycles, plurality rule and strategic manipulation", Annals of Operations Research, 23, (1990), 247-256. Zbl0723.90005MR1066335
  7. Borda J.C. (de), "Mémoire sur les élections au scrutin", Histoire de l'académie royale des sciences, Paris, 1781. 
  8. Condorcet M.J.A. (Marquis de), Essai sur l'application de l'analyse à la probabilité des décisions rendues à la pluralité des voix, Paris, 1785. Zbl16.0247.01
  9. Feller W., An introduction to probability theory and its applications, New York, Wiley, 1957. Zbl0077.12201MR88081
  10. Fishburn P.C., "Monotonicity paradox in the theory of elections", Discrete Applied Mathematics, 4, (1982), 119-134. Zbl0475.90009MR677878
  11. Fishburn P.C. et W.V. Gehrlein, "Majorities efficiencies for simple voting procedures", Theory and Decision, 14, (1982), 141-153. Zbl0482.90006MR665582
  12. Gehrlein W.V., "Single-stage election procedures for large electorates", Journal of Mathematical Economics, 8, (1981), 263-275. Zbl0461.90005MR631008
  13. Gehrlein W.V., "Condorcet efficiency and constant scoring rules", Mathematical Social Sciences, 2, (1982), 123-130. Zbl0479.90015
  14. Gehrlein W.V., "Condorcet's paradox", Theory and Decision, 15, (1983), 161-197. Zbl0512.90009MR709402
  15. Gehrlein W.V., A variant interpretation of the impartial anonymous culture condition, document dactylographié, University of Delaware, 1984. 
  16. Gehrlein W.V., "The expected likelihood of transitivity for a probabilistic chooser", Annals of Operations Research, 23, (1990), 235-246. Zbl0708.90004MR1066334
  17. Gehrlein W.V., "Coincidence probabilities for simple majority and proportional lottery rules", Economics Letters, 35, (1991), 349-353. Zbl0725.90021
  18. Gehrlein W.V., "Condorcet efficiency and social homogeneity", papier presenté au premier meeting de la "Society for Social Choice and Welfare", Caen, 1992. Zbl0905.90006
  19. Gehrlein W.V. et S. Berg, "The effect of social homogeneity on coincidence probabilities for pairwise proportional lottery and simple majority rule", à paraître dans Social Choice and Welfare, 1992. Zbl0761.90005MR1195112
  20. Gehrlein W.V. et P.C. Fishburn, "The probability of the paradox of voting : a computable solution", Journal of Economic Theory, 13, (1976a), 14-25. Zbl0351.90002MR443842
  21. Gehrlein W.V. et P.C. Fishburn, "Condorcet's paradox and anonymous preference profiles", Public Choice, 26, (1976b), 1-18. 
  22. Gehrlein W.V. et P.C. Fishburn, "Coincidence probabilities for simple majority and positionalist voting rules", Social Science Research7, (1978), 272-283. 
  23. Gehrlein W.V. et P.C. Fishburn, "Effects of abstentions on voting procedures in three-alternative elections", Behavioral Science24, (1979), 346-354. 
  24. Gehrlein W.V. et P.C. Fishburn, "Scoring rule sensitivity to weight selection", Public Choice,40, (1983), 249-261. 
  25. Gibbard A., "Manipulation of voting schemes : a general result", Econometrica, 41, (1973),587-601. Zbl0325.90081MR441407
  26. Gillett R., "Collective Indecision", Behavioral Science, 22, (1977), 383-390. 
  27. Gillett R., "The comparative likelihood of an equivocal outcome under plurality, Condorcet and Borda voting procedures", Public choice, 35, (1980), 483-491. 
  28. Guilbaud G.Th., "Les théories de l'intérêt général et le problème logique de l'agrégation ", Économie Appliquée, 5, (1952), 501-584. 
  29. Johnson N.L. et S. Kotz, Urns models and their application, New York, Wiley, 1977. Zbl0352.60001MR488211
  30. Kreweras G., "Les décisions collectives", Mathématiques et Sciences Humaines, 2, (1962), 25-35. 
  31. Lepelley D., Remarques sur les calculs de probabilité dans la théorie des choix collectifs, document dactylographié, Université de Caen, 1984. 
  32. Lepelley D., Contribution à l'analyse des procédures de décision collective, Thèse de doctorat, Université de Caen, 1989. 
  33. Lepelley D., "On the probability of electing the Condorcet Loser", à paraître dans Mathematical Social Sciences, 1992. Zbl0769.90026MR1203962
  34. Lepelley D. et B. Mbih, "The proportion of coalitionally unstable situations under the plurality rule", Economics Letters, 24, (1987), 311-315. Zbl1328.91073MR919264
  35. Lepelley D. et B. Mbih, The vulnerability of four social choice functions to coalitional manipulation of preferences, document dactylographié, Université de Caen, 1992. Zbl0822.90006
  36. May R.M., "Some mathematical remarks on the paradox of voting", Behavioral Science, 16, (1971), 143-151. 
  37. Merrill S., Making multicandidate elections more democratic, Princeton [University Press, 1988. 
  38. Moulin H., "Condorcet's principle implies the no show paradox", Journal of Economic Theory, 45, (1988), 53-64. Zbl0649.90010MR949068
  39. Niemi R.G. et W.H. Riker, "The choice of voting systems", Scientific American, 234 (1976), 21-27 
  40. Nitzan S., "The vulnerability of point-voting schemes to preference variation and strategic manipulation", Public choice, 47 (1985) 249-270. 
  41. Nurmi H., "Probability models in constitutional choice", European Journal of Political Economy, 6, (1990), 107-117. 
  42. Nurmi H. et Y. Uusi-Heikkila, "Computer simulations of approval and plurality voting : the frequency of weak Pareto violations and Condorcet losers choice in impartial culture", European Journal of Political Economy, 2/1, (1985), 47-59. 
  43. Paris D.C., "Plurality distorsion and majority rule", Behavioral Science, 20, (1975), 125-133. 
  44. Peleg B., "A note on manipulability of large voting schemes", Theory and Decision, 11, (1979), 401-412. Zbl0417.90019MR558011
  45. Satterthwaite M.A., "Strategy-proofness and Arrow's conditions : existence and correspondence theorems for voting procedures and social welfare functions", Journal of Economic Theory, 10, (1975), 187-217. Zbl0315.90088MR414051
  46. Smith J.H., "Aggregation of preferences with variable electorates", Econometrica, 41, (1973), 1027-1041. Zbl0286.90008MR441227
  47. Young H.P., "Social choice scoring functions", SIAM Journal of Applied Mathematics, 28, (1975), 824-838. Zbl0277.92007MR371438

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.