Préférences et rationalité stochastiques

Pascal Bouyaux

Mathématiques et Sciences Humaines (1990)

  • Volume: 109, page 17-40
  • ISSN: 0987-6936

Abstract

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The aim of this article is to undertake a pedagogical presentation of a wide-spread concept of rationality, the stochastic rationality. In a first part, we set the problem with the help of a simple example and we put a set of preliminary definitions. Then, in a second part, we expound the basic result of Falmagne (1978) applied to multiple choices situations ; the set approach of this author is formalized with the Block-Marshak (1960) polynomials. In a third part, we deal with the particular case of binary choices, expanding the geometrical approach of Mac-Fadden-Richter (1970) based on a permutation polytope ; the potentials applications of this approach in voting theory, combinatorial optimization and ordinal data analysis are briefly described. The last part concludes.

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Bouyaux, Pascal. "Préférences et rationalité stochastiques." Mathématiques et Sciences Humaines 109 (1990): 17-40. <http://eudml.org/doc/94389>.

@article{Bouyaux1990,
abstract = {Le but de cet article est de procéder à une présentation pédagogique d'un concept étendu de rationalité, la rationalité stochastique. Dans une première partie, nous exposons le problème à l'aide d'un exemple simple et posons un ensemble de définitions préliminaires. Puis, dans une seconde partie, nous présentons le résultat fondamental de Falmagne (1978) s'appliquant aux situations de choix multiples ; l'approche ensembliste de cet auteur est formalisée à partir du concept de polynômes de Block-Marschak (1960). Dans une troisième partie, nous traitons du cas particulier des choix binaires, développant ainsi l'approche géométrique de Mac-Fadden-Richter (1970) reposant sur le concept de permutoèdre ; les applications potentielles de cette approche en théorie du vote, optimisation combinatoire et analyse des données ordinales sont brièvement évoquées. La dernière partie conclut.},
author = {Bouyaux, Pascal},
journal = {Mathématiques et Sciences Humaines},
keywords = {stochastic rationality; multiple choice; binary choices},
language = {fre},
pages = {17-40},
publisher = {Ecole des hautes-études en sciences sociales},
title = {Préférences et rationalité stochastiques},
url = {http://eudml.org/doc/94389},
volume = {109},
year = {1990},
}

TY - JOUR
AU - Bouyaux, Pascal
TI - Préférences et rationalité stochastiques
JO - Mathématiques et Sciences Humaines
PY - 1990
PB - Ecole des hautes-études en sciences sociales
VL - 109
SP - 17
EP - 40
AB - Le but de cet article est de procéder à une présentation pédagogique d'un concept étendu de rationalité, la rationalité stochastique. Dans une première partie, nous exposons le problème à l'aide d'un exemple simple et posons un ensemble de définitions préliminaires. Puis, dans une seconde partie, nous présentons le résultat fondamental de Falmagne (1978) s'appliquant aux situations de choix multiples ; l'approche ensembliste de cet auteur est formalisée à partir du concept de polynômes de Block-Marschak (1960). Dans une troisième partie, nous traitons du cas particulier des choix binaires, développant ainsi l'approche géométrique de Mac-Fadden-Richter (1970) reposant sur le concept de permutoèdre ; les applications potentielles de cette approche en théorie du vote, optimisation combinatoire et analyse des données ordinales sont brièvement évoquées. La dernière partie conclut.
LA - fre
KW - stochastic rationality; multiple choice; binary choices
UR - http://eudml.org/doc/94389
ER -

References

top
  1. [1]. Aizerman M.A. (1985), "New Problems in General Choice Theory" ; Social choice and welfare, Vol 2.,1985, 235-282. Zbl0583.90004MR824956
  2. [2]. Arrow K.J. (1959), "Rational choice function and ordering", Economica, 26, (1959a), 121-127. Social choice and Individual Values, New York, Wiley, 1959b. 
  3. [3]. Barbera S. (1985), "Rationalizable Stochastic Choice on Restricted domains", 5th world congress of the econometric society, Cambridge, Mass, 1985. 
  4. [4]. Barbera S., Pattanaik P.K. (1986), "Falmagne and the Rationalizability of Stochastic Choices in Terms of Random Orderings", Econometrica, 54,1986, 707-715. Zbl0607.90005MR845695
  5. [5]. Barbera S., Sonnenschein H. (1978), "Preference Aggregation with Randomized Social Orderings", Journal of Economic Theory, 18, 1978, 244-154. Zbl0386.90005MR513677
  6. [6]. Barbera S., Valenciano F. (1983), "Collective Probabilistic Judgements", Econometrica, 51,1983,1033-1046. Zbl0523.90012MR710220
  7. [7]. Barret C., Pattanaik P., Salles M. (1987), On Choosing Rationally when preferences arefuzzy,. Mimeograph, University of Binnimgham and CREMERC, 1987. 
  8. [8]. Barthélemy J.P., Monjardet B. (1981), "The Median Procedure in Cluster Analysis and Social Choice Theory", Mathematical Social Sciences, 1, 1981, 235-267. Zbl0486.62057MR616379
  9. [9]. Barthélemy J.P., Monjardet B. (1988), "The Median Procedure in Data Analysis : new results and open problems", in classification and related methods of data analysis, HH Bock Editor, Elsevier Science Publishers, North-Holland, 1988, 309-316. MR999565
  10. [10]. Block H., Marschak J. (1960), "Random Orderings and Stochastic Theories of Response ". Chapter 10 in contributions to probability and statistics, edited by J. Olkin, Stanford: Stanford University Press, 1960. Zbl0096.12104MR121236
  11. [11]. Bowman V.J. (1972), "Permutation Polyhedra ", Siam Journal of Applied Mathematics, 22, n°4,1972, 580-589. Zbl0246.90030MR305800
  12. [12]. Bouyaux P., "Une difficulté d'interprétation de l'Approche Logit : l'exemple de l'économie des transports", Économie et prévision n°91, à paraître. 
  13. [13]. Chipman J., Hurwicz L., Richter M., Sonnenschein H. (1971), Preferences, utility and demand : a minnesota symposium, Harcourt Brace Jovanovich, New York, Chicago, San-Francisco, Atlanta, 1971. Zbl0265.00026MR432198
  14. [14]. Cohen M., Falmagne J.C. (1978), Random Scale Représentation of Binary Choice Probabilities : a counterexample to a conjecture of Marschak, Mimeograph, department of Psychology, New York University, 1978. 
  15. [15]. Cohen M., Falmagne J.C. (1989), Random Utility Représentation of Binary Choice Probabilities : a new class of necessary conditions. Mimeograph, department of Psychology, New York University, 1989. 
  16. [16]. Debord B. (1987), "Caractérisation des matrices des préférences nettes et méthodes d'agrégation associées", Mathématiques et Sciences humaines, n°97, 1987, 5-17. Zbl0619.90005MR890684
  17. [17]. Debreu G. (1958), "Stochastic Choice and Cardinal Utility", Econometrica, 26, 1958, 440-444. Zbl0103.13006
  18. [18] De Palma A., et Trisse J. (1989), "Les modèles de choix discrets, Annales d'Economie et de Statistique, vol.9,1989,151-190. MR1032589
  19. [19]. Dridi T. (1980), "Sur les Distributions Binaires Associées à des Distributions Ordinales", Mathématiques et Sciences humaines, n°69,1980,15-31. Zbl0437.90003MR571613
  20. [20] Doignon J.P., Monjardet B., Roubens M., Vincke Ph., (1986), "Biorder Families, Valued Relations, and Préférence Modelling", Journal of Mathematical Psychology, 30, n°4,1986, 435-480. Zbl0612.92020MR868774
  21. [21]. Falmagne J.C. (1978), "A représentation theorem for finite random scale systems", Journal of Mathematical Psychology, 18, 1978, 52-72. Zbl0408.62093MR509827
  22. [22]. Fechner G. (1859), Elemente der Psychophysik, Leipzig, Breitkopf und Härtel, 1859. 
  23. [23]. Fishburn P. (1973), "Binary Choice Probabilities : on the varieties of stochastic transitivity", Journal of Mathematical Psychology, 10, 1973, 327-352. Zbl0277.92008MR327330
  24. [24]. Fishburn P. (1978), "Choice Probabilities and choice functions", Journal of Mathematical Psychology, 18, 1978, 205-219. Zbl0404.92024MR522387
  25. [25]. Fishburn P. (1987), "Decomposing Weighted Digraphs into Sums of Chains", Discrete Applied Mathematics, 16, 1987, 223-238. Zbl0606.05028MR878023
  26. [26]. Fishburn P.(1988), Binary Probabilities induced par rankings, Mimeograph, Bell Laboratories, Murray Hill, New-Jersey and New York University, 1988. 
  27. [27]. Fishburn P., Falmagne J.C. (1989), "Binary choice probabilities and rankings", Economic Letters, 31,1989,113-117. MR1032642
  28. [28]. Georgescu-Roegen N. (1958), "Threshold in choice and the theory of demand", Econometrica, 26, 1958, 157-168. Zbl0103.13102MR91210
  29. [29]. Gilboa I. (1985), A necessary but insufficient condition for the stochastic order problem, Mineograph, Faculty of Social Sciences, Tel Aviv University, 1985. 
  30. [30]. Gblboa I. (1989), A necessary but insufficient condition for the stochastic binary choice problem, Mimeograph, North Western University, 1989. 
  31. [31]. Guilbaud G.Th. (1953), "Sur une difficulté de la théorie du risque" in Colloques internationaux du CNRS, Paris, 12-17 mai 1952, Editions du CNRS, 1953, 19-28. Zbl0053.41804MR68803
  32. [32]. Guilbaud G.Th. (1970), "Préférences Stochastiques ", Mathématiques et Sciences humaines, n°32, 1970, 45-56. Zbl0232.90010MR305450
  33. [33]. Hausman J., Wise D. (1978), "A conditional probit model for qualitative choice : discrete décisions recognizing interdépendance ans heterogeneous preferences", Econometrica, 46, 1978, 403-426. Zbl0376.90005MR465090
  34. [34]. Houthakker H. (1950), "Revealed préférence and the utility functions", Economica, 17, 1950,159-174. MR42676
  35. [35]. Luce R.D. (1959), Individual choice behavior, New York, Wiley,1959. Zbl0093.31708MR108411
  36. [36]. Luce R.D., Suppes P. (1965), "Preference, utility and subjective probability ", Chapter 19 in Handbook of Mathematical Psychology, edited by Luce, Bush, and Galanter, Wiley, 1965. 
  37. [37]. Mac-Fadden D. (1974), "Conditional logit analysis of qualitative choice behavior", Chapter 4 in Frontiers in Econometrics, edited by P. Zarembka, New York, Academic Press, 1974. 
  38. [38]. Mac-Fadden D. (1976), "Quantal choice analysis : a survey", Annals of Economic and Social Measurement, 1976, 363-390. 
  39. [39]. Mac-Fadden D. (1981), "Econometric models of probabilistic choice", Chapter 5, in Structural Analysis of Discrete Data, edited by C. Manski et D.Mac-Fadden, Cambridge, Mass, MIT Press, 1981. Zbl0598.62145
  40. [40]. Mac-Fadden D., Richter (1970), Stochastic rationality and revealed stochastic preference, Mineograph, University of California,1970. 
  41. [41]. Machina M. (1985), "Stochastic choice functions generated from deterministic preferences over lotteries", Economic Journal, n°95,1985, 575-594. 
  42. [42]. Mac-Lennan A. (1980), "Randomized preference aggregation : additivity of power and strategy proofness", Journal of Economic Theory, 22, 1980,1-11. Zbl0437.90008MR568764
  43. [43]. Mac-Lennan A. (1983), Binary stochastic choice, Mimeograph, University of Minnesota, 1983. 
  44. [44]. Marley J.A.A. (1965), "The relation between the discard and regularity conditions for choice probabilities", Journal of Mathematical Psychology, 2, 1965, 242-253. Zbl0141.36402MR178485
  45. [45]. Marschak J. (1960), "Binary choice constraints and random utility indicators", in Mathematical Methods in the Social Sciences, edited by K.J.Arrow et als, Stanford, California: Stanford University Press, 1960. MR118556
  46. [46]. Megiddo N. (1977), "Mixtures of order matrices and generalized order matrices", Discrete Mathematics, 19, 1977, 177-181. Zbl0377.05008MR457255
  47. [47]. Mimiague F., Rousseau J.M. (1977), "Effet Condorcet : typologie et calculs de fréquence", Mathématiques et Sciences humaines, 43,1977,.7-27. MR389271
  48. [48]. Monjardet B. (1973), "Tournois et ordres médians pour une opinion", Mathématiques et Sciences humaines, 43, 1973, 55-70. Zbl0271.05114MR376451
  49. [49]. Monjardet B. (1985), "Concordance et consensus d'ordre totaux : les coefficients K et W", Revue de Statistique Appliquée, 33, n°2,1985, 55-87. Zbl0568.62054MR801504
  50. [50]. Mossin A. (1985), "Element of a stochastic theory of consumption", Swedish Journal of Economics, 70, 1985, 200-220. 
  51. [51]. Moulin H. (1985), "Choice functions over a finite set : a summary ", Social Choice and Welfare, 2, 1985, 147-160. Zbl0576.90004MR813470
  52. [52]. Pattanaik P.K., Peleg B. (1986), "Distribution of power under stochastic choice rules", Econometrica, 54, 1986, 909-921. Zbl0596.90009MR853989
  53. [53]. Quandt R. (1956),"A probabilistic theory of consumer behavior", Quaterly Journal of Economics, 70, 1956, 507-536. 
  54. [54]. Reinelt G. (1985), The linear ordering problem : algorithms and applications, Heldermann verlag, Berlin,1985. Zbl0565.68058MR831936
  55. [55]. Richter M.K. (1966), "Revealed perference theory ", Econometrica, 34, 1966, 635-645. Zbl0158.38802
  56. [56] Roberts F., (1979), Measurement Theory, with Applications to Decision-making, Utility, and the Social Sciences, Encyclopedia of Mathematics and its Applications, Vol.7, Reading, MA, Addison-Wesley, 1979. Zbl0432.92001MR551364
  57. [57]. Samuelson S. (1948), "Consumption theory in terms of revealed preferences", Economica, 15, 1948, 243-253. 
  58. [58]. Sen S.(1971), "Choice functions and revealed preferences", Review of Economic Studies, 38, 1971, 307-317. Zbl0237.90004
  59. [59]. Souza F.M.C. (1978), "Mixed models, random utilities, and the triangle inequality", Journal of Mathematical Psychology, 27,1978,183-200. Zbl0526.92029MR729028
  60. [60]. Stigler G.S., Becker G.S. (1977), "De Gustibus non est disputandum", American Economic Review, 67, 1977, 76-90. 
  61. [61]. Thurstone L. (1927), "A law of comparative judgement", Psychological Review, 34, (1927), 273-286. 
  62. [62]. Tversky A.(1972), "Elimination by aspects : a theory of choice", Psychological Review, 79, 1972, 281-289. 
  63. [63]. Tversky A., Russo J.E. (1969), "Substituability and similarity in binary choices", Journal of Mathematical Psychology, 6,1969,.1-12. 
  64. [64]. Young H.P. (1978), "On permutations and permutation polytopes" Mathematical Programming Study, 8, 1978, 128-140. Zbl0424.05001MR510372

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