Analyses géométriques et probabilistes des règles de vote, avec une application au scrutin majoritaire à deux tours

[fre] Analyses geometriques et probabilistes des regles de vote, avec une application au scrutin majoritaire a deux tours. . La theorie des choix collectifs offre un cadre d'analyse coherent des differentes procedures de decision. A cote de la demarche axiomatique classique, plusieurs outils d'analyse originaux ont ete developpes pour etudier les qualites et defauts des principales methodes de decision. Nous presentons ici ces approches alter­natives, a savoir les outils de l'analyse geometrique et le calcul des probabilites des paradoxes de vote. Les avantages et inconvenients de ces demarches par rapport a l'analyse axiomatique seront discutes. Le vote majoritaire a deux tours servira d'exemple d'application tout au long de notre discussion. [eng] Geometric and probabilistic analysis for voting rules, wtth an application to plurality run-off. . Social Choice Theory proposes a consistent framework in order to analyse the decision methods. In comparison with the classical axiomatic approach, several original tools have been developped for studying the qualities and the flaws of the main decision processes. We shall present in this paper these alternative approaches, that is the tools of the Geometry of Voting, and the computation of the likelihood of voting paradoxes. The advantages and disadvantages of these approaches compared to the axiomatic analysis will be discussed. Two stage plurality run-off will be taken as an example of application throughout the paper.

[1]  H. Young.  Social Choice Scoring Functions , 1975 .

[2]  Donald G. Saari,et al.  A dictionary for voting paradoxes , 1989 .

[3]  W. Thomson,et al.  Axiomatic Theory of Bargaining with a Variable Number of Agents , 1989 .

[4]  H. Nurmi.  Comparing Voting Systems , 1987 .

[5]  D. Saari.  Geometry of voting , 1994 .

[6]  Gordon Tullock,et al.  A Measure of the Importance of Cyclical Majorities , 1965 .

[7]  Vincent Merlin,et al.  On the relationship of the Condorcet winner and positional voting rules , 1997 .

[8]  Vincent Merlin.  L'agregation des preferences individuelles : les regles positionnelles iteratives et la methode de copeland , 1996 .

[9]  J. H. Smith.  AGGREGATION OF PREFERENCES WITH VARIABLE ELECTORATE , 1973 .

[10]  A. Gibbard.  Manipulation of Voting Schemes: A General Result , 1973 .

[11]  V Gehrlein William,et al.  CONDORCET'S PARADOX AND THE CONDORCET EFFICIENCY OF VOTING RULES. , 1997 .

[12]  F. W. Roush,et al.  Statistical manipulability of social choice functions , 1996 .

[13]  C. Plott,et al.  The Probability of a Cyclical Majority , 1970 .

[14]  M. Satterthwaite.  Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions , 1975 .

[15]  Dominique Lepelley,et al.  On the Kim and Roush Voting Procedure , 1999 .

[16]  H. Moulin.  Axioms of Cooperative Decision Making , 1988 .

[17]  D. Saari,et al.  The Copeland method , 1996 .

[18]  J. Richelson.  A comparative analysis of social choice functions, IV , 1978 .

[19]  Peter C. Fishburn,et al.  Coincidence probabilities for simple majority and positional voting rules , 1978 .

[20]  Donald G. Saari,et al.  The Borda dictionary , 1990 .

[21]  D. Lepelley,et al.  Contribution a l'analyse des procedures de decision collective , 1989 .

[22]  K. Arrow.  Social Choice and Individual Values , 1951 .

[23]  Dominique Lepelley,et al.  Note sur le calcul de la probabilité des paradoxes du vote , 1992 .

[24]  Kenneth O. May,et al.  A Set of Independent Necessary and Sufficient Conditions for Simple Majority Decision , 1952 .

[25]  A. Sen,et al.  Collective Choice and Social Welfare , 2017 .

[26]  William V. Gehrlein.  Condorcet efficiency and constant scoring rules , 1982, Math. Soc. Sci..

[27]  Sven Berg,et al.  The likelihood of monotonicity paradoxes in run-off elections , 1996 .

[28]  Williams V. Gehrlein.  Condorcet efficiency of two stage constant scoring rules , 1993 .

[29]  Sven Berg,et al.  On probability models in voting theory , 1994 .

[30]  Peter C. Fishburn,et al.  Probabilities of election outcomes for large electorates , 1978 .