, Pour ce premier profil, nous allons distinguer huit cas

, ? ? (d, a, ?) ? V a 1 (?), ? (d, b, ?) ? V b 1 (?) et ? (d, c, ?) ? V c 1 (?)

, ? ? (d, a, ?) ? V a 1 (?), ? (d, b, ?) ? V b 1 (?) et ? (d, c, ?) > V c 1 (?)

?. ,

?. ,

, ? ? (d, a, ?) ? V a 1 (?), ? (d, b, ?) > V b 1 (?) et ? (d, c, ?) > V c 1 (?)

, ? ? (d, a, ?) > V a 1 (?), ? (d, b, ?) ? V b 1 (?) et ? (d, c, ?) > V c 1 (?)

, ? ? (d, a, ?) > V a 1 (?), ? (d, b, ?) > V b 1 (?) et ? (d, c, ?) ? V c 1 (?)

?. , V a 1 (?), ? (d, b, ?) > V b 1 (?) et ? (d, c, ?) > V c 1 (?)

. Références,

N. G. Andjiga, B. Mbih, I. ;. Moyouwou, and C. Crem, From gehrlein-fishburn's method on frequencies representation to a straightforward proof of ehrhart's extended conjecture, vol.52, pp.67-76, 2006.

G. E. Anscombe, On frustration of the majority by fulfilment of the majority's will, Analysis, vol.36, issue.4, pp.161-168, 1976.

K. Arrow, Social Choice and Individual Values, 1951.

K. J. Arrow, Social choice and individual values, 1963.

E. Baharad and S. Et-nitzan, The inverse plurality rule-an axiomatization, Social Choice and Welfare, vol.25, issue.1, pp.173-178, 2005.

M. Balinski and R. Laraki, A theory of measuring, electing, and ranking, Proceedings of the National Academy of Sciences, vol.104, issue.21, pp.8720-8725, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00243040

A. I. Barvinok, A polynomial time algorithm for counting integral points in polyhedra when the dimension is fixed, Mathematics of Operations Research, vol.19, issue.4, pp.769-779, 1994.

J. Bentham, An Introduction to the Principles of Morals and Legislation, 1789.

A. Bergson, A reformulation of certain aspects of welfare economics, The Quarterly Journal of Economics, vol.52, issue.2, pp.310-334, 1938.

N. Betzler, J. Guo, and R. Niedermeier, Parameterized computational complexity of dodgson and young elections, Information and Computation, vol.208, pp.165-177, 2010.

B. Bjurulf, A probabilistic analysis of voting blocs and the occurrence of the paradox of voting, Charles E Merrill, pp.232-251, 1972.

D. Black, On the rationale of group decision-making, Journal of Political Economy, vol.56, issue.1, pp.23-34, 1948.

D. Black, The Theory of Committee and Elections, 1958.

J. C. Borda, Mémoire sur les élections au scrutin. Histoire de l'Académie Royale des Sciences, 1781.

D. Bouyssou, Ranking methods based on valued preference relations : A characterization of the net flow method, European Journal of Operational Research, vol.60, issue.1, pp.61-67, 1992.

D. Bouyssou and P. Perny, Aide multicritère à la décision et théorie du choix social. Nouvelles de la sciences et de la technologie, vol.15, pp.61-72, 1997.

S. Brams and P. Et-fishburn, Approval Voting, 1983.
URL : https://hal.archives-ouvertes.fr/hal-00119047

S. J. Brams, Paradoxes in politics : an introduction to the nonobvious in political science, 1976.

S. J. Brams and P. C. Et-fishburn, Approval voting, American Political Science Review, vol.72, issue.03, pp.831-847, 1978.
URL : https://hal.archives-ouvertes.fr/hal-00119047

S. J. Brams and P. C. Et-fishburn, Going from theory to practice : the mixed success of approval voting, Social Choice and Welfare, vol.25, issue.2, pp.457-474, 2005.

F. Brandt, Some remarks on dodgson's voting rule, Math. Log. Q, vol.55, issue.4, pp.460-463, 2009.

M. Brion, Points entiers dans les polytopes convexes, Séminaire Bourbaki n 780, vol.227, pp.145-169, 1993.

M. Brion, The structure of the polytope algebra, Tohoku Mathematical Journal, vol.49, issue.1, pp.1-32, 1997.

W. Bruns, B. Ichim, and C. Soger, Computations of volumes and ehrhart series in four candidates elections. Working paper, 2017.

C. D. Campbell and G. Tullock, A measure of the importance of cyclical majorities, The Economic Journal, vol.75, pp.853-857, 1965.

I. Caragiannis, J. A. Covey, M. Feldman, C. M. Homan, C. Kaklamanis et al., , 2012.

, On the approximability of dodgson and young elections, Artificial Intelligence, vol.187, pp.31-51

I. Caragiannis, C. Kaklamanis, N. Karanikolas, and A. Procaccia, Socially desirable approximations for dodgson's voting rule, Proceedings of the 11th ACM Conference on Electronic Commerce, pp.253-262, 2010.

D. P. Cervone, W. V. Gehrlein, and W. S. Zwicker, Which scoring rule maximizes condorcet efficiency under iac ?, Theory and Decision, vol.58, pp.145-185, 2005.

S. Ching, A simple characterization of plurality rule, Journal of Economic Theory, vol.71, issue.1, pp.298-302, 1996.

J. Condorcet, Essai sur l'application de l'analyse à la probabilité des décisions rendues à la pluralité des voix, 1785.

S. Courtin, B. Mbih, and I. Moyouwou, Are condorcet procedures so bad according to the reinforcement axiom ?, Social Choice and Welfare, vol.42, issue.4, pp.927-940, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00914870

S. Courtin, B. Mbih, I. Moyouwou, and T. Senné, The reinforcement axiom under sequential positional rules, Social Choice and Welfare, vol.35, pp.473-500, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00914864

R. R. Davidson and R. E. Odeh, Some inconsistencies in judging problems, Journal of Combinatorial Theory, Series A, vol.13, issue.2, pp.162-169, 1972.

F. Demeyer and C. R. Plott, The probabilityof a cyclical majority, Econometrica, vol.38, issue.2, pp.345-354, 1970.

C. L. Dodgson, E. B. Gardner, P. Hall, E. Stasy, and J. H. , University of Oxford.( Rééditionné dans McLean, I. and Urken, A. B. Classics of social choice, pp.279-286, 1873.

C. L. Dodgson, A method of taking votes on more than two issues, 1876.

I. Rééditionné-dans-mclean and A. B. Urken, Classics of social choice, pp.287-288

E. Black and D. , , 1958.

K. Dougherty and J. Edward, The Calculus of Consent and Constitutional Design. Studies in Public Choice, 2011.

B. Dutta, M. Jackson, and M. Et-le-breton, Strategic candidacy and voting procedures, Econometrica, vol.69, issue.4, pp.1013-1050, 2001.

F. Edgeworth, Mathematical Psychics : An Essay on the Application of Mathematics to the Moral Sciences. Reprints of economic classics, 1881.

K. Paul,

E. Ehrhart, Sur les polyhèdres rationnels homothétiques à n dimensions. Compte-rendus de l'académie des sciences, vol.254, pp.616-618, 1962.

E. Ehrhart, Sur un problème de géométrie diophantienne linéaire, J. Reine Angew. Math, vol.226, pp.1-49, 1967.

E. Ehrhart, Polynômes arithmétiques et méthode des polyèdres en combinatoire, de International Series of Numerical Mathematics, vol.35, 1977.

R. Farquharson, Theory of Voting, 1969.

M. Fellows, B. Jansen, D. Lokshtanov, F. Rosamond, and S. Saurabh, Determining the winner of a dodgson election is hard, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2010, pp.459-468, 2010.

M. Fellows, B. M. Jansen, D. Lokshtanov, F. A. Et-rosamond, and S. , Determining the winner of a dodgson election is hard, ARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Scienc, vol.8, 2010.

B. Fine and K. Fine, Social choice and individual ranking i. The Review of Economic Studies, vol.41, pp.303-322, 1974.

B. Fine and K. Fine, Social choice and individual rankings ii, The Review of Economic Studies, vol.41, issue.4, pp.459-475, 1974.

K. Fine, Conditions for the existence of cycles under majority and non-minority rules, Econometrica, vol.41, issue.5, pp.889-899, 1973.

P. Fishburn, A comparative analysis of group decision methods, Behavioral Science, vol.16, pp.538-544, 1971.

P. Fishburn, Condorcet social choice functions, SIAM Journal on Applied Mathematics, vol.33, pp.469-489, 1977.

P. Fishburn, Empirical comparisons of voting procedures, Behavioral Science, vol.31, pp.82-88, 1986.

P. Fishburn and W. Et-gehrlein, Borda's rule, positional voting, and condorcet's simple majority principle, Public Choice, vol.28, issue.1, pp.79-88, 1976.

P. Fishburn and W. Et-gehrlein, Borda's rule, positional voting, and condorcet's simple majority principle, Public Choice, vol.28, issue.1, pp.79-88, 1976.

P. Fishburn and W. Et-gehrlein, Social homogeneity and condorcet's paradox, Public Choice, vol.35, pp.403-419, 1980.

P. C. Fishburn, Voter concordance, simple majorities and group decision methods, Behavioral Science, vol.18, pp.364-376, 1973.

P. C. Fishburn, Paradoxes of voting, American Political Science Review, vol.68, issue.02, pp.537-546, 1974.

P. C. Fishburn, Axioms for approval voting : Direct proof, Journal of Economic Theory, vol.19, issue.1, pp.180-185, 1978.

P. C. Fishburn, Monotonicity paradoxes in the theory of elections, Discrete Applied Mathematics, vol.4, pp.119-134, 1982.

P. C. Fishburn and S. J. Brams, Paradoxes of preferential voting. Mathematics Magazine, vol.56, pp.207-214, 1983.

P. C. Fishburn and W. V. Et-gehrlein, Majority efficiencies for simple voting procedures : Summary and interpretation, Theory and Decision, vol.14, issue.2, pp.141-153, 1982.

W. Gehrlein, Probabilities of election outcomes with two parameters : The relative impact of unifying and polarizing candidates, Review of Economic Design, vol.9, issue.4, pp.317-336, 2005.

W. Gehrlein and P. Et-fishburn, Condorcet's paradox and anonymous preference profiles, Public Choice, vol.26, issue.1, pp.1-18, 1976.

W. V. Gehrlein, Condorcet's paradox, Theory and Decision, vol.15, issue.2, pp.161-197, 1983.
URL : https://hal.archives-ouvertes.fr/hal-01452557

W. V. Gehrlein, Condorcet efficiency of simple voting rules for large electorates, Economics Letters, vol.40, issue.1, pp.61-66, 1992.

W. V. Gehrlein, Obtaining representations for probabilities of voting outcomes with effectively unlimited precision integer arithmetic, Social Choice and Welfare, vol.19, issue.3, pp.503-512, 2002.

W. V. Gehrlein and P. Et-fishburn, The probability of the paradox of voting : a computable solution, Journal of Economic Theory, vol.13, pp.14-25, 1976.

W. V. Gehrlein and P. C. Et-fishburn, The probability of the paradox of voting : A computable solution, Journal of Economic Theory, vol.13, issue.1, pp.14-25, 1976.

W. V. Gehrlein and P. C. Et-fishburn, An analysis of voting procedures with nonranked voting, Behavioral Science, vol.22, pp.178-185, 1977.

W. V. Gehrlein and D. Lepelley, Voting Paradoxes and Group Coherence, 2011.
URL : https://hal.archives-ouvertes.fr/hal-01243452

A. Gibbard, Manipulation of voting schemes : a general result, Econometrica, vol.41, issue.4, pp.587-601, 1973.

A. Gueye-lô, Failures of reversal symmetry under two common voting rules, Economics Bulletin, vol.34, issue.3, pp.1970-1975, 2014.

G. T. Guilbaud, Les théories de l'intérêt général et le problème logique de l'agrégation, Economie appliquée, vol.5, issue.4, pp.501-551, 1952.

E. Hemaspaandra, L. A. Hemaspaandra, and J. Et-rothe, Exact analysis of dodgson elections : Lewis carroll's 1876 voting system is complete for parallel access to np, J. ACM, vol.44, issue.6, pp.806-825, 1997.

C. Hillinger, On the possibility of democracy and rational collective choice, 2004.

C. Homan and L. A. Hemaspaandra, Guarantees for the success frequency of an algorithm for finding dodgson election winners, Journal of Heuristics, vol.15, pp.403-423, 2009.

H. Huang and V. Chua, Analytical representation of probabilities under the iac condition, Social Choice and Welfare, vol.17, pp.143-155, 2000.

K. Inada, A note on the simple majority decision rule, Econometrica, vol.32, issue.4, pp.525-531, 1964.

K. Inada, The simple majority decision rule, Econometrica, vol.37, issue.3, pp.490-506, 1969.

J. S. Kelly, Voting anomalies, the number of voters, and the number of alternatives, Econometrica, vol.42, issue.2, pp.239-251, 1974.

J. S. Kelly, Strategy-proofness and social choice functions without singlevaluedness, Econometrica, vol.45, issue.2, pp.439-485, 1977.

J. G. Kemeny, Mathematics without numbers, Daedalus, vol.88, issue.4, pp.577-591, 1959.

C. Klamler, A comparison of the dodgson method and the copeland rule, Economics Bulletin, vol.4, pp.1-7, 2003.

C. Klamler, The dodgson ranking and its relation to kemeny's method and slater's rule, Social Choice and Welfare, vol.23, pp.91-102, 2004.

K. Kuga and H. Nagatani, Voter antagonism and the paradox of voting, Econometrica, vol.42, issue.6, pp.1045-1067, 1974.

T. Kurihara, A simple characterization of the anti-plurality rule, Economics Letters, vol.168, issue.C, pp.110-111, 2018.

D. Lepelley, Une caractérisation du vote à la majorité simple, RAIRO-Oper. Res, vol.26, pp.361-365, 1992.

D. Lepelley, On the probability of electing the condorcet, Mathematical Social Sciences, vol.25, pp.105-116, 1993.

D. Lepelley and W. Et-gehrlein, Strong condorcet efficiency of scoring rules, Economics Letters, vol.68, pp.157-164, 2000.

D. Lepelley, A. Louichi, and H. Smaoui, On ehrhart polynomials and probability calculations in voting theory, Social Choice and Welfare, vol.30, issue.3, pp.363-383, 2008.
URL : https://hal.archives-ouvertes.fr/hal-01245310

D. Lepelley and B. Mbih, The proportion of coalitionally unstable situations under the plurality rule, Economics Letters, vol.24, pp.311-315, 1987.

D. Lepelley and B. Mbih, The vulnerability of four social choice functions to coalitional manipulation of preferences, Social Choice and Welfare, vol.11, pp.253-265, 1994.

D. Lepelley and B. Mbih, Strategic manipulation in committees using the plurality rule : Alternative concepts and frequency calculations, Group Decision and Negotiation, vol.6, pp.119-138, 1997.

D. Lepelley and V. Et-merlin, Scoring run-off paradoxes for variable electorates, Economic Theory, vol.17, issue.1, pp.53-80, 2001.

D. Lepelley, I. Moyouwou, and H. Smaoui, Monotonicity paradoxes in three-candidate elections using scoring elimination rules, Social Choice and Welfare, vol.50, issue.1, pp.1-33, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01697627

T. Marchant, Valued relations aggregation with the borda method, Journal of Multi-criteria Decision Analysis, vol.5, pp.127-132, 1996.

A. Marshall, de Principles of Economics, Principles of Economics. Numéro, vol.1, 1890.

M. Martin and V. Et-merlin, The stability set as a social choice correspondence, Mathematical Social Sciences, vol.44, issue.1, pp.91-113, 2002.
URL : https://hal.archives-ouvertes.fr/halshs-00069520

M. May, A set of independent necessary and sufficient conditions for simple majority decision, Econometrica, vol.20, issue.4, pp.680-684, 1952.

B. Mbih and A. Valeu, La vulnérabilité de la règle de la majorité aux paradoxes d'anscombe et d'ostrogorski : une analyse comparative, Revue Internationale Des Economistes De Langue Française, vol.1, issue.1, pp.171-191, 2016.

B. Mbih and X. Zhao, No-show paradoxes under parliamentary agendas, Annals of Economics and Statistics, pp.127-147, 2011.
URL : https://hal.archives-ouvertes.fr/halshs-00656614

J. Mccabe-dansted, Approximability and computational feasibility of dodgson's rule, 2006.

J. Mccabe-dansted, Dodgson's rule : Approximations and absurdity, Proceedings of the 2nd International Workshop on Computational Social Choice (COMSOC), pp.371-382, 2008.

J. Mccabe-dansted, G. Pritchard, and A. Slinko, Approximability of dodgson's rule. Social Choice and Welfare, vol.31, pp.311-330, 2008.

D. Mcgarvey, A theorem on the construction of voting paradoxes, Econometrica, vol.21, pp.608-610, 1953.

V. Merlin, The axiomatic characterizations of majority voting and scoring rules, Mathematical Social Sciences, pp.87-109, 2003.

V. Merlin, M. , T. Valognes, and F. , On the probability that all the voting rules select the same winner, Journal of Mathematical Economics, vol.33, pp.183-207, 2000.

V. Merlin and J. Et-naeve, Implementation of social choice functions via demanding equilibria. Diskussionspapiere aus dem Institut für Volkswirtschaftslehre der Universität Hohenheim 191, 2000.

V. Merlin and M. Tataru, On the relationship of the condorcet winner and positional voting rules, Mathematical Social Sciences, vol.34, issue.1, pp.81-90, 1997.

V. Merlin, M. Tataru, and F. Valognes, On the likelihood of condorcet's profiles, Social Choice and Welfare, vol.19, issue.1, pp.193-206, 2002.

I. Merrill and S. , A comparison of efficiency of multicandidate electoral systems, American Journal of Political Science, vol.28, pp.23-48, 1984.

I. Merrill and S. , A comparison of efficiency of multicandidate electoral systems, American Journal of Political Science, vol.28, pp.23-48, 1984.

I. Merrill and S. , A statistical model for condorcet efficiency based on simulation under spatial model assumptions, Public Choice, vol.47, pp.389-403, 1985.

I. Merrill and S. , Making Multicandidate Elections More Democratic, 1988.

H. Moulin, Axioms of Cooperative Decision Making, 1988.

R. B. Myerson, Axiomatic derivation of scoring rules without the ordering assumption, Social Choice and Welfare, vol.12, pp.59-74, 1995.

H. Nurmi, Comparing Voting Systems, 1987.

H. Nurmi, Probability models in constitutional choice, European Journal of Political Economy, vol.6, issue.1, pp.107-117, 1990.

H. Nurmi, An assessment of voting system simulations, Public Choice, vol.73, issue.4, pp.459-87, 1992.

H. Nurmi, Voting paradoxes and referenda, Social Choice and Welfare, vol.15, issue.3, pp.333-350, 1998.

H. Nurmi, Voting Paradoxes and How to Deal with Them, 1999.

H. Nurmi, Voting Procedures under Uncertainty, 2002.

H. Nurmi, A comparison of some distance-based choice rules in ranking environments, Theory and Decision, vol.57, issue.1, pp.5-24, 2004.

H. Nurmi, A responsive voting system, Economics of Governance, vol.6, issue.1, pp.63-74, 2005.

H. Nurmi, Voting Theory, Group Decision and Negotiation Perspective, vol.5, pp.101-123, 2010.

D. Springer,

H. Nurmi, On the relevance of theoretical results to voting system choice, Electoral Systems, Studies in Choice and Welfare, pp.255-274, 2012.

H. Nurmi and T. Et-meskanen, Voting paradoxes and mcdm. Group Decision and Negotiation, vol.9, pp.297-313, 2000.

M. Ostrogorski, La démocratie et l'organisation des partis politiques, 1902.

P. K. Pattanaik, Voting and Collective Choice, 1971.

P. K. Pattanaik, Strategy and Group Choice, 1978.

A. C. Pigou, The economics of welfare, 1920.

J. Pérez, The strong no show paradoxes are a common flaw in condorcet voting correspondences, Social Choice and Welfare, vol.18, issue.3, pp.601-616, 2001.

D. W. Rae and H. Daudt, he ostrogorski paradox : a peculiarity of compound majority decision, European Journal of Political Research, vol.4, pp.391-398, 1976.

T. C. Ratliff, A comparison of dodgson's method and kemeny's rule, Social Choice and Welfare, vol.18, pp.79-89, 2001.

T. C. Ratliff, A comparison of dodgson's method and the borda count, economic theory, Economic Theory, vol.20, pp.357-372, 2002.

A. Recknagel, An approach to efficiently calculating dodgson-scores using heuristics and parallel computing, Publications of the Institute of Cognitive Science, vol.1, 2015.

M. Regenwetter, B. Grofman, A. A. Marley, and I. Et-tsetlin, , 2006.

, Behavioral Social Choice : Probabilistic Models, Statistical Inference, and Applications

J. Richelson, A comparative analysis of social choice functions, Behavioral Science, vol.20, pp.331-337, 1975.

J. Richelson, Conditions on social choice functions, Public Choice, vol.31, issue.1, pp.79-110, 1977.
DOI : 10.1007/bf01718975

J. Richelson, Some further results on consistency, rationality and collective choice, Review of Economic Studies, vol.45, issue.2, pp.343-346, 1978.
DOI : 10.2307/2297348

J. Richelson, A comparative-analysis of social choice functions, i, ii, iii : A summary, Behavioral Science, vol.24, pp.355-355, 1979.

J. T. Richelson, Characterization result for plurality rule, Journal of Economic Theory, vol.19, pp.548-550, 1978.

F. S. Roberts, Characterizations of the plurality function, Mathematical Social Sciences, vol.21, pp.101-127, 1991.

D. Saari, Consistency of decision processes, Annals of Operations Research, vol.23, pp.103-137, 1990.
DOI : 10.1007/bf02204841

URL : http://www.kellogg.northwestern.edu/research/math/papers/842.pdf

D. Saari, Geometry of Voting, 1994.
DOI : 10.1007/978-3-642-48644-9

D. Saari, Which is better : the condorcet or borda winner ? Social Choice and Welfare, vol.26, pp.107-129, 2006.
DOI : 10.1007/s00355-005-0046-2

D. G. Saari, The source of some paradoxes from social choice and probability, Journal of Economic Theory, vol.41, issue.1, pp.1-22, 1987.
DOI : 10.1016/0022-0531(87)90002-0

URL : http://www.kellogg.northwestern.edu/research/math/papers/609.pdf

D. G. Saari, A dictionary for voting paradoxes, Journal of Economic Theory, vol.48, issue.2, pp.443-475, 1989.
DOI : 10.1016/0022-0531(89)90037-9

URL : http://www.kellogg.northwestern.edu/research/math/papers/745.pdf

D. G. Saari, Basic Geometry of Voting, 1995.
DOI : 10.1007/978-3-642-57748-2

D. G. Saari, Informational geometry of social choice, Social Choice and Welfare, vol.14, issue.2, pp.211-232, 1997.
DOI : 10.1007/978-3-642-60891-9_4

D. G. Saari, Explaining all three-alternative voting outcomes, Journal of Economic Theory, vol.87, issue.2, pp.313-355, 1999.
DOI : 10.1006/jeth.1999.2541

D. G. Saari, Mathematical structure of voting paradoxes, Economic Theory, vol.15, pp.1-53, 2000.
DOI : 10.1007/s001990050001

D. G. Saari, Disposing Dictators, Demystifying Voting Paradoxes, 2008.
DOI : 10.1016/j.mcm.2008.05.016

URL : https://doi.org/10.1016/j.mcm.2008.05.016

D. G. Saari and S. Barney, Consequences of reversing preferences, The Mathematical Intelligencer, vol.25, pp.17-31, 2003.
DOI : 10.1007/bf02984858

D. G. Saari and M. M. Tataru, The likelihood of dubious election outcomes, Economic Theory, vol.13, issue.2, pp.345-363, 1999.

M. Salles, The best voting method : A review of voting procedures by michael dummett, Social Choice and Welefare, vol.6, pp.337-346, 1989.

P. Samuelson, Foundations of economic analysis. Cambridge, 1947.

M. A. Satterthwaite, Strategy-proofness and arrow's conditions : Existence and correspondence theorems for voting procedures and social welfare functions, Journal of Economic Theory, vol.10, issue.2, pp.187-217, 1975.

M. Schulze, A new monotonic, clone independent, reversal symmetric, and condorcet-consistent single winner election method, Social Choice and Welfare, vol.36, pp.267-303, 2011.

M. Schulze, The schulze method of voting, 2018.

A. Sen, Quasi transitivity, rational choice and collective decisions, Review of Economic Studies, vol.36, issue.3, pp.381-393, 1969.

A. Sen, The impossibility of a paretian liberal, Journal of Political Economy, vol.78, issue.1, pp.152-57, 1970.

A. Sen and P. K. Pattanaik, Necessary and sufficient conditions for rational choice under majority decision, Journal of Economic Theory, vol.1, issue.2, pp.178-202, 1969.

A. K. Sen, A possibility theorem on majority decisions, Econometrica, vol.34, issue.2, pp.491-499, 1966.

A. K. Sen, Collective choice and social welfare, vol.5, 1970.

P. Slater, Inconsistencies in a schedule of paired comparisons, Biometrika, vol.48, issue.3/4, pp.303-312, 1961.

J. H. Smith, Aggregation of preferences with variable electorate, Econometrica, vol.41, issue.6, pp.1027-1068, 1973.

T. N. Tideman, Independence of clones as a criterion for voting rules, Social Choice and Welfare, vol.4, pp.185-206, 1987.

O. Williamson and T. Sergent, Social choice : A probabilistic approach, Economic Journal, vol.77, pp.797-813, 1967.

H. P. Young, An axiomatization of borda's rule, Journal of Economic Theory, vol.9, issue.1, pp.43-52, 1974.

H. P. Young, A note on preference aggregation, Econometrica, vol.42, issue.6, pp.1129-1160, 1974.

H. P. Young, Social choice scoring functions, SIAM Journal on Applied Mathematics, vol.28, pp.824-838, 1975.

H. P. Young and A. Et-levenglick, A consistent extension of condorcet's election principle, SIAM Journal on Applied Mathematics, vol.35, issue.2, pp.285-300, 1978.

L. and .. .. , , vol.21

A. .. Le-reste-des-pré-ordres-complets-sur, , p.22

. , Les règles positionnelles à deux tours

.. .. Le-paradoxe-d'ostrogorski,

S. .. , Exemple 2.3.9 : la symétrie inverse sous les RP, p.60

S. .. , Exemple 2.3.10 : La symétrie inverse sous des RP, p.61

. , 12 : la symétrie inverse sous les règles positionnelles à deux tours

. , Les fréquences de violation de la symétrie inverse par les RP

. , Les fréquences de violation de la symétrie inverse sous les RP 2T

. , 13 : La symétrie inverse sous les RP S pour quatre candidats, vol.87

. , Les fréquences de violation de la symétrie inverse sous les RP S en domaine bipolaire sous les modèles IAC et IC

. .. , 17 : La symétrie inverse sous des RPS, p.111

, Les fréquences de violation de la symétrie inverse par les RPS en domaine bipolaire {ab} {cd} sous les modèles IAC et IC, p.116

. .. , Les fréquences de violation de la symétrie inverse sous les RP S en domaine bipolaire {a} {b, c, d} sous le modèles IAC, vol.118

. Le-score-de-dodgson,

. Le-score-de-dodgson,

. , Les seize ordres de préférence possibles

L. .. Huit-ordres-de-préférence-possibles, , p.153

. .. Les-quatre-ordres-de-préférence-possibles, , p.155

. , Les deux ordres de préférence possibles

L. .. Dix-huit-ordres-de-préférence-possibles, , p.160

. .. Les-douze-ordres-de-préférence-possibles, , p.165

. , Les six ordres de préférence possibles

, 10 Les fréquences de violation de l'homogénéité par la règle de Dodgson, p.177

. Le-score-de-dodgson,