. La-méthode-de-baldwin, P. Vtid, and M. La-méthode-de-schulze, De nouveau, ces deux derniers présentent des performances très similaires

. Démonstration, Puisque g ne dépend que de P(?), on peut dénir h : (R C ) V ? E de telle sorte que g = h ? P. Puisque (R C ) V est muni de la mesure discrète, h est mesurable ; et par dénition d'un espace électoral mesurable

. Dans-le-théorème-de-tranchage, 9, ce lemme assure que, pour tout y, l'indicatrice de manipulabilité MC fy est mesurable. Par conséquent, ? ? MC (f y ) est bien déni. De même, dans le théorème d'optimalité 5.15, ce lemme assure que MC g?P est mesurable

. Cet-exemple-nlabovitz, Par exemple, une telle topologie plate de connexion dière de la topologie hiérarchique BGP historique d'Internet. Néanmoins, notre but ici est de donner un modèle simple où les coûts dérivent d'une forme de métrique sous-jacente. C'est pourquoi se baser sur la géographie du réseau est un choix naturel. On notera que certaines études récentes montrent une évolution vers des topologies plus plates que dans le passé, 2010.

F. Critère-du-favori-majoritaire, CVTI Condorcication de VTI

. Max and . Maximin, MC Manipulation / manipulable par coalition MCI Manipulation / manipulable par coalition ignorante. MI Manipulation individuelle / manipulable individuellement. MT Manipulation triviale / manipulable trivialement

N. Méthode-de-nanson, PO Méthode par paires ordonnées. ssi Si et seulement si

D. Bibliographie-fuad-aleskerov, R. Karabekyan, V. Sanver, and . Yakuba, Computing the degree of manipulability in the case of multiple choice, Computational Social Choice (COMSOC, p.27, 2008.

F. Aleskerov and E. Kurbanov, Degree of manipulability of social choice procedures In Society for the Advancement of Economic Theory, éditeur : Current trends in economics : theory and applications, Studies in economic theory, p.1327, 1999.

K. Arrow, A diculty in the concept of social welfare, The Journal of Political Economy, vol.58, issue.4, p.328346, 1950.

N. Aswal, S. Chatterji, and A. Sen, Dictatorial domains, Economic Theory, vol.22, issue.1, p.4562, 2003.
DOI : 10.1007/s00199-002-0285-8

H. Aziz, S. Gaspers, N. Mattei, N. Narodytska, and T. Walsh, Ties matter : Complexity of manipulation when tie-breaking with a random vote, AAAI, 2013.

M. Balinski and R. Laraki, Majority Judgment : Measuring, Ranking, and Electing, 2010.
DOI : 10.7551/mitpress/9780262015134.001.0001

S. Barberá, Strategy-Proofness and Pivotal Voters: A Direct Proof of the Gibbard-Satterthwaite Theorem, International Economic Review, vol.24, issue.2, pp.413-417, 1983.
DOI : 10.2307/2648754

S. Barberà, An introduction to strategy-proof social choice functions, Social Choice and Welfare, vol.18, issue.4, p.619653, 2001.
DOI : 10.1007/s003550100151

S. Barberá and . Peleg, Strategy-proof voting schemes with continuous preferences, Social Choice and Welfare, vol.48, issue.1, p.3138, 1990.
DOI : 10.1007/BF01832918

J. Bartholdi and J. Orlin, Single transferable vote resists strategic voting, Social Choice and Welfare, vol.8, issue.4, p.341354, 1991.
DOI : 10.1007/BF00183045

J. Bartholdi, C. Tovey, and M. Trick, The computational diculty of manipulating an election, Social Choice and Welfare, vol.6, p.227241, 1989.

J. Bartholdi, C. Tovey, and M. Trick, Voting schemes for which it can be dicult to tell who won the election, Social Choice and welfare, vol.6, issue.2, p.157165, 1989.

E. Beltrami, Résolution du problème de reporter les points d'une surface sur un plan, de manière que les lignes géodésiques soient représentée par des lignes droites, 1866.

E. Beltrami, Essai d'interprétation de la géométrie noneuclidéenne, Trad. par J. Hoüel. Ann. Sci. École Norm. Sup, vol.6, p.251288, 1869.

J. Benoît, The Gibbard???Satterthwaite theorem: a simple proof, Economics Letters, vol.69, issue.3, p.319322, 2000.
DOI : 10.1016/S0165-1765(00)00312-8

D. Bernheim, B. Peleg, and M. Whinston, Coalition-Proof Nash Equilibria I. Concepts, Journal of Economic Theory, vol.42, issue.1, p.112, 1987.
DOI : 10.1016/0022-0531(87)90099-8

N. Betzler, J. Guo, and R. Niedermeier, Parameterized computational complexity of Dodgson and Young elections, Information and Computation, vol.208, issue.2, p.165177, 2010.

N. Betzler, R. Niedermeier, and G. Woeginger, Unweighted coalitional manipulation under the Borda rule is NP-hard, Proceedings of the 22th International Joint Conference on Articial Intelligence (IJCAI '11), 2011.

D. Black, The theory of committees and elections, 1958.
DOI : 10.1007/978-94-009-4225-7

J. Blin and M. Satterthwaite, Strategy-proofness and singlepeakedness, Public Choice, vol.26, p.5158, 1976.
DOI : 10.1007/bf01725792

K. Border and J. S. Jordan, Straightforward Elections, Unanimity and Phantom Voters, The Review of Economic Studies, vol.50, issue.1, p.153170, 1983.
DOI : 10.2307/2296962

S. Brams, Voting procedures éditeurs : Handbook of Game Theory with Economic Applications, de Handbook of Game Theory with Economic Applications, chapitre 30, p.10551089, 1994.

S. Brams, Approval voting éditeurs : The Encyclopedia of Public Choice, p.344346, 2003.

S. Brams and P. Fishburn, Approval voting, American Political Science Review, vol.72, p.831847, 1978.
URL : https://hal.archives-ouvertes.fr/hal-00119047

F. Brandt and M. Brill, Necessary and sucient conditions for the strategyproofness of irresolute social choice functions, Proceedings of the 13th Conference on Theoretical Aspects of Rationality and Knowledge, p.136142, 2011.

S. Brânzei, I. Caragiannis, J. Morgenstern, and A. Procaccia, How bad is selsh voting, Twenty-Seventh AAAI Conference on Articial Intelligence, 2013.

M. Brill and V. Conitzer, Strategic voting and strategic candidacy, Proceedings of the Twenty-Ninth AAAI Conference on Articial Intelligence, 2015.

M. Brill and F. Fischer, The price of neutrality for the ranked pairs method, COMSOC, vol.2012, p.95, 2012.

C. Campbell and G. Tullock, A Measure of the Importance of Cyclical Majorities, The Economic Journal, vol.75, issue.300, p.853857, 1965.
DOI : 10.2307/2229705

I. Caragiannis, J. Covey, M. Feldman, C. Homan, C. Kaklamanis et al., Ariel Procaccia et Jerey Rosenschein : On the approximability of Dodgson and Young elections, Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms, p.10581067, 2009.

I. Caragiannis, C. Kaklamanis, N. Karanikolas, and A. Procaccia, Socially desirable approximations for dodgson's voting rule, ACM Transactions on Algorithms (TALG), vol.10, issue.2, p.6, 2014.

J. Chamberlin, J. Cohen, and C. Coombs, Social Choice Observed: Five Presidential Elections of the American Psychological Association, The Journal of Politics, vol.46, issue.2, p.479502, 1984.
DOI : 10.2307/2130971

G. Chichilnisky, Von Neumann-Morgenstern Utilities and Cardinal Preferences, Mathematics of Operations Research, vol.10, issue.4, p.633641, 1985.
DOI : 10.1287/moor.10.4.633

T. Coleman and V. Teague, On the complexity of manipulating elections, Thirteenth Computing : The Australasian Theory Symposium (CATS2007), volume 65 de CRPIT, p.2533, 2007.

M. J. , A. Nicolas-de-caritat, and C. Marquis-de, Essai sur l'application de l'analyse à la probabilité des décisions rendues à la pluralité des voix, p.1785

V. Conitzer, J. Lang, and T. Sandholm, How many candidates are needed to make elections hard to manipulate?, Proceedings of the 9th conference on Theoretical aspects of rationality and knowledge , TARK '03, p.201214, 2003.
DOI : 10.1145/846241.846268

V. Conitzer and T. Sandholm, Complexity of manipulating elections with few candidates, Eighteenth national conference on Articial intelligence, p.314319, 2002.

V. Conitzer and T. Sandholm, Universal voting protocol tweaks to make manipulation hard, Proceedings of the 18th international joint conference on Articial intelligence, p.781788, 2003.

V. Conitzer and T. Sandholm, Nonexistence of voting rules that are usually hard to manipulate, Proceedings of the 21st national conference on Articial intelligence, p.627634, 2006.

V. Conitzer, T. Sandholm, and J. Lang, When are elections with few candidates hard to manipulate?, Journal of the ACM, vol.54, issue.3, 2007.
DOI : 10.1145/1236457.1236461

J. Davies, G. Katsirelos, N. Narodytska, and T. Walsh, Complexity of and algorithms for Borda manipulation, p.657662, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00642093

J. Davies, G. Katsirelos, N. Narodytska, T. Walsh, and L. Xia, Complexity of and algorithms for the manipulation of Borda, Nanson's and Baldwin's voting rules, Artificial Intelligence, vol.217, p.2042, 2014.
DOI : 10.1016/j.artint.2014.07.005

F. Demeyer and C. Plott, The Probability of a Cyclical Majority, Econometrica, vol.38, issue.2, p.345354, 1970.
DOI : 10.2307/1913015

A. Dhamdhere and C. Dovrolis, The Internet is flat, Proceedings of the 6th International COnference on, Co-NEXT '10, p.21, 2010.
DOI : 10.1145/1921168.1921196

T. Downs, Some Relationships Among the Von Mises Distributions of Different Dimensions, Biometrika, vol.53, issue.1/2, p.269272, 1966.
DOI : 10.2307/2334080

J. Duggan and T. Schwartz, Strategic manipulability without resoluteness or shared beliefs : Gibbard-Satterthwaite generalized. Social Choice and Welfare, p.8593, 2000.

F. Durand, B. Kloeckner, F. Mathieu, and L. Noirie, Geometry on the utility sphere, Proceedings of the 4th International Conference on Algorithmic Decision Theory (ADT), 2015.

F. Durand, F. Mathieu, and L. Noirie, Manipulability of voting systems Groupe de travail Displexity, 2012.

F. Durand, F. Mathieu, and L. Noirie, On the manipulability of voting systems: application to multi-operator networks, Proceedings of the 9th International Conference on Network and Service Management (CNSM 2013), p.292297, 2013.
DOI : 10.1109/CNSM.2013.6727849
URL : https://hal.archives-ouvertes.fr/hal-00874096

F. Durand, F. Mathieu, and L. Noirie, Élection du best paper AlgoTel 2012 : étude de la manipulabilité, AlgoTel 2014 16èmes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications, 2014.

F. Durand, F. Mathieu, and L. Noirie, Élection d'un chemin dans un réseau : étude de la manipulabilité, AlgoTel 2014 16èmes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications, 2014.

F. Durand, F. Mathieu, and L. Noirie, Making a voting system depend only on orders of preference reduces its manipulability rate, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01009136

F. Durand, F. Mathieu, and L. Noirie, Making most voting systems meet the Condorcet criterion reduces their manipulability, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01009134

F. Durand, F. Mathieu, and L. Noirie, Reducing manipulability, Poster présenté au 5th International Workshop on Computational Social Choice (COMSOC), 2014.
URL : https://hal.archives-ouvertes.fr/hal-01095992

M. Bhaskar-dutta, M. L. Jackson, and . Breton, Strategic candidacy and voting procedures, Econometrica, vol.69, issue.4, p.10131037, 2001.

M. Bhaskar-dutta, M. L. Jackson, and . Breton, Voting by Successive Elimination and Strategic Candidacy, Journal of Economic Theory, vol.103, issue.1, pp.190-218, 2002.
DOI : 10.1006/jeth.2001.2862

L. Ehlers, H. Peters, and T. Storcken, Threshold strategy-proofness: on manipulability in large voting problems, Games and Economic Behavior, vol.49, issue.1, p.103116, 2004.
DOI : 10.1016/j.geb.2003.10.004

E. Elkind and H. Lipmaa, Hybrid Voting Protocols and Hardness of Manipulation, Xiaotie Deng et Ding-Zhu Du, éditeurs : Algorithms and Computation, p.206215, 2005.
DOI : 10.1007/11602613_22

E. Elkind and H. Lipmaa, Small coalitions cannot manipulate voting éditeurs : Financial Cryptography and Data Security, Lecture Notes in Computer Science, vol.3570, p.578578, 2005.

P. Faliszewski and A. Procaccia, AI's war on manipulation : Are we winning ? AI Magazine, p.5364, 2010.

P. Favardin and D. Lepelley, Some Further Results on the Manipulability of Social Choice Rules, Social Choice and Welfare, vol.16, issue.3, p.485509, 2006.
DOI : 10.1007/s00355-006-0106-2
URL : https://hal.archives-ouvertes.fr/halshs-00068839

P. Favardin, D. Lepelley, and J. Serais, Borda rule, Copeland method and strategic manipulation, Review of Economic Design, vol.7, issue.2, p.213228, 2002.
DOI : 10.1007/s100580200073
URL : https://hal.archives-ouvertes.fr/halshs-00069522

A. Feldman, Welfare economics and social choice theory, 1980.
DOI : 10.1007/978-1-4615-8141-3

P. Fishburn, Utility Theory for Decision Making, 1970.

P. Fishburn, Nonlinear preference and utility theory. Johns Hopkins series in the mathematical sciences, 1988.

P. Fishburn and S. Brams, Ecacy, power and equity under approval voting, Public Choice, vol.37, issue.3, p.425434, 1981.

P. Fishburn and W. Gehrlein, Borda's rule, positional voting, and Condorcet's simple majority principle, Public Choice, vol.9, issue.1, p.7988, 1976.
DOI : 10.1007/BF01718459

P. Fishburn, W. Gehrlein, and E. Maskin, Condorcet proportions and Kelly's conjectures, Discrete Applied Mathematics, vol.1, issue.4, p.229252, 1979.
DOI : 10.1016/0166-218X(79)90001-5

M. Garman and M. Kamien, The paradox of voting: Probability calculations, Behavioral Science, vol.41, issue.4, p.306316, 1968.
DOI : 10.1002/bs.3830130405

S. Gaspers, T. Kalinowski, N. Narodytska, and T. Walsh, Coalitional manipulation for Schulze's rule, Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems International Foundation for Autonomous Agents and Multiagent Systems, p.431438, 2013.

J. Geanakoplos, Three brief proofs of Arrow's impossibility theorem, Economic Theory, vol.26, issue.1, p.211215, 2005.

W. Gehrlein, The expected probability of Condorcet's paradox, Economics Letters, vol.7, issue.1, p.3337, 1981.
DOI : 10.1016/0165-1765(81)90107-5

W. Gehrlein, Approximating the probability that a Condorcet winner exists, 1999.

W. Gehrlein, Condorcet's Paradox. Theory and Decision Library C, 2006.
URL : https://hal.archives-ouvertes.fr/hal-01452557

W. Gehrlein and P. Fishburn, The probability of the paradox of voting: A computable solution, Journal of Economic Theory, vol.13, issue.1, p.1425, 1976.
DOI : 10.1016/0022-0531(76)90063-6

A. Gibbard, Manipulation of Voting Schemes: A General Result, Econometrica, vol.41, issue.4, p.587601, 1973.
DOI : 10.2307/1914083

A. Gibbard, Manipulation of Schemes that Mix Voting with Chance, Econometrica, vol.45, issue.3, p.665681, 1977.
DOI : 10.2307/1911681

A. Gibbard, Straightforwardness of Game Forms with Lotteries as Outcomes, Econometrica, vol.46, issue.3, p.595614, 1978.
DOI : 10.2307/1914235

A. Gibbard, SOCIAL CHOICE AND THE ARROW CONDITIONS, Economics and Philosophy, vol.30, issue.03, p.269284, 2014.
DOI : 10.1017/S026626711400025X

P. Gärdenfors, Manipulation of social choice functions, Journal of Economic Theory, vol.13, issue.2, p.217228, 1976.
DOI : 10.1016/0022-0531(76)90016-8

P. Gärdenfors, A concise proof of theorem on manipulation of social choice functions, Public Choice, vol.10, issue.1, p.137142, 1977.
DOI : 10.1007/BF01718676

J. Green-armytage, Four Condorcet-Hare hybrid methods for singlewinner elections. Voting matters, p.114, 2011.

J. Green-armytage, Strategic voting and nomination. Social Choice and Welfare, p.111138, 2014.

J. Green-armytage, N. Tideman, and R. Cosman, Statistical evaluation of voting rules, Social Choice and Welfare, vol.21, issue.954, 2014.
DOI : 10.1007/s00355-015-0909-0

B. Grofman and S. Feld, If you like the alternative vote (a.k.a. the instant runo), then you ought to know about the Coombs rule, Electoral Studies, vol.23, issue.4, p.641659, 2004.

F. Guénard and G. Lelièvre, Compléments d'analyse. Numéro 1 in Compléments d'analyse, E.N.S, 1985.

P. Hammond, Interpersonal comparisons of utility: Why and how they are and should be made, Interpersonal Comparisons of Well-Being, 1991.
DOI : 10.1017/CBO9781139172387.008

L. Hemaspaandra, R. Lavaee, and C. Menton, Schulze and rankedpairs voting are xed-parameter tractable to bribe, manipulate, and control, Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems International Foundation for Autonomous Agents and Multiagent Systems, p.13451346, 2013.

A. Jennings, Monotonicity and Manipulability of Ordinal and Cardinal Social Choice Functions, BiblioBazaar, 2011.

B. Jones, B. Radcliff, C. Taber, and R. Timpone, Condorcet Winners and the Paradox of Voting: Probability Calculations for Weak Preference Orders, American Political Science Review, vol.82, issue.01, p.137144, 1995.
DOI : 10.1017/CBO9780511666742

N. Keller, A tight quantitative version of Arrow???s impossibility theorem, Journal of the European Mathematical Society, vol.14, issue.5, p.13311355, 2012.
DOI : 10.4171/JEMS/334

J. Kelly, Voting Anomalies, the Number of Voters, and the Number of Alternatives, Econometrica, vol.42, issue.2, p.239251, 1974.
DOI : 10.2307/1911974

J. Kelly, Almost all social choice rules are highly manipulable, but a few aren't. Social Choice and Welfare, p.161175, 1993.

J. Kemeny, Mathematics without numbers, Daedalus, vol.88, p.575591, 1959.

K. H. Kim and F. W. Roush, Statistical manipulability of social choice functions. Group Decision and Negotiation, p.263282, 1996.

B. Kloeckner, Un bref aperçu de la géométrie projective, Calvage & Mounet, 2012.

K. Konczak and J. Lang, Voting procedures with incomplete preferences, Proc. IJCAI-05 Multidisciplinary Workshop on Advances in Preference Handling, 2005.

D. Kreps, A Course in Microeconomic Theory, 1990.

C. Labovitz, S. Iekel-johnson, and D. Mcpherson, Jon Oberheide et Farnam Jahanian : Internet inter-domain trac, Proceedings of the ACM SIGCOMM 2010 conference, p.7586, 2010.

J. Lang, N. Maudet, and M. Polukarov, New Results on Equilibria in Strategic Candidacy, Algorithmic Game Theory, p.1325, 2013.
DOI : 10.1007/978-3-642-41392-6_2
URL : https://hal.archives-ouvertes.fr/hal-01216397

J. Laslier, Spatial Approval Voting, Political Analysis, vol.4, issue.02, pp.160-185, 2006.
DOI : 10.1007/s00355-003-0232-z

J. Laslier, The Leader Rule, Journal of Theoretical Politics, vol.86, issue.1, p.113136, 2009.
DOI : 10.1177/0951629808097286
URL : https://hal.archives-ouvertes.fr/hal-00363218

J. Laslier and K. Van-der-straeten, A live experiment on approval voting, Experimental Economics, vol.18, issue.1, p.97105, 2008.
DOI : 10.1007/s10683-006-9149-6
URL : https://hal.archives-ouvertes.fr/hal-00363212

J. Laslier, Le vote et la règle majoritaire. CNRS science politique, CNRS Editions, 2004.

S. Laveau and O. Faugeras, Oriented projective geometry for computer vision, ECCV96, pages 147156, 1996.
DOI : 10.1007/BFb0015531

D. Lepelley, A. Louichi, and H. Smaoui, On Ehrhart polynomials and probability calculations in voting theory, Social Choice and Welfare, vol.25, issue.6, p.363383, 2008.
DOI : 10.1007/s00355-007-0236-1
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, issue.4, p.311315, 1987.
DOI : 10.1016/0165-1765(87)90062-0

D. Lepelley and B. Mbih, The vulnerability of four social choice functions to coalitional manipulation of preferences, Social Choice and Welfare, vol.11, issue.3, p.253265, 1994.
DOI : 10.1007/BF00193810

D. Lepelley and V. Merlin, Choix social positionnel et principe majoritaire, Annales d'Economie et de Statistique, p.2948, 1998.
DOI : 10.2307/20076136

D. Lepelley and V. Merlin, Scoring run-off paradoxes for variable electorates, Economic Theory, vol.17, issue.1, p.5380, 2001.
DOI : 10.1007/PL00004103

D. Lepelley and F. Valognes, On the Kim and Roush voting procedure. Group Decision and Negotiation, p.109123, 1999.

D. Lepelley and F. Valognes, Voting rules, manipulability and social homogeneity, Public Choice, vol.116, p.165184, 2003.
URL : https://hal.archives-ouvertes.fr/halshs-00069239

H. Maassen and T. Bezembinder, Generating random weak orders and the probability of a Condorcet winner, Social Choice and Welfare, vol.19, issue.3, p.517532, 2002.
DOI : 10.1007/s003550100129

A. Mao, A. Procaccia, and Y. Chen, Better human computation through principled voting, Proceedings of of the 27th Conference on Articial Intelligence (AAAI'13), 2013.

K. V. Mardia, Statistics of directional data, Journal of the Royal Statistical Society. Series B (Methodological), vol.37, issue.3, p.349393, 1975.

N. Mattei and T. Walsh, Preib : A library of preference data, Proceedings of Third International Conference on Algorithmic Decision Theory, 2013.

K. May, A set of independent, necessary and sucient conditions for simple majority decision, Econometrica, vol.20, issue.4, p.680684, 1952.

R. May, Some mathematical remarks on the paradox of voting, Behavioral Science, vol.11, issue.2, p.143151, 1971.
DOI : 10.1002/bs.3830160204

I. Mclean, The borda and condorcet principles: Three medieval applications, Social Choice and Welfare, vol.52, issue.2, p.99108, 1990.
DOI : 10.1007/BF01560577

V. Merlin, Les caract??risations axiomatiques du vote majoritaire et des classements par points, Math??matiques et sciences humaines, issue.163, 2003.
DOI : 10.4000/msh.2919

V. Merlin, M. Tataru, and F. Valognes, On the probability that all decision rules select the same winner, Journal of Mathematical Economics, vol.33, issue.2, p.183207, 2000.
DOI : 10.1016/S0304-4068(99)00012-9

V. Merlin, M. Tataru, and F. Valognes, On the likelihood of Condorcet's proles, Social Choice and Welfare, vol.19, 2002.

H. Moulin, La Stratégie du vote. Cahiers du CEREMADE, 1978.

H. Moulin, Condorcet's principle implies the no show paradox, Journal of Economic Theory, vol.45, issue.1, p.5364, 1988.
DOI : 10.1016/0022-0531(88)90253-0

E. Muller and M. Satterthwaite, The equivalence of strong positive association and strategy-proofness, Journal of Economic Theory, vol.14, issue.2, pp.412-418, 1977.
DOI : 10.1016/0022-0531(77)90140-5

R. Myerson, Theoretical comparisons of electoral systems, European Economic Review, vol.43, issue.4-6, p.671697, 1999.
DOI : 10.1016/S0014-2921(98)00089-0

K. Nakamura, The vetoers in a simple game with ordinal preferences, International Journal of Game Theory, vol.7, issue.1, p.5561, 1979.
DOI : 10.1007/BF01763051

N. Narodytska, T. Walsh, and L. Xia, Manipulation of Nanson's and Baldwin's rules, In Workshop on Social Choice and Articial Intelligence, p.64, 2011.

R. Niemi and H. Weisberg, A mathematical solution for the probability of the paradox of voting, Behavioral Science, vol.41, issue.4, p.317323, 1968.
DOI : 10.1002/bs.3830130406

N. Nisam and T. Roughgarden, Éva Tardos et Vijay Vazirani : Algorithmic Game Theory, 2007.

S. Nitzan, The vulnerability of point-voting schemes to preference variation and strategic manipulation, Public Choice, vol.80, issue.2, p.349370, 1985.
DOI : 10.1007/BF00127531

S. Obraztsova and E. Elkind, On the complexity of voting manipulation under randomized tie-breaking, COMSOC, vol.2012, p.347, 2012.

S. Obraztsova, E. Elkind, and N. Hazon, Ties matter : Complexity of voting manipulation revisited International Foundation for Autonomous Agents and Multiagent Systems, The 10th International Conference on Autonomous Agents and Multiagent Systems, p.7178, 2011.

D. Parkes and L. Xia, A complexity-of-strategic-behavior comparison between Schulze's rule and ranked pairs, Proceedings of the 26th AAAI Conference on Articial Intelligence (AAAI'12). American Association for Articial Intelligence, 2012.

B. Peleg, Game theoretic analysis of voting in committees. Numéro 7 in Econometric Society monographs in pure theory, 1984.

E. Penn, J. Patty, and S. Gailmard, Manipulation and Single-Peakedness: A General Result, American Journal of Political Science, vol.9, issue.1, pp.436-449, 2011.
DOI : 10.1111/j.1540-5907.2010.00502.x

J. Pérez, The strong no show paradoxes are a common aw in Condorcet voting correspondences, Social Choice and Welfare, vol.18, issue.3, p.601616, 2001.

J. Pomeranz-et-roman-weil-jr, The cyclical majority problem, Commun. ACM, vol.13, p.251254, 1970.

G. Pritchard and A. Slinko, On the Average Minimum Size of a Manipulating Coalition, Social Choice and Welfare, vol.16, issue.3, p.263277, 2006.
DOI : 10.1007/s00355-006-0130-2

G. Pritchard and M. Wilson, Exact results on manipulability of positional voting rules, Social Choice and Welfare, vol.16, issue.4, p.487513, 2007.
DOI : 10.1007/s00355-007-0216-5

A. Procaccia and J. Rosenschein, Junta distributions and the averagecase complexity of manipulating elections, Proceedings of the fth international joint conference on Autonomous agents and multiagent systems, AA- MAS '06, p.497504, 2006.

A. Procaccia and J. Rosenschein, Average-case tractability of manipulation in voting via the fraction of manipulators, Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems , AAMAS '07, p.105, 2007.
DOI : 10.1145/1329125.1329255

M. Regenwetter and B. Grofman, Anthony Marley et Ilia Tsetlin : Behavioral social choice, p.5868, 2006.

P. Reny, Arrow???s theorem and the Gibbard-Satterthwaite theorem: a unified approach, Economics Letters, vol.70, issue.1, p.99105, 2001.
DOI : 10.1016/S0165-1765(00)00332-3

R. Reyhani, Strategic manipulation in voting systems, Thèse de doctorat, 2013.

R. Reyhani, G. Pritchard, and M. Wilson, A new measure of the diculty of manipulation of voting rules, 2009.

H. Ruben, On the moments of order statistics in samples from normal populations, Biometrika, vol.41, issue.12, p.200227, 1954.

D. Saari, Susceptibility to manipulation, Public Choice, vol.56, issue.1, p.2141, 1990.
DOI : 10.1007/BF00125915

D. Saari, Geometry of voting, 2012.
DOI : 10.1007/978-3-642-48644-9

D. Saari and V. Merlin, A geometric examination of Kemeny's rule. Social Choice and Welfare, p.403438, 2000.

M. 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, p.187217, 1975.
DOI : 10.1016/0022-0531(75)90050-2

M. Schulze, A new monotonic, clone-independent, reversal symmetric, and condorcet-consistent single-winner election method, Social Choice and Welfare, vol.4, issue.2, p.267303, 2011.
DOI : 10.1007/s00355-010-0475-4

A. Sen, Another direct proof of the Gibbard???Satterthwaite Theorem, Economics Letters, vol.70, issue.3, p.381385, 2001.
DOI : 10.1016/S0165-1765(00)00362-1

M. Sertel and R. Sanver, Strong equilibrium outcomes of voting games ???are the generalized Condorcet winners, Social Choice and Welfare, vol.22, issue.2, p.331347, 2004.
DOI : 10.1007/s00355-003-0218-x

A. Slinko, How large should a coalition be to manipulate an election?, Mathematical Social Sciences, vol.47, issue.3, p.289293, 2004.
DOI : 10.1016/j.mathsocsci.2003.09.007

A. Slinko and S. White, Nondictatorial social choice rules are safely manipulable, COMSOC'08, p.403413, 2008.

D. Smith, Manipulability measures of common social choice functions, Social Choice and Welfare, vol.16, issue.4, p.639661, 1999.
DOI : 10.1007/s003550050166

J. Smith, Aggregation of Preferences with Variable Electorate, Econometrica, vol.41, issue.6, p.10271041, 1973.
DOI : 10.2307/1914033

M. Spivak, A comprehensive introduction to dierential geometry Publish or Perish Inc., second édition, 1979.

M. Spivak, A comprehensive introduction to dierential geometry Publish or Perish Inc., second édition, 1979.

J. Stolfi, Oriented projective geometry, Proceedings of the third annual symposium on Computational geometry , SCG '87, p.7685, 1987.
DOI : 10.1145/41958.41966

A. Taylor, Social choice and the mathematics of manipulation. Outlooks Series, 2005.

N. Tideman, Collective Decisions And Voting : The Potential for Public Choice. Ashgate, 2006.

I. Tsetlin, M. Regenwetter, and B. Grofman, The impartial culture maximizes the probability of majority cycles, Social Choice and Welfare, vol.21, issue.3, p.387398, 2003.
DOI : 10.1007/s00355-003-0269-z

G. Tullock and C. Campbell, Computer Simulation of a Small Voting System, The Economic Journal, vol.80, issue.317, p.97104, 1970.
DOI : 10.2307/2230441

G. Ulrich, Computer Generation of Distributions on the m-Sphere, Applied Statistics, vol.33, issue.2, p.158163, 1984.
DOI : 10.2307/2347441

K. Van-der-straeten, J. Laslier, N. Sauger, and A. Blais, Strategic, sincere, and heuristic voting under four election rules: an experimental study, Social Choice and Welfare, vol.4, issue.3, p.435472, 2010.
DOI : 10.1007/s00355-010-0448-7
URL : https://hal.archives-ouvertes.fr/hal-00335046

J. Von-neumann and O. Morgenstern, Theory of games and economic behavior, 1944.

J. Von-neumann, O. Morgenstern, H. Kuhn, and A. Rubinstein, Theory of Games and Economic Behavior (Commemorative Edition) Princeton Classic Editions, 2007.

T. Walsh, An empirical study of the manipulability of single transferable voting, ECAI, p.257262, 2010.

T. Walsh, F. Brandt, V. Conitzer, L. Hemaspaandra, J. Laslier et al., Manipulability of single transferable vote, éditeurs : Computational Foundations of Social Choice, numéro 10101 in Dagstuhl Seminar Proceedings . Schloss Dagstuhl -Leibniz-Zentrum für Informatik, 2010.

T. Wang, P. Cuff, and S. Kulkarni, Condorcet methods are less susceptible to strategic voting, 2014.

G. S. Watson and E. J. Williams, On the construction of signicance tests on the circle and the sphere, Biometrika, vol.43, issue.34, p.344352, 1956.

T. Weber, Alternatives vs. outcomes : A note on the Gibbard-Satterthwaite theorem, 2009.

A. Wood, Simulation of the von mises fisher distribution, Communications in Statistics - Simulation and Computation, vol.48, issue.1, p.157164, 1994.
DOI : 10.1111/j.1467-842X.1993.tb01313.x

E. Xavier, A note on a Maximum k-Subset Intersection problem, Information Processing Letters, vol.112, issue.12, p.471472, 2012.
DOI : 10.1016/j.ipl.2012.03.007

L. Xia and V. Conitzer, Generalized scoring rules and the frequency of coalitional manipulability, Proceedings of the 9th ACM conference on Electronic commerce, EC '08, p.109118, 2008.
DOI : 10.1145/1386790.1386811

L. Xia, M. Zuckerman, A. Procaccia, V. Conitzer, and J. Rosenschein, Complexity of unweighted coalitional manipulation under some common voting rules, International Joint Conference on Articial Intelligence, p.348353, 2009.

P. Young and A. Levenglick, A Consistent Extension of Condorcet???s Election Principle, SIAM Journal on Applied Mathematics, vol.35, issue.2, 1978.
DOI : 10.1137/0135023

M. Zuckerman, O. Lev, and J. Rosenschein, An algorithm for the coalitional manipulation problem under Maximin, The 10th International Conference on Autonomous Agents and Multiagent Systems, p.845852, 2011.

M. Zuckerman, A. Procaccia, and J. Rosenschein, Algorithms for the coalitional manipulation problem, Artificial Intelligence, vol.173, issue.2, pp.392-412, 2009.
DOI : 10.1016/j.artint.2008.11.005