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- Social Choice and the Mathematics of Manipulation , pp. 167 - 172Publisher: Cambridge University PressPrint publication year: 2005
References
Arrow's theorem with restricted coalition algebras. Journal of Mathematical Economics 7 (1980), 55–75CrossRefGoogle Scholar
A difficulty in the concept of social welfare. The Journal of Political Economy 58 (1950), 328–46CrossRefGoogle Scholar
Arrow, K. Social choice and individual values (2nd ed.). Yale University Press: New Haven, 1963
Arrow, K. and A. Sen and K. Suzumura (Eds.), Handbook of social choice and welfare, vol. I, North-Holland, New York, 2002
Austen-Smith, D. and J. Banks, Positive political theory I: collective preferences. University of Michigan Press: Ann Arbor, 2000
Manipulation of social choice mechanisms that do not leave ‘too much’ to chance. Econometrica 45 (1977a), 1573–88CrossRefGoogle Scholar
Manipulation of social decision functions. Journal of Economic Theory 15 (1977b), 266–78CrossRefGoogle Scholar
Pivotal voters. A new proof of Arrow's theorem. Economic Letters 6 (1980), 13–16CrossRefGoogle Scholar
Strategy-proofness and pivotal voters: a direct proof of the Gibbard-Satterthwaite theorem. International Economic Review 24 (1983), 413–17CrossRefGoogle Scholar
and and , Strategy-proof set valued social choice functions. Journal of Economic Theory 101 (2001), 374–94CrossRefGoogle Scholar
and , Single-transferable vote resists strategic voting. Social Choice and Welfare 8 (1991), 341–54CrossRefGoogle Scholar
, , and , Stability of aggregation procedures, ultrafilters, and simple games. Econometrica 49 (1981), 527–34CrossRefGoogle Scholar
Arrow and Gibbard-Satterthwaite theorem re-visited. Extended domains and shorter proofs. Mathematical Social Sciences 25 (1993), 281–6CrossRefGoogle Scholar
Bell, J. and A. Slomson, Models and ultraproducts: An Introduction. North Holland: Amsterdam-London, 1969
Strategic manipulation in voting games when lotteries and ties are permitted. Journal of Economic Theory 102 (2002), 421–36CrossRefGoogle Scholar
The Gibbard-Satterthwaite theorem: a simple proof. Economic Letters 69 (2000), 319–22CrossRefGoogle Scholar
Black, D. Theory of committees and elections. Cambridge University Press, Cambridge, 1958
Social choice functions and simple games. Bulletin of the American Mathematical Society 63 (1957), 243–4Google Scholar
Brams, S. and P. Fishburn, Approval voting. Birkhäuser Boston, Cambridge, MA, 1983
Brams, S. and P. Fishburn, Voting procedures. In the Handbook of Social Choice and Welfare. Arrow, Sen, and Suzumura, eds. (2002), 175–236
Burani, N. and W. Zwicker, Coalition formation games with separable preferences (preprint). Department of Mathematics, Union College (2000)
Campbell, D. Equity, efficiency, and social choice. Clarendon Press, Oxford, 1992
and . A trade-off result for preference revelation. Journal of Mathematical Economics 34 (2000), 129–42CrossRefGoogle Scholar
and . A leximin characterization of strategy-proof non-resolute social choice procedures. Economic Theory 20 (2002), 809–29CrossRefGoogle Scholar
and , Multi-valued strategy-proof social choice rules. Social Choice and Welfare 19 (2002), 569–80CrossRefGoogle Scholar
COMAP [Consortium for Mathematics and Its Applications] For all practical purposes: Introduction to contemporary mathematics (6th ed.) W. H. Freeman: New York, 2003
Comfort, W. and S. Negrepontis, The theory of ultrafilters. Springer-Verlag: New York, 1974
Condorcet, M. Essai sur l'application de l' analyse ‘a la probabiliti'e des d'ecisions rendues ‘a la pluralit'e des voix. De L'Imprimerie royale, Paris, (1785)
La pr'evision ses lois logiques, ses sources subjectives. Ann. Inst. H. Poincaré 7 (1937), 1–68Google Scholar
Independent social choice functions are dictatorial. Economics Letters 19 (1985), 9–12CrossRefGoogle Scholar
Fixed agenda social choice theory: correspondence and impossibility theorems for social choice correspondences and social decision functions. Journal of Economic Theory 59 (1993), 324–32CrossRefGoogle Scholar
A geometric proof of Gibbard's random dictator theorem. Economic Theory 7 (1996), 365–9Google Scholar
Duggan, J. and T. Schwartz, Strategic manipulability is inescapable: Gibbard-Satterthwaite without resoluteness (preprint). Department of Economics, University of Rochester, (1993)
and , Strategic manipulability without resoluteness or shared beliefs: Gibbard-Satterthwaite generalized. Social Choice and Welfare 17 (2000), 85–93CrossRefGoogle Scholar
Non-manipulable multi-valued social decision functions. Public Choice 34 (1979a), 177–88CrossRefGoogle Scholar
Manipulation and the Pareto rule. Journal of Economic Theory 21 (1979b), 473–82CrossRefGoogle Scholar
Strongly nonmanipulable multi-valued collective choice rules. Public Choice 35 (1980a), 503–9CrossRefGoogle Scholar
Feldman, A. Welfare economics and social choice theory. Kluwer: Nijhoff, 1980b
Felsenthal, D. and M. Machover, The measurement of voting power: theory and practice, problems and paradoxes. Edward Elgar: Cheltenham, UK, 1998CrossRef
and , After two centuries, should Condorcet's voting procedure be implemented?Behavorial Sciences 37 (1992), 250–74CrossRefGoogle Scholar
Arrow's impossibility theorem: concise proof and infinite voters. Journal of Economic Theory 2 (1970), 103–6CrossRefGoogle Scholar
Fishburn, P. The theory of social choice. Princeton University Press: Princeton, NJ, 1973
A concise proof of theorem on manipulation of social choice functions. Public Choice 32 (1977), 137–42CrossRefGoogle Scholar
Gärdenfors, P. On definitions of manipulation of social choice functions. Aggregation and Revelation of Preferences, edited by Jean-Jacques Laffont. North Holland, Amsterdam, 1979
Geanakoplos. Three brief proofs of Arrow's impossibility theorem. Cowles Discussion Paper 1123R, 1996
Manipulation of voting schemes: a general result. Econometrica 41 (1973), 587–601CrossRefGoogle Scholar
Manipulation of schemes that mix voting with chance. Econometrica 45 (1977) 665–81CrossRefGoogle Scholar
Straightforwardness of game forms with lotteries as outcomes. Econometrica 46 (1978), 595–614CrossRefGoogle Scholar
Les théories de l'intérêt général et le problème logique de lagrégation. Economie Appliquée 5 (1952), 501–84Google Scholar
Strategy-proofness and social choice functions without single-valuedness. Econometrica 45 (1977), 439–46CrossRefGoogle Scholar
Kelly, J. Arrow impossibility theorems. Academic Press: New York, 1978
Kelly, J. Social choice theory: an introduction. Springer-Verlag: New York, 1987
and , Arrow's theorem, many agents and invisible dictators. Journal of Economic Theory 5, (1972), 267–77CrossRefGoogle Scholar
and . Ultraproducts and aggregation. Journal of Mathematical Economics 24 (1995), 217–37CrossRefGoogle Scholar
and , Strategic voting under minimally binary group decision functions. Journal of Economic Theory 25 (1981), 338–52CrossRefGoogle Scholar
Combinatorial versus decision-theoretic components of impossibility theorems. Theory and Decision 40 (1996), 181–90CrossRefGoogle Scholar
A set of independent, necessary and sufficient conditions for simple majority decision. Econometrica 20 (1952), 680–4CrossRefGoogle Scholar
McLean, I. and A. Urken (ed. and transl.), Classics of social choice. Michigan University Press: Ann Arbor, MI, 1993
and , A geometric examination of the Kemeny rule. Social Choice and Welfare 17 (2000), 403–38Google Scholar
Coalitionally strategyproof functions depend only on the most-preferred alternative. Social Choice and Welfare 17 (2000), 393–402CrossRefGoogle Scholar
Existence of a coalitionally strategyproof social choice function: A constructive proof. Social Choice and Welfare 18 (2001), 543–53CrossRefGoogle Scholar
Mill, J. Considerations on representative government. Harper and Brothers: New York, 1862
Monjardet, B. Introduction to social choice theory: The Arrow and Gibbard-Satterthwaite theorem. Cahiers MSE: CERMSEM. Université Paris 1, (1999)
Social choice and the “Centre de Mathématique Sociale”: Some historical notes. Social Choice and Welfare (to appear in 2005)
Moulin, H. The strategy of social choice. North-Holland: New York, 1983
Fairness and strategy in voting. Proceedings of Symposia in Applied Mathematics 33 (1985), 109–42CrossRefGoogle Scholar
Moulin, H. Fair division and collective welfare. The MIT Press: Cambridge, MA, 2003
and . The equivalence of strong positive association and strategy proofness. Journal of Economic Theory 14 (1977), 412–18CrossRefGoogle Scholar
An alternative proof of Gibbard's random dictatorship result. Social Choice and Welfare 15 (1998), 509–19CrossRefGoogle Scholar
Nurmi, H. Comparing voting systems. D. Reidel Publishing Company: Dordrecht, Holland, 1987
and , Stability properties of social choices in infinitely large societies. Journal of Economic Theory 14 (1977), 252–62CrossRefGoogle Scholar
and , Cheatproofness of the plurality rule in large societies. Review of Economic Studies 45 (1978), 85–91CrossRefGoogle Scholar
Ramamurthy, K. Coherent structures and simple games. Kluwer: Dordrecht, Netherlands, 1990
Riker, W. Liberalism against populism: a confrontation between the theory of democracy and the theory of social choice. W. H. Freeman: San Francisco, 1982
Riker, W. The art of political manipulation. Yale University Press: New Haven and London, 1986
Saari, D. The geometry of voting. Springer-Verlag: New York, 1994
Saari, D. Basic geometry of voting. Springer-Verlag: New York, 1995
Saari, D. Choatic elections: a mathematician looks at voting. The American Mathematical Society, 2001
Strategy-proofness and Arrow's conditions: existence and correspondence theorems for voting procedures and social welfare functions. Journal of Economic Theory 10 (1975), 187–217CrossRefGoogle Scholar
Savage, L. The foundations of statistics. Wiley: New York, 1954
Schmeidler, D. and H. Sonnenschein, Two proofs of the Gibbard-Satterthwaite theorem on the possibility of a strategy-proof social choice function, in Decision Theory and Social Ethics Issues in Social Choice. H. Gottinger and W. Leinfellner, editors. Reidel: Dordrecht (1978), 227–34
Schofield, N. Social choice and democracy. Springer Verlag: Berlin, 1985
Sen, A. Collective choice and social welfare. Holden Day: San Francisco, 1970
Sen, A. Choice, welfare, and measurement. MIT Press: Cambridge, MA, 1982
, Another direct proof of the Gibbard-Satterthwaite theorem. Economic Letters 70 (2001), 381–5CrossRefGoogle Scholar
Shepsle, K. and M. Bonchek, Analyzing politics: rationality, behavior, and institutions. Norton: New York and London, 1997
Manipulability measures of common social choice functions. Social Choice and Welfare 16 (1999), 639–61CrossRefGoogle Scholar
Straffin, P. Topics in the theory of voting. Birkhauser: Boston, 1980
Tanaka, Y. An alternative direct proof of Gibbard's random dictatorship theorem, preprint, 2004
Taylor, A. Mathematics and politics: strategy, voting, power, and proof. Springer-Verlag: New York, 1995CrossRef
2002. The manipulability of voting systems. The American Mathematical Monthly 109, 321–37CrossRefGoogle Scholar
Taylor, A. and W. Zwicker, Simple games: desirability relations, trading, and pseudoweightings. Princeton University Press: Princeton, NJ, 1999
Zur Theorie der Gesellschaftsspiele. Mathematische Annalen 100 (1928), 295–320CrossRefGoogle Scholar
von Neumann, J. and O. Morgenstern, Theory of games and economic behavior. Princeton University Press: Princeton, NJ, 1944
Social choice theory without the Pareto principle. Journal of Economic Theory 3 (1972), 478–86CrossRefGoogle Scholar
Social choice scoring functions. SIAM Journal on Applied Mathematics 28 (1975), 824–38CrossRefGoogle Scholar
and . A consistent extension of Condorcet's election principle. SIAM Journal on Applied Mathematics 35 (1978), 285–300CrossRefGoogle Scholar