Social choice and the mathematics of manipulation

1. Introduction 2. The Gibbard-Satterthwaite theorem 3. Additional results for single-valued elections 4. The Duggan-Schwartz theorem 5. Additional results for multi-valued elections 6. Ballots that rank sets 7. Elections with outcomes that are lotteries 8. Elections with variable agendas References Index.

[1]  Vincenzo Denicolò.  Independent social choice correspondences are dictatorial , 1985 .

[2]  John Duggan,et al.  Strategic Manipulability is Inescapable: Gibbard-Satterthwaite without Resoluteness , 1992 .

[3]  A. Gibbard.  Manipulation of Schemes That Mix Voting with Chance , 1977 .

[4]  Salvador Barberà,et al.  Strategy-Proofness and Pivotal Voters: A Direct Proof of the Gibbard-Satterthwaite Theorem , 1983 .

[5]  P. Fishburn.  The Theory Of Social Choice , 1973 .

[6]  Dieter Sondermann,et al.  Arrow's theorem, many agents, and invisible dictators☆ , 1972 .

[7]  J. Kelly.  Social Choice Theory: An Introduction , 1988 .

[8]  J. Neumann.  Zur Theorie der Gesellschaftsspiele , 1928 .

[9]  Salvador Barberà,et al.  Pivotal voters: A new proof of arrow's theorem , 1980 .

[10]  Thomas E. Armstrong,et al.  Arrow's theorem with restricted coalition algebras , 1980 .

[11]  Hervé Moulin,et al.  Fair division and collective welfare , 2003 .

[12]  W. Riker.  The art of political manipulation , 1987 .

[13]  John Duggan,et al.  A geometric proof of Gibbard's random dictatorship theorem , 1996 .

[14]  Shasikanta Nandeibam,et al.  An alternative proof of Gibbard's random dictatorship result , 1998 .

[15]  Peter C. Fishburn,et al.  Chapter 4 Voting procedures , 2002 .

[16]  Robert B. Wilson,et al.  Social choice theory without the Pareto Principle , 1972 .

[17]  J. Kelly.  Social choice bibliography , 1991 .

[18]  A. Feldman,et al.  Strongly nonmanipulable multi-valued collective choice rules , 1980 .

[19]  John Duggan,et al.  Strategic manipulability without resoluteness or shared beliefs: Gibbard-Satterthwaite generalized , 2000, Soc. Choice Welf..

[20]  D. Black.  The theory of committees and elections , 1959 .

[21]  Alan D. Taylor,et al.  The Manipulability of Voting Systems , 2002, Am. Math. Mon..

[22]  Jerry S. Kelly,et al.  STRATEGY-PROOFNESS AND SOCIAL CHOICE FUNCTIONS WITHOUT SINGLEVALUEDNESS , 1977 .

[23]  A. Sen,et al.  Social Choice Theory: A Re-Examination , 1977 .

[24]  Donald E. Campbell,et al.  A leximin characterization of strategy-proof and non-resolute social choice procedures , 2002 .

[25]  Arunava Sen.  Another direct proof of the Gibbard–Satterthwaite Theorem , 2001 .

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

[27]  Hervé Moulin.  Fairness and strategy in voting , 1985 .

[28]  W. Wistar Comfort,et al.  The Theory of Ultrafilters , 1974 .

[29]  Mark S. Bonchek,et al.  Analyzing politics : rationality, behavior, and institutions , 1996 .

[30]  Allan Gibbard,et al.  Straightforwardness of Game Forms with Lotteries as Outcomes , 1978 .

[31]  Donald E. Campbell,et al.  A trade-off result for preference revelation , 2000 .

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

[33]  Donald E. Campbell.  Equity, Efficiency, and Social Choice , 1992 .

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

[35]  H. Young,et al.  A Consistent Extension of Condorcet’s Election Principle , 1978 .

[36]  Eitan Muller,et al.  The equivalence of strong positive association and strategy-proofness , 1977 .

[37]  Allan M. Feldman.  Manipulation and the Pareto rule , 1979 .

[38]  Luc Lauwers,et al.  Ultraproducts and aggregation , 1995 .

[39]  Avraham Beja,et al.  Arrow and Gibbard-Satterthwaite revisited: Extended domains and shorter proofs , 1993 .

[40]  Eugene Wesley,et al.  Cheatproofness Properties of the Plurality Rule in Large Societies , 1978 .

[41]  Vincenzo Denicolò.  Fixed Agenda Social Choice Theory: Correspondence and Impossibility Theorems for Social Choice Correspondences and Social Decision Functions , 1993 .

[42]  D. Saari.  Basic Geometry of Voting , 1995 .

[43]  Prasanta K. Pattanaik,et al.  Strategic voting under minimally binary group decision functions , 1981 .

[44]  N. Schofield.  The Geometry of Voting , 1983 .

[45]  Jerry S. Kelly,et al.  SIMPLICITY: IMPOSSIBILITY THEOREMS , 1978 .

[46]  Yasuhito Tanaka.  An alternative direct proof of Gibbard’s random dictatorship theorem , 2003 .

[47]  Salvador Barberà.  Manipulation of social decision functions , 1977 .

[48]  H. Reiju Mihara,et al.  Existence of a coalitionally strategyproof social choice function: A constructive proof , 2001, Soc. Choice Welf..

[49]  K. Ramamurthy.  Coherent Structures and Simple Games , 1990 .

[50]  A. Feldman,et al.  Manipulating Voting Procedures , 1979 .

[51]  John L. Bell,et al.  Models and Ultraproducts: An Introduction. , 1969 .

[52]  K. Arrow.  A Difficulty in the Concept of Social Welfare , 1950, Journal of Political Economy.

[53]  John J. Bartholdi,et al.  Single transferable vote resists strategic voting , 2015 .

[54]  A. Feldman,et al.  Nonmanipulable multi-valued social decision functions , 1979 .

[55]  Norman Schofield,et al.  Social choice and democracy , 1985 .

[56]  H. Reiju Mihara.  Coalitionally strategyproof functions depend only on the most-preferred alternatives , 2000, Soc. Choice Welf..

[57]  Dan S. Felsenthal,et al.  After two centuries, should condorcet's voting procedure be implemented? , 1992 .

[58]  J. Benoît,et al.  The Gibbard-Satterthwaite theorem: a simple proof , 2000 .

[59]  P. Fishburn.  The Axioms of Subjective Probability , 1986 .

[60]  Donald G. Saari,et al.  Chaotic Elections! - A Mathematician Looks at Voting , 2001 .

[61]  L. J. Savage,et al.  The Foundations of Statistics , 1955 .

[62]  J. Neumann,et al.  Theory of games and economic behavior , 1945, 100 Years of Math Milestones.

[63]  Kotaro Suzumura,et al.  Introduction, Handbook of Social Choice and Welfare, Edited by Kenneth Arrow, Amartya Sen and Kotaro Suzumura, Amsterdam: Elsevier/North-Holland , 2001 .

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

[65]  Lin Zhou,et al.  Multi-valued strategy-proof social choice rules , 2002, Soc. Choice Welf..

[66]  Salvador Barberà,et al.  Voting by Committees , 1991 .

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

[68]  Bernard Monjardet,et al.  Stability of Aggregation Procedures, Ultrafilters, and Simple Games , 1981 .

[69]  Jean-Pierre Benoît,et al.  Strategic Manipulation in Voting Games When Lotteries and Ties Are Permitted , 2002, J. Econ. Theory.

[70]  A. Feldman.  Welfare economics and social choice theory , 1980 .

[71]  Peter Gärdenfors,et al.  A concise proof of theorem on manipulation of social choice functions , 1977 .

[72]  J. Geanakoplos.  Three brief proofs of Arrow’s Impossibility Theorem , 2001 .

[73]  Amartya Sen,et al.  A Possibility Theorem on Majority Decisions , 1966 .

[74]  Peter C. Fishburn,et al.  Arrow's impossibility theorem: Concise proof and infinite voters , 1970 .

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

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

[77]  Salvador Barberà,et al.  THE MANIPULATION OF SOCIAL CHOICE MECHANISMS THAT DO NOT LEAVE "TOO MUCH" TO CHANCE' , 1977 .

[78]  Rajat Deb,et al.  Social Decision Functions and the Veto , 1977 .

[79]  J. Kelly.  Arrow Impossibility Theorems , 1978 .

[80]  Arunava Sen,et al.  Strategy-proof Social Choice Correspondences , 2001, J. Econ. Theory.

[81]  Philip D. Straffin,et al.  Topics in the theory of voting , 1980 .

[82]  William S. Zwicker,et al.  Simple games - desirability relations, trading, pseudoweightings , 1999 .

[83]  B. D. Finetti.  La prévision : ses lois logiques, ses sources subjectives , 1937 .

[84]  P. Gärdenfors.  Manipulation of social choice functions , 1976 .

[85]  David A. Smith.  Manipulability measures of common social choice functions , 1999 .

[86]  David Schmeidler,et al.  Two Proofs of the Gibbard-Satterthwaite Theorem on the Possibility of a Strategy-Proof Social Choice Function , 1978 .

[87]  Hervé Moulin,et al.  The Proportional Veto Principle , 1981 .

[88]  H. Moulin.  The strategy of social choice , 1983 .

[89]  David Makinson,et al.  Combinatorial versus decision-theoretic components of impossibility theorems , 1996 .

[90]  J. H. Blau,et al.  A Direct Proof of Arrow's Theorem , 1972 .

[91]  Donald G. Saari,et al.  A geometric examination of Kemeny's rule , 2000, Soc. Choice Welf..

[92]  Eugene Wesley,et al.  Stability of social choices in infinitely large societies , 1977 .

[93]  W. Riker,et al.  Liberalism Against Populism: A Confrontation Between the Theory of Democracy and the Theory of Social Choice , 1982 .