Encyclopedia of Complexity and Systems Science

Living Edition
| Editors: Robert A. Meyers

Social Choice Theory

  • Salvador BarberàEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27737-5_666-1

Glossary

Aggregation Rules

These are methods that combine information about the preferences of agents in society and turn them into binary relations, interpreted as “collective preferences,” that may or may not inherit the properties of those attributed to individuals.

Arrow’s Impossibility theorem

This pioneering result expresses the logical impossibility of aggregating individual transitive preferences into social transitive preferences, when a society faces more than two alternatives, while respecting the Arrowian conditions of Independence of Irrelevant Alternatives, Non-Dictatorship, Universal Domain, and Pareto.

Chaos theorems

Cyclical patterns in social preferences arise in many cases, under a wide variety of aggregation rules. In multidimensional settings, where social alternatives can be identified with vectors of characteristics, chaos theorems prove that such cyclical patterns can emerge, even if individual preferences are restricted to be saturated and concave, in almost...

Keywords

Aggregation rules Voting methods Social choice functions Impossibility theorems Arrow’s impossibility theorem Chaos theorems Characterizations Strategy-proofness Single peakedness Liberalism 
This is a preview of subscription content, log in to check access.

Bibliography

  1. Alcantud JC, Laruelle A (2014) Disapproval voting: a characterization. Soc Choice Welf 43:1–10MathSciNetzbMATHCrossRefGoogle Scholar
  2. Apesteguia J, Ballester MA, Masatlioglu Y (2014) A foundation for strategic agenda voting. Games Econom Behav 87:91–99MathSciNetzbMATHCrossRefGoogle Scholar
  3. Austen-Smith D, Banks JS (1996) Information aggregation, rationality and the Condorcet Jury Theorem. Am Polit Sci Rev 90(1):34–45CrossRefGoogle Scholar
  4. Austen-Smith D, Feddersen T (2006) Deliberation, preference uncertainty and voting rules. Am Polit Sci Rev 100(2):209–217zbMATHCrossRefGoogle Scholar
  5. Austen-Smith D, Feddersen T (2009) Information aggregation and communication in committees. Philos Trans R Soc B 364(1518):763–769CrossRefGoogle Scholar
  6. Baigent N (2002) Chapter 18, Topological theories of social choice. In: Arrow KJ, Sen AK, Suzumura K (eds) Handbook of social choice and welfare, vol 2. Elsevier, Amsterdam, pp 301–334Google Scholar
  7. Ballester MA, Haeringer G (2011) A characterization of the single-peaked domain. Soc Choice Welf 36:305–322MathSciNetzbMATHCrossRefGoogle Scholar
  8. Banks JS (1985) Sophisticated voting outcomes and agenda control. Soc Choice Welf 1:295–306zbMATHCrossRefGoogle Scholar
  9. Banks JS, Bordes G (1988) Voting games, indifference, and consistent sequential choice rules. Soc Choice Welf 5:31–44MathSciNetzbMATHCrossRefGoogle Scholar
  10. Barberà S (1977) The manipulation of social choice mechanisms that do not leave too much to chance. Econometrica 45(7):1573–1588MathSciNetzbMATHCrossRefGoogle Scholar
  11. Barberà S (1979) Majority and positional is voting in a probabilistic framework. Rev Econ Stud 46(2):379–389zbMATHCrossRefGoogle Scholar
  12. Barberà S (1983a) Strategy-Proofness and pivotal voters: a direct proof of the Gibbard-Satterthwaite Theorem. Int Econ Rev 24(2):413–418MathSciNetzbMATHCrossRefGoogle Scholar
  13. Barberà S (1983b) Pivotal voters: a simple proof of Arrow’s Theorem. In: Pattanaik PK, Salles M (eds) Social choice and welfare. North-Holland, Amsterdam, pp 31–35CrossRefGoogle Scholar
  14. Barberà S (2001) An introduction to strategy-proof social choice functions. Soc Choice Welf 18:619–653MathSciNetzbMATHCrossRefGoogle Scholar
  15. Barbera S, Coelho D (2010) On the rule of k names. Games Econom Behav 70:44–61MathSciNetzbMATHCrossRefGoogle Scholar
  16. Barbera S, Coelho D (2017) Balancing the power to appoint officers. Games Econom Behav 101:189–203MathSciNetzbMATHCrossRefGoogle Scholar
  17. Barbera S, Gerber A (2017) Sequential voting and agenda manipulation. Theor Econ 12(1):211–247MathSciNetzbMATHCrossRefGoogle Scholar
  18. Barberà S, Peleg B (1990) Strategy-proof voting schemes with continuous preferences. Soc Choice Welf 7:31–38MathSciNetzbMATHCrossRefGoogle Scholar
  19. Barberà S, Sonnenschein H (1978) Preference aggregation with randomized social orderings. J Econ Theory 18(2):244–254MathSciNetzbMATHCrossRefGoogle Scholar
  20. Barberà S, Valenciano F (1983) Collective probabilistic judgements. Econometrica 51(4):1033–1046MathSciNetzbMATHCrossRefGoogle Scholar
  21. Barberà S, Sonnenschein H, Zhou L (1991) Voting by committees. Econometrica 59:595–609MathSciNetzbMATHCrossRefGoogle Scholar
  22. Barberà S, Gul F, Stacchetti E (1993) Generalized median voter schemes and committees. J Econ Theory 61:262–289MathSciNetzbMATHCrossRefGoogle Scholar
  23. Barberà S, Massó J, Neme A (1997) Voting under constraints. J Econ Theory 76(2):298–321MathSciNetzbMATHCrossRefGoogle Scholar
  24. Barberà S, Bogomolnaia A, van der Stel H (1998) Strategy-proof probabilistic rules for expected utility maximizers. Math Soc Sci 35(2):89–103MathSciNetzbMATHCrossRefGoogle Scholar
  25. Barberà S, Dutta B, Sen A (2001) Strategy-proof social choice correspondences. J Econ Theory 101(2):374–394MathSciNetzbMATHCrossRefGoogle Scholar
  26. Barberà S, Massó J, Neme A (2005) Voting by committees under constraints. J Econ Theory 122:185–205MathSciNetzbMATHCrossRefGoogle Scholar
  27. Barberà S, Berga D, Moreno B (2010) Individual versus group strategy- Proofness: when do they coincide? J Econ Theory 145(5):1648–1674MathSciNetzbMATHCrossRefGoogle Scholar
  28. Barberà S, Moreno B (2011) Top monotonicity: a common root for single peakedness, single crossing and the median voter result. Games Econom Behav 73(2):345–359MathSciNetzbMATHCrossRefGoogle Scholar
  29. Benoît J-P (2002) Strategic manipulation in voting games when lotteries and ties are permitted. J Econ Theory 1023(2):421–436MathSciNetzbMATHCrossRefGoogle Scholar
  30. Berga D (1998) Strategy-Proofness and single-plateaued preferences. Math Soc Sci 35:105–120MathSciNetzbMATHCrossRefGoogle Scholar
  31. Bergson A (1938) A reformulation of certain aspects of welfare economics. Q J Econ 52(2):310–334CrossRefGoogle Scholar
  32. Black D (1948) On the rationale of group decision making. J Polit Econ 56:23–34CrossRefGoogle Scholar
  33. Blackorby C, Donaldson D, Weymark JA (1984) Social choice with interpersonal utility comparisons: a diagrammatic introduction. Int Econ Rev 25:327–356MathSciNetzbMATHCrossRefGoogle Scholar
  34. Blair D, Bordes G, Kelly J, Suzumura K (1976) Impossibility theorems without collective rationality. J Econ Theory 13(3):361–379MathSciNetzbMATHCrossRefGoogle Scholar
  35. Blair DH, Muller E (1983) Essential aggregation procedures on restricted domains of preferences. J Econ Theory 30(1):34–53MathSciNetzbMATHCrossRefGoogle Scholar
  36. Blair D, Pollak R (1979) Collective rationality and dictatorship: the scope of the arrow theorem. J Econ Theory 21:186–194MathSciNetzbMATHCrossRefGoogle Scholar
  37. Blin JM, Satterthwaite MA (1976) Strategy-proofness and single peakedness. Public Choice 26:51–58CrossRefGoogle Scholar
  38. Border K, Jordan JS (1983) Straightforward elections, unanimity and phantom voters. Rev Econ Stud 50:153–170MathSciNetzbMATHCrossRefGoogle Scholar
  39. Brams SJ, Fishburn PC (1978) Approval voting. Am Polit Sci Rev 72(3):831–847zbMATHCrossRefGoogle Scholar
  40. Brams SJ, Fishburn PC (2002) Voting procedures. In: Arrow KJ, Sen AK, Suzumura K (eds) Handbook of social choice and welfare, vol 1. North-Holland, Amsterdam, pp 173–236CrossRefGoogle Scholar
  41. Campbell D, Kelly J (2002a) Impossibility theorems in the Arrovian framework. In: Arrow K, Sen A, Suzumura K (eds) Handbook of social choice and welfare, vol 1. Elsevier Science, AmsterdamGoogle Scholar
  42. Campbell DE, Kelly JS (2002b) Impossibility theorems in the Arrowian framework. In: Arrow KJ, Sen AK, Suzumura K (eds) Handbook of social choice and welfare, vol 1. North-Holland, AmsterdamGoogle Scholar
  43. Campbell DE, Kelly JS (2009) Gains from manipulating social choice rules. Econ Theory 40(3):349–371MathSciNetzbMATHCrossRefGoogle Scholar
  44. Campbell DE, Kelly JS (2010) Losses due to manipulation of social choice rules. Econ Theory 45(3):453–467MathSciNetzbMATHCrossRefGoogle Scholar
  45. Casella A (2005) Storable votes. Games Econom Behav, special issue: In Honor of Richard D. McKelvey. Elsevier 51(2):391–419MathSciNetzbMATHCrossRefGoogle Scholar
  46. Chichilnisky G (1980) Social choice and the topology of spaces of preferences. Adv Math 37:165–176MathSciNetzbMATHCrossRefGoogle Scholar
  47. D’Aspremont C, Gevers L (1977) Equity and the informational basis of collective choice. Rev Econ Stud 44:199–209zbMATHCrossRefGoogle Scholar
  48. de Borda JC (1781) Mémoire sur les élections au scrutin. Hist Acad Roy Sci:657–665Google Scholar
  49. de Condorcet M (1785) Essai sur l’application de l’analyse à la probabilité dés décisions rendues à la pluralité des voix, ParisGoogle Scholar
  50. Demange G (1982) Single-peaked orders on a tree. Math Soc Sci 3(4):389–396MathSciNetzbMATHCrossRefGoogle Scholar
  51. Dietrich F (2006) Judgment aggregation: (im)possibility theorems. J Econ Theory 126(1):286–298MathSciNetzbMATHCrossRefGoogle Scholar
  52. Duggan J, Schwartz T (2000) Strategic manipulability without resoluteness or shared beliefs: Gibbard–Satterthwaite generalized. Soc Choice Welf 17(1):85–93MathSciNetzbMATHCrossRefGoogle Scholar
  53. Dutta B, Peters H, Sen A (2002) Strategy-proof probabilistic mechanisms in economies with pure public goods. J Econ Theory 106(2):392–416MathSciNetzbMATHCrossRefGoogle Scholar
  54. Dutta B, Peters H, Sen A (2007) Strategy-proof cardinal decision schemes. Soc Choice Welf 28(1):163–179MathSciNetzbMATHCrossRefGoogle Scholar
  55. Eliaz K (2004) Social aggregators. Soc Choice Welf 22:317–330MathSciNetzbMATHCrossRefGoogle Scholar
  56. Farquharson R (1969) Theory of voting. Yale University Press, New HavenGoogle Scholar
  57. Feldman A, Serrano R (2008) Arrow’s impossibility theorem: two simple single-profile versions. Harv Coll Math Rev 2:46–57Google Scholar
  58. Felsenthal DS (1989) On combining approval with disapproval voting. Soc Choice Welf 34(1):53–60MathSciNetGoogle Scholar
  59. Fishburn PC (1970) Arrow’s impossibility theorem: concise proof and infinite voters. J Econ Theory 2:103–106MathSciNetCrossRefGoogle Scholar
  60. Fishburn PC (1973) The theory of social choice. Princeton University Press, PrincetonzbMATHGoogle Scholar
  61. Fishburn PC (1984) Discrete mathematics in voting and group choice. SIAM J Algebra Discrete Methods 5(2):263–275MathSciNetzbMATHCrossRefGoogle Scholar
  62. Gaertner W (1986) Pareto, interdependent rights exercising and strategic behaviour. J Econ, SuppL: 5:79–98Google Scholar
  63. Gaertner W (1993) Rights and game forms, types of preference orderings and Pareto inefficiency. In: Diewert WE, Spremann K, Stehling E (eds) Mathematical modelling in economics. Essays in honor of Wolfgang Eichhorn. Springer, Berlin/Heidelberg/New YorkGoogle Scholar
  64. Gaertner W (2009) A primer in social choice theory, revised. Oxford University Press, New YorkzbMATHGoogle Scholar
  65. Gaertner W, Pattanaik PK, Suzumura K (1992) Individual rights revisited. Economica 59:161–177CrossRefGoogle Scholar
  66. Gans JS, Smart M (1996) Majority voting with single-crossing preferences. J Public Econ 59:219–237CrossRefGoogle Scholar
  67. Gardenfors P (1973) Positionalist voting functions. Theor Decis 4:1–24MathSciNetzbMATHCrossRefGoogle Scholar
  68. Geanakoplos J (2005) Three brief proofs of Arrow’s Impossibility Theorem. Econ Theory 26(1):211–215MathSciNetzbMATHCrossRefGoogle Scholar
  69. Gibbard A (1973) Manipulation of voting schemes: a general result. Econometrica 41:587–602MathSciNetzbMATHCrossRefGoogle Scholar
  70. Gibbard A (1974) A Pareto-consistent libertarian claim. J Econ Theory 7(4):388–410MathSciNetCrossRefGoogle Scholar
  71. Gibbard A (1977) Manipulation of schemes that mix voting with chance. Econometrica 45:665–681MathSciNetzbMATHCrossRefGoogle Scholar
  72. Gibbard A (1978) Straightforwardness of game forms with lotteries as outcomes. Econometrica 46(3):595–614MathSciNetzbMATHCrossRefGoogle Scholar
  73. Grandmont JM (1978) Intermediate preferences and the majority rule. Econometrica 46:317–330MathSciNetzbMATHCrossRefGoogle Scholar
  74. Hammond PJ (1976) Equity, Arrow’s conditions, and Rawls’ difference principie. Econometrica 44:793–804MathSciNetzbMATHCrossRefGoogle Scholar
  75. Harsanyi JC (1953) Cardinal utility in welfare economics and in the theory of risk- taking. J Polit Econ 61:434–435CrossRefGoogle Scholar
  76. Harsanyi JC (1955) Cardinal welfare, individualistic ethics, and lnterpersonal comparisons of utility. J Polit Econ 63:309–321CrossRefGoogle Scholar
  77. Inada KI (1964) A note on the simple majority decision rule. Econometrica 32:316–338MathSciNetCrossRefGoogle Scholar
  78. Inada KI (1969) The simple majority decision rule. Econometrica 37:490–506zbMATHCrossRefGoogle Scholar
  79. Inada KI (1970) Majority rule and rationality. J Econ Theory 2:27–40MathSciNetCrossRefGoogle Scholar
  80. Kalai E, Muller E (1977) Characterization of domains admitting nondictatorial social welfare functions and nonmanipulable voting procedures. J Econ Theory 16(2):457–469MathSciNetzbMATHCrossRefGoogle Scholar
  81. Kalai E, Ritz Z (1980) Characterization of the private alternatives domains admitting arrow social welfare functions. J Econ Theory 22(1):23–36MathSciNetzbMATHCrossRefGoogle Scholar
  82. Kelly JS (1977) Strategy-proofness and social welfare functions without single- valuedness. Econometrica 45(2):439–446MathSciNetzbMATHCrossRefGoogle Scholar
  83. Kirman AP, Sondermann D (1972) Arrow’s theorem, many agents and invisible dictators. J Econ Theory 5(2):267–277MathSciNetCrossRefGoogle Scholar
  84. Le Breton M, Sen A (1999) Separable preferences, strategyproofness and decomposability. Econometrica 67(3):605–628MathSciNetzbMATHCrossRefGoogle Scholar
  85. Le Breton M, Weymark J (1996) An introduction to Arrovian social welfare functions on economic and political domains. In: Schofield N (ed) Collective decision making: social choice and political economy. Kluwer, DordrechtGoogle Scholar
  86. Le Breton M, Zaporozhets V (2009) On the equivalence of coalitional and individual strategy-proofness properties. Soc Choice Welf 33(2):287–309MathSciNetzbMATHCrossRefGoogle Scholar
  87. List C (2012) The theory of judgment aggregation: an introductory review. Synthese 187(1):179–207MathSciNetzbMATHCrossRefGoogle Scholar
  88. List C, Pettit P (2002) Aggregating sets of judgments: an impossibility result. Econ Philos 18(1):89–110CrossRefGoogle Scholar
  89. List C, Polak B (eds) (2010) Symposium: judgment aggregation, J Econ Theory 145(2):441–638Google Scholar
  90. Mas-Colell A, Sonnenschein H (1972) General possibility theorems for group decisions. Rev Econ Stud 39:185–192zbMATHCrossRefGoogle Scholar
  91. Maskin E (1995) Majority rule, social welfare functions, and game forms. In: Basu K, Pattanaik PK, Suzumura K (eds) Choice, welfare and development. Festschrift for Amartya Sen. Clarendon Press, OxfordGoogle Scholar
  92. Maskin E, Sjöström T (2002) Implementation theory. In: Arrow K, Sen AK, Suzumura K (eds) Handbook of social choice and welfare, vol 1. Elsevier Science, AmsterdamGoogle Scholar
  93. May KO (1952) A set of lndependent necessary and suffcient conditions for simple majority decision. Econometrica 20:680–684zbMATHCrossRefGoogle Scholar
  94. McKelvey RD (1976) Intransitivities in multidimensional voting models and some implications for agenda control. J Econ Theory 12(3):472–482MathSciNetzbMATHCrossRefGoogle Scholar
  95. McKelvey R (1979) General conditions for global intransitivities in formal voting models. Econometrica 47:1085–1111MathSciNetzbMATHCrossRefGoogle Scholar
  96. McLennan A (1980) Randomized preference aggregation: additivity of power and strategy proofness. J Econ Theory 22(1):1–11MathSciNetzbMATHCrossRefGoogle Scholar
  97. Moulin H (1979) Dominance solvable voting schemes. Econometrica 47(6):1337–1351MathSciNetzbMATHCrossRefGoogle Scholar
  98. Moulin H (1980a) On strategy-proofness and single-peakedness. Public Choice 35(4):437–455CrossRefGoogle Scholar
  99. Moulin H (1980b) Implementing efficient, anonymous and neutral social choice functions. J Math Econ 7(3):249–269MathSciNetzbMATHCrossRefGoogle Scholar
  100. Moulin H (1983) The strategy of social choice, Advanced textbooks in economics, vol 18. North-Holland, AmsterdamzbMATHGoogle Scholar
  101. Moulin H (1994) Social choice. In: Aumann RJ, Hart S (eds) Handbook of game theory with economic applications, vol 2. Elsevier, North Holland, Amsterdam. pp 1091–1125Google Scholar
  102. Moulin H, Peleg B (1982) Cores of effectivity functions and implementation theory. J Math Econ 10(1):115–145MathSciNetzbMATHCrossRefGoogle Scholar
  103. Mueller D (1978) Voting by veto. J Public Econ 10:57–75CrossRefGoogle Scholar
  104. Muller E, Satterthwaite MA (1977) The equivalence of strong positive association and strategy-proofness. J Econ Theory 14:412–418MathSciNetzbMATHCrossRefGoogle Scholar
  105. Muller E, Satterthwaite MA (1985) Strategy-proofness: the existence of dominant-strategy mechanisms. In: Hurwicz L, Schmeidler D, Sonnenschein H (eds) Social goals and social organization. Essays in memory of Elisha Pazner. Cambridge University Press, New York, 131–172Google Scholar
  106. Myerson RB (2008) Perspectives on mechanism design in economic theory. Am Econ Rev 98(3):586–603CrossRefGoogle Scholar
  107. Nehring K, Puppe C (2007a) Efficient and strategy-proof voting rules: a characterization. Games Econom Behav 59(1):132–153MathSciNetzbMATHCrossRefGoogle Scholar
  108. Nehring K, Puppe C (2007b) The structure of strategy-proof social choice: general characterization and possibility results on median spaces. J Econ Theory 135(1):269–305MathSciNetzbMATHCrossRefGoogle Scholar
  109. Nicolò A (2004) Efficiency and truthfulness with Leontief preferences. A note on two- agent, two-good economies. Rev Econ Des 8(4):373–382zbMATHGoogle Scholar
  110. Pattanaik PK (1976) Threats, counterthreats and strategic voting. Econometrica 44:91–103MathSciNetzbMATHCrossRefGoogle Scholar
  111. Pattanaik PK (1978) Strategy and group choice. North-Holland, AmsterdamzbMATHGoogle Scholar
  112. Pattanaik PK (1996) On modelling individual rights: some conceptual issues. In: Arrow KJ, Sen AK, Suzumura K (eds) Social choice reexamined. Palgrave Macmillan, UK. ISBN: 978-0-312-12741-1CrossRefGoogle Scholar
  113. Pattanaik PK, Peleg B (1986) Distribution of power under stochastic social choice rules. Econometrica 54(4):909–921MathSciNetzbMATHCrossRefGoogle Scholar
  114. Pattanaik PK, Suzumura K (1996) Individual rights and social evaluation. Oxf Econ Pap 48:194–212CrossRefGoogle Scholar
  115. Peremans W, Peters H, van der Stel H, Storcken T (1997) Strategy-proofness on Euclidean spaces. Soc Choice Welf 14:379–401MathSciNetzbMATHCrossRefGoogle Scholar
  116. Peters H, van der Stel H, Storken T (1991) On uncompromisingness and strategy-proofness, Reports in operations research and systems theory-report M 91–15. University of Limburg, HollandGoogle Scholar
  117. Peters H, van der Stel H, Storken T (1992) Pareto optimality, anonymity, and strategy-proofness in location problems. Int J Game Theory 21:221–235MathSciNetzbMATHCrossRefGoogle Scholar
  118. Plott CR (1973) Path independence, rationality and social choice. Econometrica 41(6):1075–1091MathSciNetzbMATHCrossRefGoogle Scholar
  119. Reffgen A (2015) Strategy-proof social choice on multiple and multi-dimensional single peaked domains. J Econ Theory 157:349–383MathSciNetzbMATHCrossRefGoogle Scholar
  120. Reffgen A, And Svensson L-G (2012) Strategy-proof voting for multiple public goods. Theor Econ 7(3):663–688MathSciNetzbMATHCrossRefGoogle Scholar
  121. Reny PJ (2001) Arrow’s theorem and the Gibbard-Satterthwaite theorem: a unified approach. Econ Lett 70:99–105MathSciNetzbMATHCrossRefGoogle Scholar
  122. Roberts K (1980) Possibility theorems with interpersonally comparable welfare levels. Rev Econ Stud 47:409–420MathSciNetzbMATHCrossRefGoogle Scholar
  123. Roth A (2008) What have we learned from market design?, Hahn Lecture. Econ J 118(527):285–310CrossRefGoogle Scholar
  124. Saari DG (2000) Mathematical structure of voting paradoxes. II positional voting. Econ Theory 15(1):55–102MathSciNetzbMATHCrossRefGoogle Scholar
  125. Samuelson PA (1967) Arrow’s Mathematical politics. In: Hook S (ed) Human values and economic policy. New York University Press, New York, pp 41–52Google Scholar
  126. Saporiti A (2009) Strategy-proofness and single crossing. Theor Econ 4:127–163Google Scholar
  127. Satterthwaite MA (1975) Strategy-proofness and Arrow’s conditions: existence and correspondence theorems for voting procedures and social welfare functions. J Econ Theory 10:187–217MathSciNetzbMATHCrossRefGoogle Scholar
  128. Satterthwaite MA, Sonnenschein H (1981) Strategy-proof allocation mechanisms at differentiable points. Rev Econ Stud 48:587–597MathSciNetzbMATHCrossRefGoogle Scholar
  129. Schmeidler D, Sonnenschein H (1978) Two proofs of the Gibbard-Satterthwaite theorem on the possibility of a strategy-proof social choice function. In: Gottinger HW, Leinfellner W (eds) Decision theory and social ethics. Reidel, Dordrecht, pp 227–234CrossRefGoogle Scholar
  130. Schofield N (1978) Instability in simple dynamic games. Rev Econ Stud 45:575–594zbMATHCrossRefGoogle Scholar
  131. Schummer J (1977) Strategy-proofness versus efficiency on restricted domains of exchange economies. Soc Choice Welf 14(1):47–56MathSciNetzbMATHCrossRefGoogle Scholar
  132. Sen AK (1966) A possibility theorem on majority decisions’. Econometrica 34(2):491–499zbMATHCrossRefGoogle Scholar
  133. Sen AK (1970) The impossibility of a Paretian liberal. J Polit Econ 78:152–157CrossRefGoogle Scholar
  134. Sen AK (1977a) Social choice theory: a re-examination. Econometrica 45:53–89MathSciNetzbMATHCrossRefGoogle Scholar
  135. Sen AK (1977b) On weights and measures: informational constraints in social welfare analysis. Econometrica 45:1539–1572MathSciNetzbMATHCrossRefGoogle Scholar
  136. Sen AK, Pattanaik PK (1969) Necessary and sufficient conditions for rational choice under majority decision. J Econ Theory 1:178–202MathSciNetCrossRefGoogle Scholar
  137. Serizawa S (1999) Strategy-proof and symmetric social choice functions for public good economies. Econometrica 67(1):121–145MathSciNetzbMATHCrossRefGoogle Scholar
  138. Shepsle KA, Weingast BR (1984) Uncovered sets and sophisticated voting outcomes with implications for agenda institutions. Am J Polit Sci 28:49–74CrossRefGoogle Scholar
  139. Slinko A (2002) The asymptotic strategy-proofness of the plurality and the run-off rules. Soc Choice Welf 19:313–324MathSciNetzbMATHCrossRefGoogle Scholar
  140. Smith J (1973) Aggregation of preferences with variable electorate. Econometrica 41(6):1027–1041MathSciNetzbMATHCrossRefGoogle Scholar
  141. Sönmez T (1999) Strategy-proofness and essentially single-valued cores. Econometrica 67:677–689MathSciNetzbMATHCrossRefGoogle Scholar
  142. Taylor AD (2005) Social choice and the Mathematics of manipulation. Cambridge University Press, New YorkzbMATHCrossRefGoogle Scholar
  143. Vickrey W (1960) Utility, strategy and social decision rules. Q J Econ 74:507–535CrossRefGoogle Scholar
  144. Vorsatz M (2007) Approval voting on dichotomous preferences. Soc Choice Welf 28(1):127–141MathSciNetzbMATHCrossRefGoogle Scholar
  145. Weymark JA (1999) Decomposable strategy-proof social choice functions. Jpn Econ Rev 50(3):343–355MathSciNetCrossRefGoogle Scholar
  146. Wilson R (1972) Social choice without the Pareto principle. J Econ Theory 5:478–486MathSciNetCrossRefGoogle Scholar
  147. Young HP (1974) An axiomatization of Borda’s rule. J Econ Theory 9:43–52MathSciNetCrossRefGoogle Scholar
  148. Young HP (1975) Social choice scoring functions. SIAM J Appl Math 28:824–838MathSciNetzbMATHCrossRefGoogle Scholar
  149. Young HP (1988) Condorcet’s theory of voting. Am Polit Sci Rev 82:1231–1244CrossRefGoogle Scholar
  150. Yu NN (2012) A one-shot proof of Arrow’s impossibility theorem. Econ Theory 50(2):523–525MathSciNetzbMATHCrossRefGoogle Scholar
  151. Yu NN (2013) A one-shot proof of Arrow’s theorem and the Gibbard-Satterthwaite theorem. Econ Theory Bull 1(2):145–149CrossRefGoogle Scholar
  152. Zeckhauser R (1973) Voting systems, honest preferences and Pareto optimality. Am Polit Sci Rev 67:934–946CrossRefGoogle Scholar
  153. Zhou L (1991) Impossibility of strategy-proof mechanisms in economies with pure public goods. Rev Econ Stud 58:107–119MathSciNetzbMATHCrossRefGoogle Scholar

Reference Books

  1. Arrow KJ (1951, 1963) Social choice and individual values, 2nd edn. Wiley, New YorkGoogle Scholar
  2. Arrow KJ, Sen AK, Suzumura K (eds) (2001/2010) Handbook of social choice and welfare, vols 1 and 2. North-Holland, AmsterdamGoogle Scholar
  3. Austen-Smith D, Banks JS (1999) Positive political theory I. Collective preference. The University of Michigan Press, Michigan. ISBN: 9780472068944Google Scholar
  4. Austen-Smith D, Banks JS (2005) Positive political theory II: strategy and structure. University of Michigan Press, MichiganGoogle Scholar
  5. Balinski M, Laraki R (2010) Majority judgment: measuring, ranking, and electing. MIT Press, Cambridge, MAGoogle Scholar
  6. Black D (1958) The theory of committees and elections. Cambridge University Press, CambridgezbMATHGoogle Scholar
  7. Bossert W, Suzumura K (2010) Consistency choice and rationality. Harvard University Press, Cambridge, MAGoogle Scholar
  8. Brandt F, Conitzer V, Endriss U, Lang J, Procaccia AD (eds) (2016) Handbook of computational social choice. Cambridge University Press, Cambridge, UKGoogle Scholar
  9. Fishburn P (1973) The theory of social choice. Princeton University Press, PrincetonzbMATHGoogle Scholar
  10. Gaertner W (2001) Domain conditions in social choice theory. Oxford University Press, Oxford, UK.Google Scholar
  11. Gaertner W (2006) A primer in social choice theory. Oxford University Press, Oxford, UKGoogle Scholar
  12. Kelly JS (1988) Social choice theory. An introduction. Springer, Berlin/Heidelberg/New YorkzbMATHCrossRefGoogle Scholar
  13. Krantz DH, Luce RD, Suppes P, Tversky A (1971) Foundations of measurement, vol I: Additive and polynomial representations. Academic Press, New YorkzbMATHGoogle Scholar
  14. Luce RD, Krantz DH, Suppes P, Tversky A (1990) Foundations of measurement, vol III: representation, axiomatization, and invariance. Academic, New YorkzbMATHGoogle Scholar
  15. Mas-Colell A, Whinston MD, Green J (1995) Microeconomic theory. Oxford University Press, Oxford (Part 5)Google Scholar
  16. McLean I, Urken AB (1995) Classics of social choice. The University of Michigan Press, MichiganGoogle Scholar
  17. Moulin H (1988) Axioms of cooperative decision making. Econometric society monographs, vol 15. Cambridge University Press, Cambridge, UK. ISBN: 9780521360555Google Scholar
  18. Nitzan S, Paroush J (1985) Collective decision making: an economic outlook. Cambridge University Press, New YorkGoogle Scholar
  19. Pattanaik PK (1978) Strategy and group choice. North-Holland, AmsterdamzbMATHGoogle Scholar
  20. Peleg B (1984) Game theoretic analysis of voting in committees. Cambridge University Press, CambridgezbMATHCrossRefGoogle Scholar
  21. Rawls J (1971) A theory of justice. Harvard University Press, Cambridge, MA. ISBN: 9780674000780Google Scholar
  22. Saari DG (1995) Basic geometry of voting. Springer, Berlin/Heidelberg/New YorkzbMATHCrossRefGoogle Scholar
  23. Sen AK (1970) Collective choice and social welfare. Holden-Day, San Francisco/CambridgezbMATHGoogle Scholar
  24. Sen AK (1982) Choice, welfare and measurement. Basil Blackwell, Oxford, UKGoogle Scholar
  25. Sen AK (1992) Inequality reexamined. Harvard University Press, Cambridge, MAGoogle Scholar
  26. Suppes P, Krantz DH, Luce RD, Tversky A (1989) Foundations of measurement, vol II: Geometrical, threshold, and probabilistic respresentations. Academic, New YorkzbMATHGoogle Scholar
  27. Suzumura K (1983) Rational choice, collective decisions, and social welfare. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  28. Suzumura K (2016) Choice, preferences and procedures. Harvard University Press, Cambridge, MAGoogle Scholar
  29. Young P (1994) Equity: in theory and practice. Princeton University Press, PrincetonGoogle Scholar

Copyright information

© Springer Science+Business Media LLC 2018

Authors and Affiliations

  1. 1.MOVE, Universitat Autònoma de Barcelona and Barcelona GSEBarcelonaSpain