Glossary
- Aggregation Rules :
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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 :
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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 :
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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...
Bibliography
Alcantud JC, Laruelle A (2014) Disapproval voting: a characterization. Soc Choice Welf 43:1–10
Apesteguia J, Ballester MA, Masatlioglu Y (2014) A foundation for strategic agenda voting. Games Econom Behav 87:91–99
Austen-Smith D, Banks JS (1996) Information aggregation, rationality and the Condorcet Jury Theorem. Am Polit Sci Rev 90(1):34–45
Austen-Smith D, Feddersen T (2006) Deliberation, preference uncertainty and voting rules. Am Polit Sci Rev 100(2):209–217
Austen-Smith D, Feddersen T (2009) Information aggregation and communication in committees. Philos Trans R Soc B 364(1518):763–769
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 301–334
Ballester MA, Haeringer G (2011) A characterization of the single-peaked domain. Soc Choice Welf 36:305–322
Banks JS (1985) Sophisticated voting outcomes and agenda control. Soc Choice Welf 1:295–306
Banks JS, Bordes G (1988) Voting games, indifference, and consistent sequential choice rules. Soc Choice Welf 5:31–44
Barberà S (1977) The manipulation of social choice mechanisms that do not leave too much to chance. Econometrica 45(7):1573–1588
Barberà S (1979) Majority and positional is voting in a probabilistic framework. Rev Econ Stud 46(2):379–389
Barberà S (1983a) Strategy-Proofness and pivotal voters: a direct proof of the Gibbard-Satterthwaite Theorem. Int Econ Rev 24(2):413–418
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 31–35
Barberà S (2001) An introduction to strategy-proof social choice functions. Soc Choice Welf 18:619–653
Barbera S, Coelho D (2010) On the rule of k names. Games Econom Behav 70:44–61
Barbera S, Coelho D (2017) Balancing the power to appoint officers. Games Econom Behav 101:189–203
Barbera S, Gerber A (2017) Sequential voting and agenda manipulation. Theor Econ 12(1):211–247
Barberà S, Peleg B (1990) Strategy-proof voting schemes with continuous preferences. Soc Choice Welf 7:31–38
Barberà S, Sonnenschein H (1978) Preference aggregation with randomized social orderings. J Econ Theory 18(2):244–254
Barberà S, Valenciano F (1983) Collective probabilistic judgements. Econometrica 51(4):1033–1046
Barberà S, Sonnenschein H, Zhou L (1991) Voting by committees. Econometrica 59:595–609
Barberà S, Gul F, Stacchetti E (1993) Generalized median voter schemes and committees. J Econ Theory 61:262–289
Barberà S, Massó J, Neme A (1997) Voting under constraints. J Econ Theory 76(2):298–321
Barberà S, Bogomolnaia A, van der Stel H (1998) Strategy-proof probabilistic rules for expected utility maximizers. Math Soc Sci 35(2):89–103
Barberà S, Dutta B, Sen A (2001) Strategy-proof social choice correspondences. J Econ Theory 101(2):374–394
Barberà S, Massó J, Neme A (2005) Voting by committees under constraints. J Econ Theory 122:185–205
Barberà S, Berga D, Moreno B (2010) Individual versus group strategy- Proofness: when do they coincide? J Econ Theory 145(5):1648–1674
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):345–359
Benoît J-P (2002) Strategic manipulation in voting games when lotteries and ties are permitted. J Econ Theory 1023(2):421–436
Berga D (1998) Strategy-Proofness and single-plateaued preferences. Math Soc Sci 35:105–120
Bergson A (1938) A reformulation of certain aspects of welfare economics. Q J Econ 52(2):310–334
Black D (1948) On the rationale of group decision making. J Polit Econ 56:23–34
Blackorby C, Donaldson D, Weymark JA (1984) Social choice with interpersonal utility comparisons: a diagrammatic introduction. Int Econ Rev 25:327–356
Blair D, Bordes G, Kelly J, Suzumura K (1976) Impossibility theorems without collective rationality. J Econ Theory 13(3):361–379
Blair DH, Muller E (1983) Essential aggregation procedures on restricted domains of preferences. J Econ Theory 30(1):34–53
Blair D, Pollak R (1979) Collective rationality and dictatorship: the scope of the arrow theorem. J Econ Theory 21:186–194
Blin JM, Satterthwaite MA (1976) Strategy-proofness and single peakedness. Public Choice 26:51–58
Border K, Jordan JS (1983) Straightforward elections, unanimity and phantom voters. Rev Econ Stud 50:153–170
Brams SJ, Fishburn PC (1978) Approval voting. Am Polit Sci Rev 72(3):831–847
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 173–236
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, Amsterdam
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, Amsterdam
Campbell DE, Kelly JS (2009) Gains from manipulating social choice rules. Econ Theory 40(3):349–371
Campbell DE, Kelly JS (2010) Losses due to manipulation of social choice rules. Econ Theory 45(3):453–467
Casella A (2005) Storable votes. Games Econom Behav, special issue: In Honor of Richard D. McKelvey. Elsevier 51(2):391–419
Chichilnisky G (1980) Social choice and the topology of spaces of preferences. Adv Math 37:165–176
D’Aspremont C, Gevers L (1977) Equity and the informational basis of collective choice. Rev Econ Stud 44:199–209
de Borda JC (1781) Mémoire sur les élections au scrutin. Hist Acad Roy Sci:657–665
de Condorcet M (1785) Essai sur l’application de l’analyse à la probabilité dés décisions rendues à la pluralité des voix, Paris
Demange G (1982) Single-peaked orders on a tree. Math Soc Sci 3(4):389–396
Dietrich F (2006) Judgment aggregation: (im)possibility theorems. J Econ Theory 126(1):286–298
Duggan J, Schwartz T (2000) Strategic manipulability without resoluteness or shared beliefs: Gibbard–Satterthwaite generalized. Soc Choice Welf 17(1):85–93
Dutta B, Peters H, Sen A (2002) Strategy-proof probabilistic mechanisms in economies with pure public goods. J Econ Theory 106(2):392–416
Dutta B, Peters H, Sen A (2007) Strategy-proof cardinal decision schemes. Soc Choice Welf 28(1):163–179
Eliaz K (2004) Social aggregators. Soc Choice Welf 22:317–330
Farquharson R (1969) Theory of voting. Yale University Press, New Haven
Feldman A, Serrano R (2008) Arrow’s impossibility theorem: two simple single-profile versions. Harv Coll Math Rev 2:46–57
Felsenthal DS (1989) On combining approval with disapproval voting. Soc Choice Welf 34(1):53–60
Fishburn PC (1970) Arrow’s impossibility theorem: concise proof and infinite voters. J Econ Theory 2:103–106
Fishburn PC (1973) The theory of social choice. Princeton University Press, Princeton
Fishburn PC (1984) Discrete mathematics in voting and group choice. SIAM J Algebra Discrete Methods 5(2):263–275
Gaertner W (1986) Pareto, interdependent rights exercising and strategic behaviour. J Econ, SuppL: 5:79–98
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 York
Gaertner W (2009) A primer in social choice theory, revised. Oxford University Press, New York
Gaertner W, Pattanaik PK, Suzumura K (1992) Individual rights revisited. Economica 59:161–177
Gans JS, Smart M (1996) Majority voting with single-crossing preferences. J Public Econ 59:219–237
Gardenfors P (1973) Positionalist voting functions. Theor Decis 4:1–24
Geanakoplos J (2005) Three brief proofs of Arrow’s Impossibility Theorem. Econ Theory 26(1):211–215
Gibbard A (1973) Manipulation of voting schemes: a general result. Econometrica 41:587–602
Gibbard A (1974) A Pareto-consistent libertarian claim. J Econ Theory 7(4):388–410
Gibbard A (1977) Manipulation of schemes that mix voting with chance. Econometrica 45:665–681
Gibbard A (1978) Straightforwardness of game forms with lotteries as outcomes. Econometrica 46(3):595–614
Grandmont JM (1978) Intermediate preferences and the majority rule. Econometrica 46:317–330
Hammond PJ (1976) Equity, Arrow’s conditions, and Rawls’ difference principie. Econometrica 44:793–804
Harsanyi JC (1953) Cardinal utility in welfare economics and in the theory of risk- taking. J Polit Econ 61:434–435
Harsanyi JC (1955) Cardinal welfare, individualistic ethics, and lnterpersonal comparisons of utility. J Polit Econ 63:309–321
Inada KI (1964) A note on the simple majority decision rule. Econometrica 32:316–338
Inada KI (1969) The simple majority decision rule. Econometrica 37:490–506
Inada KI (1970) Majority rule and rationality. J Econ Theory 2:27–40
Kalai E, Muller E (1977) Characterization of domains admitting nondictatorial social welfare functions and nonmanipulable voting procedures. J Econ Theory 16(2):457–469
Kalai E, Ritz Z (1980) Characterization of the private alternatives domains admitting arrow social welfare functions. J Econ Theory 22(1):23–36
Kelly JS (1977) Strategy-proofness and social welfare functions without single- valuedness. Econometrica 45(2):439–446
Kirman AP, Sondermann D (1972) Arrow’s theorem, many agents and invisible dictators. J Econ Theory 5(2):267–277
Le Breton M, Sen A (1999) Separable preferences, strategyproofness and decomposability. Econometrica 67(3):605–628
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, Dordrecht
Le Breton M, Zaporozhets V (2009) On the equivalence of coalitional and individual strategy-proofness properties. Soc Choice Welf 33(2):287–309
List C (2012) The theory of judgment aggregation: an introductory review. Synthese 187(1):179–207
List C, Pettit P (2002) Aggregating sets of judgments: an impossibility result. Econ Philos 18(1):89–110
List C, Polak B (eds) (2010) Symposium: judgment aggregation, J Econ Theory 145(2):441–638
Mas-Colell A, Sonnenschein H (1972) General possibility theorems for group decisions. Rev Econ Stud 39:185–192
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, Oxford
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, Amsterdam
May KO (1952) A set of lndependent necessary and suffcient conditions for simple majority decision. Econometrica 20:680–684
McKelvey RD (1976) Intransitivities in multidimensional voting models and some implications for agenda control. J Econ Theory 12(3):472–482
McKelvey R (1979) General conditions for global intransitivities in formal voting models. Econometrica 47:1085–1111
McLennan A (1980) Randomized preference aggregation: additivity of power and strategy proofness. J Econ Theory 22(1):1–11
Moulin H (1979) Dominance solvable voting schemes. Econometrica 47(6):1337–1351
Moulin H (1980a) On strategy-proofness and single-peakedness. Public Choice 35(4):437–455
Moulin H (1980b) Implementing efficient, anonymous and neutral social choice functions. J Math Econ 7(3):249–269
Moulin H (1983) The strategy of social choice, Advanced textbooks in economics, vol 18. North-Holland, Amsterdam
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 1091–1125
Moulin H, Peleg B (1982) Cores of effectivity functions and implementation theory. J Math Econ 10(1):115–145
Mueller D (1978) Voting by veto. J Public Econ 10:57–75
Muller E, Satterthwaite MA (1977) The equivalence of strong positive association and strategy-proofness. J Econ Theory 14:412–418
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, 131–172
Myerson RB (2008) Perspectives on mechanism design in economic theory. Am Econ Rev 98(3):586–603
Nehring K, Puppe C (2007a) Efficient and strategy-proof voting rules: a characterization. Games Econom Behav 59(1):132–153
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):269–305
Nicolò A (2004) Efficiency and truthfulness with Leontief preferences. A note on two- agent, two-good economies. Rev Econ Des 8(4):373–382
Pattanaik PK (1976) Threats, counterthreats and strategic voting. Econometrica 44:91–103
Pattanaik PK (1978) Strategy and group choice. North-Holland, Amsterdam
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: 978-0-312-12741-1
Pattanaik PK, Peleg B (1986) Distribution of power under stochastic social choice rules. Econometrica 54(4):909–921
Pattanaik PK, Suzumura K (1996) Individual rights and social evaluation. Oxf Econ Pap 48:194–212
Peremans W, Peters H, van der Stel H, Storcken T (1997) Strategy-proofness on Euclidean spaces. Soc Choice Welf 14:379–401
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, Holland
Peters H, van der Stel H, Storken T (1992) Pareto optimality, anonymity, and strategy-proofness in location problems. Int J Game Theory 21:221–235
Plott CR (1973) Path independence, rationality and social choice. Econometrica 41(6):1075–1091
Reffgen A (2015) Strategy-proof social choice on multiple and multi-dimensional single peaked domains. J Econ Theory 157:349–383
Reffgen A, And Svensson L-G (2012) Strategy-proof voting for multiple public goods. Theor Econ 7(3):663–688
Reny PJ (2001) Arrow’s theorem and the Gibbard-Satterthwaite theorem: a unified approach. Econ Lett 70:99–105
Roberts K (1980) Possibility theorems with interpersonally comparable welfare levels. Rev Econ Stud 47:409–420
Roth A (2008) What have we learned from market design?, Hahn Lecture. Econ J 118(527):285–310
Saari DG (2000) Mathematical structure of voting paradoxes. II positional voting. Econ Theory 15(1):55–102
Samuelson PA (1967) Arrow’s Mathematical politics. In: Hook S (ed) Human values and economic policy. New York University Press, New York, pp 41–52
Saporiti A (2009) Strategy-proofness and single crossing. Theor Econ 4:127–163
Satterthwaite MA (1975) Strategy-proofness and Arrow’s conditions: existence and correspondence theorems for voting procedures and social welfare functions. J Econ Theory 10:187–217
Satterthwaite MA, Sonnenschein H (1981) Strategy-proof allocation mechanisms at differentiable points. Rev Econ Stud 48:587–597
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 227–234
Schofield N (1978) Instability in simple dynamic games. Rev Econ Stud 45:575–594
Schummer J (1977) Strategy-proofness versus efficiency on restricted domains of exchange economies. Soc Choice Welf 14(1):47–56
Sen AK (1966) A possibility theorem on majority decisions’. Econometrica 34(2):491–499
Sen AK (1970) The impossibility of a Paretian liberal. J Polit Econ 78:152–157
Sen AK (1977a) Social choice theory: a re-examination. Econometrica 45:53–89
Sen AK (1977b) On weights and measures: informational constraints in social welfare analysis. Econometrica 45:1539–1572
Sen AK, Pattanaik PK (1969) Necessary and sufficient conditions for rational choice under majority decision. J Econ Theory 1:178–202
Serizawa S (1999) Strategy-proof and symmetric social choice functions for public good economies. Econometrica 67(1):121–145
Shepsle KA, Weingast BR (1984) Uncovered sets and sophisticated voting outcomes with implications for agenda institutions. Am J Polit Sci 28:49–74
Slinko A (2002) The asymptotic strategy-proofness of the plurality and the run-off rules. Soc Choice Welf 19:313–324
Smith J (1973) Aggregation of preferences with variable electorate. Econometrica 41(6):1027–1041
Sönmez T (1999) Strategy-proofness and essentially single-valued cores. Econometrica 67:677–689
Taylor AD (2005) Social choice and the Mathematics of manipulation. Cambridge University Press, New York
Vickrey W (1960) Utility, strategy and social decision rules. Q J Econ 74:507–535
Vorsatz M (2007) Approval voting on dichotomous preferences. Soc Choice Welf 28(1):127–141
Weymark JA (1999) Decomposable strategy-proof social choice functions. Jpn Econ Rev 50(3):343–355
Wilson R (1972) Social choice without the Pareto principle. J Econ Theory 5:478–486
Young HP (1974) An axiomatization of Borda’s rule. J Econ Theory 9:43–52
Young HP (1975) Social choice scoring functions. SIAM J Appl Math 28:824–838
Young HP (1988) Condorcet’s theory of voting. Am Polit Sci Rev 82:1231–1244
Yu NN (2012) A one-shot proof of Arrow’s impossibility theorem. Econ Theory 50(2):523–525
Yu NN (2013) A one-shot proof of Arrow’s theorem and the Gibbard-Satterthwaite theorem. Econ Theory Bull 1(2):145–149
Zeckhauser R (1973) Voting systems, honest preferences and Pareto optimality. Am Polit Sci Rev 67:934–946
Zhou L (1991) Impossibility of strategy-proof mechanisms in economies with pure public goods. Rev Econ Stud 58:107–119
Reference Books
Arrow KJ (1951, 1963) Social choice and individual values, 2nd edn. Wiley, New York
Arrow KJ, Sen AK, Suzumura K (eds) (2001/2010) Handbook of social choice and welfare, vols 1 and 2. North-Holland, Amsterdam
Austen-Smith D, Banks JS (1999) Positive political theory I. Collective preference. The University of Michigan Press, Michigan. ISBN: 9780472068944
Austen-Smith D, Banks JS (2005) Positive political theory II: strategy and structure. University of Michigan Press, Michigan
Balinski M, Laraki R (2010) Majority judgment: measuring, ranking, and electing. MIT Press, Cambridge, MA
Black D (1958) The theory of committees and elections. Cambridge University Press, Cambridge
Bossert W, Suzumura K (2010) Consistency choice and rationality. Harvard University Press, Cambridge, MA
Brandt F, Conitzer V, Endriss U, Lang J, Procaccia AD (eds) (2016) Handbook of computational social choice. Cambridge University Press, Cambridge, UK
Fishburn P (1973) The theory of social choice. Princeton University Press, Princeton
Gaertner W (2001) Domain conditions in social choice theory. Oxford University Press, Oxford, UK.
Gaertner W (2006) A primer in social choice theory. Oxford University Press, Oxford, UK
Kelly JS (1988) Social choice theory. An introduction. Springer, Berlin/Heidelberg/New York
Krantz DH, Luce RD, Suppes P, Tversky A (1971) Foundations of measurement, vol I: Additive and polynomial representations. Academic Press, New York
Luce RD, Krantz DH, Suppes P, Tversky A (1990) Foundations of measurement, vol III: representation, axiomatization, and invariance. Academic, New York
Mas-Colell A, Whinston MD, Green J (1995) Microeconomic theory. Oxford University Press, Oxford (Part 5)
McLean I, Urken AB (1995) Classics of social choice. The University of Michigan Press, Michigan
Moulin H (1988) Axioms of cooperative decision making. Econometric society monographs, vol 15. Cambridge University Press, Cambridge, UK. ISBN: 9780521360555
Nitzan S, Paroush J (1985) Collective decision making: an economic outlook. Cambridge University Press, New York
Pattanaik PK (1978) Strategy and group choice. North-Holland, Amsterdam
Peleg B (1984) Game theoretic analysis of voting in committees. Cambridge University Press, Cambridge
Rawls J (1971) A theory of justice. Harvard University Press, Cambridge, MA. ISBN: 9780674000780
Saari DG (1995) Basic geometry of voting. Springer, Berlin/Heidelberg/New York
Sen AK (1970) Collective choice and social welfare. Holden-Day, San Francisco/Cambridge
Sen AK (1982) Choice, welfare and measurement. Basil Blackwell, Oxford, UK
Sen AK (1992) Inequality reexamined. Harvard University Press, Cambridge, MA
Suppes P, Krantz DH, Luce RD, Tversky A (1989) Foundations of measurement, vol II: Geometrical, threshold, and probabilistic respresentations. Academic, New York
Suzumura K (1983) Rational choice, collective decisions, and social welfare. Cambridge University Press, Cambridge
Suzumura K (2016) Choice, preferences and procedures. Harvard University Press, Cambridge, MA
Young P (1994) Equity: in theory and practice. Princeton University Press, Princeton
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Barberà, S. (2018). Social Choice Theory. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27737-5_666-1
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