Northwestern University

J. L. Kellogg Graduate School of Management

Social Choice and Voting Models

Professor Roger Myerson

General references:

• Herve Moulin, Axioms of Cooperative Decision Making, Cambridge, 1988. (ACDM), the reference for start of course.
• Dennis C. Mueller, Public Choice II, Cambridge, 1989, encyclopedic survey with great bibliography
• William H. Riker, Liberalism against Populism, Freeman, 1982, profound new political ideas, and a survey of social choice
• Kenneth A. Shepsle, Models of Multiparty Competition, Harwood, 1991, a short book on competition in spatial models
• Amartya K. Sen, Collective Choice and Social Welfare, Holden-Day, 1970, definitive text of social choice before Gibbard-Satterthwaite
• Duncan Black, Theory of Committees and Elections, Cambridge, 1958, ends with a fascinating survey of ancients Borda, Condorcet, & Dodgson
• Carl Friedrich, Constitutional Government and Democracy, Ginn, 1968, comparative politics classic
• Rein Taagepera and Matthew S. Shugart, Seats and Votes, Yale, 1989, encyclopedic comparative review of existing electoral systems

I. Fundamentals of majority rule; binary voting in committees

A. Majority rule

• Moulin, ACDM, section 11.1
• K. O. May, "A set of independent necessary and sufficient conditions for simple majority decision," Econometrica 20, 1952.
• D. C. McGarvey, "A theorem in the construction of voting paradoxes," Econometrica 21, 1953.

B. Binary agendas

• Moulin, ACDM, section 9.4
• Moulin, "Dominance solvable voting schemes," Econometrica 47, 1979.
• R. Farquharson, Theory of Voting, Yale, 1969.

C. Top Cycle

• Moulin, ACDM, pages 253-4.
• N. Miller, "Graph theoretical approaches to the theory of voting," American Journal of Political Science 21, 1977.
• R. B. Myerson, Game Theory, Section 4.10.
• R. McKelvey, "Intransitivities in multidimensional voting models and some implications for agenda control," Journal of Economic Theory 12, 1976.
• R. D. McKelvey, "General conditions for global intransitivities in formal voting models," Econometrica 47, 1979.

D. Uncovered set, Banks set, and other tournament solutions

• Moulin, ACDM, pages 246-7 and 254-5, and sections 9.1 and 9.2.
• N. Miller, "A new solution set for tournaments and majority voting," American Journal of Political Science 24, 1980 (erratum 1983).
• K. Shepsle and B. Weingast, "Uncovered sets and sophisticated voting outcomes, with implications for agenda institutions," American Journal of Political Science 28, 1984.
• J. Banks, "Sophisticated voting outcomes and agenda control," Social Choice and Welfare 1, 1985.
• Moulin, "Choosing from a tournament," Social Choice and Welfare 3, 1986.

II. Two-party competition

A.General tournaments

• R. McKelvey, "Covering, dominance, and institution-free properties of social choice," American Journal of Political Science 30, 1986.
• David C. Fisher and Jennifer Ryan, "Optimal strategies for a generalized 'scissors, paper, and stone' game," American Mathematical Monthly 99 (1992), 935-942.
• G. Laffond, J.F. Laslier, and M. Le Breton, "The bipartisan set of a tournament game," Games and Economic Behavior 5 (1993), 182-201.

B. Euclidean policy space

• H. Hotelling, "Stability in competition," Economic Journal 39 (1929), 41-57.
• P. Ordeshook, Game Theory and Political Theory, Cambridge (1986), Sections 4.5-4.9
• Mueller, Public Choice II, Chapters 10 and 11
• Black, Theory of Committees and Elections, chapter 4.
• O. Gross and R. Wagner, "A continuous Colonel Blotto game," RAND Research Memorandum RM-408 (1950), Santa Monica, CA.
• "Example IV.6.3" in G. Owen, Game Theory, Academic Press (1982), 78-83.
• G. Kramer, "A dynamical model of political equilibrium," Journal of Economic Theory 16 (1977), 310-334.

C. Supermajority voting with a status quo

• Moulin, ACDM, Sections 10.3, 10.4, 11.4
• A. Caplin and B. Nalebuff, "On 64% majority rule," Econometrica 56, 1988; and
• "Aggregation and social choice: a mean voter theorem," Econometrica 59, 1991.

D. Costly voting

• Mueller, Public Choice, chapter 18
• T. R. Palfrey and H. Rosenthal, "A strategic calculus of voting," Public Choice 41, 1983.
• T. R. Palfrey and H. Rosenthal, "Voter participation and strategic uncertainty," American Political Science Review 79, 1985.
• J. Ledyard, "The pure theory of large two-candidate elections," Public Choice 44 (1984), 7-41.
• C. J. Uhlaner, "Rational turnout: the neglected role of groups," American Journal of Political Science 33 (1989), 390-422.

E. Private information

• T. Feddersen and W. Pesendorfer, "The Swing Voter's Curse," Northwestern U. discussion paper (1993).

III. Aggregation of preferences with multiple options

A. Independence of irrelevant alternatives, and consistency

• Moulin, ACDM, Section 11.2, 11.6, 11.7
• K. J. Arrow, Social Choice and Individual Values, Wiley, 1951.
• Sen, Collective Choice and Social Welfare.
• J. C. Harsanyi, "Cardinal welfare, individualistic ethics, and interpersonal comparisons of utility," Journal of Political Economy 63 (1955).

B. Strategyproof voting systems

• Moulin, ACDM, Sections 10.1 and 10.2, 11.5
• A. Gibbard, "Manipulation of voting rules: a general result," Econometrica 41, 1973.
• M. A. Satterthwaite, "Strategy-proofness and Arrow's conditions," Journal of Economic Theory 10, 1975.
• D. Schmeidler and H. Sonnenschein, "Two proofs of the Gibbard-Satterthwaite theorem on the possibility of a strategy-proof social choice function," in H. W. Gottinger and W. Leinfeller eds., Decision Theory and Social Ethics, Issues in Social Choice, Reidel (1978).
• A. Gibbard, "Straightforwardness of game forms with lotteries as outcomes," Econometrica 46 (1978).

C. Implementation by Nash equilibrium

• Moulin, ACDM, section 10.5.
• E. Muller and M. Satterthwaite, "The equivalence of strong positive association and strategy-proofness," Journal of Economic Theory 14 (1977), 412-418.
• E. Maskin, "The theory of implementation in Nash equilibrium: a survey," in L. Hurwicz, D. Schmeidler, and H. Sonnenschein eds., Social Goals and Social Organization, Cambridge U. Press (1985).
• D. Abreu and A. Sen, "Virtual implementation in Nash equilibrium," Econometrica 59 (1991).
• J. Moore, "Implementation in Environments with Complete Information," in Advances in Economic Theory: Proceedings of the 6th World Congress of the Econometric Society, J.-J.Laffont ed., Cambridge U. Press (1992).
• M. Jackson, "Implementation in undominated strategies: a look at bounded mechanisms," Review of Economic Studies 59 (1992) 757-775.

D. Scoring rules

• Moulin, ACDM, Sections 9.1 and 9.3
• H. P. Young, "Social choice scoring functions," SIAM Journal of Applied Mathematics 28, 1975.
• J. Smith, "Aggregation of preferences with a variable electorate," Econometrica 41, 1973.
• R. Myerson, "Axiomatic derivation of scoring rules without the ordering assumption," Northwestern U. Math Center DP 1063 (1993).

IV. Multiparty competition in policy space

A. Competition with a fixed number of parties

• Shepsle, Models of Multiparty Competition, Parts I and II.
• R. Myerson and R. Weber, "A theory of voting equilibria," American Political Science Review 87 (1993) 102-114.
• D. Rae, V. Hanby, J. Loosemore, "Thresholds of representation and thresholds of exclusion," Comparative Political Studies 3 (1971), 479-488.
• G. Cox, "Electoral equilibrium under alternative voting institutions," American Journal of Political Science 31 (1987), 82-108.
• G. Cox, "Centripital and centrifugal incentives in electoral systems," American Journal of Political Science 34 (1990), 903-935.
• R. Myerson, "Incentives to cultivate favored minorities under alternative electoral systems," American Political Science Review 87 (1993), 856-869.

B. Competition with entry

• Shepsle, Models of Multiparty Competition, Parts III and IV.
• T. J. Feddersen, I. Sened, and S. G. Wright, "Rational voting and candidate entry under plurality rule," American Journal of Political Science 34 (1990), 1005-1016.
• M. Osborne, "Candidate positioning and entry in a political competition," Games and Economic Behavior 5 (1993), 133-151.
• W. H. Riker, "The two-party system and Duverger's law," American Political Science Review 76 (1982), 753-766.
• T. R. Palfrey, "A mathematical proof of Duverger's law," in Models of Strategic Choice in Politics, ed. by P. C. Ordeshook, University of Michigan Press (1989), 69-91.
• T. Feddersen "A Voting Model implying Duverger's Law and Positive Turnout," American Journal of Political Science 36, 938-962 (1992).
• G. Cox, "Strategic Voting Equilibria under SNTV: the M+1 rule," UCSD (1992).
• S. R. Reed, "Structure and behavior: extending Duverger's law to the Japanese case," British J. of Political Science 20 (1990), 335-356.
• A. Lijphart, "The political consequences of electoral laws, 1945-1985," American Political Science Review 84 (1990), 481-496.
• J. Carey and M. Shugart, "Incentives to Cultivate a Personal Vote: A Rank Ordering of Electoral Formulas," Electoral Studies 14 (1995).

V. Rikerian liberalism: voters against politicians

A. Abuse of power

• Riker, Liberalism against Populism, chapters 1 and 10.
• R. Myerson, "Effectiveness of electoral systems for reducing government corruption," Games and Economic Behavior 5 (1993), 118-132.
• R. Myerson "Proportional representation, approval voting, and coalitionally straightforward elections," in Political Economy: Institutions, Competition, and Representation, edited by W. Barnett, M. Hinich, and N. Schofield, Cambridge U. Press (1993).
• J. S. Banks and R. K. Sundaram, "Adverse selection and moral hazard in a repeated elections model," in Barnett, Hinich, and Schofield, eds., Political Economy (1993).
• D. Austen-Smith and J. Banks, "Electoral accountability and incumbency," in P. Ordeshook, ed., Models of Strategic Choice in Politics, U. of Michigan Press (1989), 121-148.

B. Campaign contributions

• R. Morton and R. Myerson, "Campaign spending with impressionable voters."
• J. M. Snyder, "Campaign contributions as investment," Journal of Political Economy 98 (1990), 1195-1227.

VI. Multi-member councils and legislatures

A. Power measures

• P. Ordeshook, Game Theory and Political Theory, section 10.4.
• L. Shapley and M. Shubik, "A method for evaluating the distribution of power in a committee system," American Political Science Review 48 (1954), 787-792.
• M. Shubik and H. P. Young, "The nucleolus as a noncooperative game solution," in P. Ordeshook, ed., Game Theory and Political Science, New York U. Press (1978), 511-527.
• H. P. Young, "Power, prices, and incomes in voting systems," Mathematical Programming 14 (1978), 129-148.
• D. P. Baron and J. Ferejohn, "Bargaining in legislatures," American Political Science Review 83 (1989), 1181-1206.

B. Strategic voting and coalition formation in legislatures

• D. Austen-Smith and J. Banks, "Elections, coalitions, and legislative outcomes," American Political Science Review 82 (1988), 405-422.
• B. Peleg, Coalition formation with dominant players, International Journal of Game Theory 10, (1981) 11-33.
• M. Laver and N. Schofield, Multiparty Government: The Politics of Coalition Formation in Europe, Oxford University Press (1990).
• G. Cox, The Efficient Secret, Cambridge U. Press, (1987).
• R. Taagepera and M. S. Shugart, Seats and Votes, Yale (1989).
• M. S. Shugart and J. M. Carey, Presidents and Assemblies, Cambridge U. Press (1992).
• V. V. Chari, L. E. Jones, and R. Marimon, "The economics of split voting in representative democracies," Northwestern U. (1994).

C. Subcommittees and specialization in legislatures

• K. A. Shepsle, "Institutional arrangements and equilibrium in multidimensional voting models," American Journal of Political Science 23 (1979), 27-59.
• B. R. Weingast and W. J. Marshall, "The industrial organization of congress" Journal of Political Economy 96 (1988), 132-163.
• T. W. Gilligan and K. Krehbiel, "Organization of Informative Committees by a Rational Legislature," American Journal of Political Science 34 (1990), 531-564.
• R. D. McKelvey and R. Riezman, "Seniority in legislatures," American Political Science Review 86 (1992), 951-965.
• D. Diermeier and R. Myerson, "Bargaining, veto power, and legislative committees," Northwestern U. (1994).

D. PR formulas

• M. L. Balinski and H. P. Young, Fair Representation (1982), Yale U. Press.