The logical space of Democracy

Philosophy and Public Affairs

Volumn 39, Issue 3, 2011, Pages 262-297

  List, Christian ^a  

^a LONDON SCHOOL OF ECONOMICS   (United Kingdom)

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[No Author keywords available]

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EID: 82755190002     PISSN: 00483915     EISSN: 10884963     Source Type: Journal    
DOI: 10.1111/j.1088-4963.2011.01206.x     Document Type: Article

References (131)

1. See Nicolas de Condorcet, Essay sur l'Application de l'Analyse à la Probabilité des Décisions Rendue à la Pluralité des Voix (Paris, 1785), and for an English translation and commentary, Iain McLean and Arnold B. Urken, eds., Classics of Social Choice (Ann Arbor: University of Michigan Press), 1995.
2. Bernard Grofman, Guillermo Owen, and Scott L. Feld, "Thirteen Theorems in Search of the Truth," Theory and Decision 15 (1983): 261-78 See, among many others
3. Philip J. Boland, "Majority Systems and the Condorcet Jury Theorem," The Statistician 38 (1989): 181-89
4. Christian List and Robert E. Goodin, "Epistemic Democracy: Generalizing the Condorcet Jury Theorem," Journal of Political Philosophy 9 (2001): 277-306.
5. Joshua Cohen, "An Epistemic Conception of Democracy," Ethics 97 (1986): 26-38 Contributions include
6. Jules L. Coleman and John Ferejohn, "Democracy and Social Choice," Ethics 97 (1986): 6-25
7. David Estlund, Jeremy Waldron, Bernard Grofman, and Scott L. Feld, "Controversy: Democratic Theory and the Public Interest: Condorcet and Rousseau Revisited," American Political Science Review 83 (1989): 1317-40
8. Estlund, "Making Truth Safe for Democracy," in The Idea of Democracy, ed. David Copp, Jean Hampton, and John E. Roemer (Cambridge: Cambridge University Press), 1993, pp. 71-100
9. Estlund, "Beyond Fairness and Deliberation: The Epistemic Dimension of Democratic Authority," in Deliberative Democracy: Essays on Reason and Politics, ed. James Bohman and William Rehg (Cambridge, Mass.: MIT Press), 1997, pp. 173-204
10. List and Goodin, "Epistemic Democracy." In his book Democratic Authority: A Philosophical Framework (Princeton, N.J.: Princeton University Press), 2009
11. Estlund distances himself from Condorcet's jury theorem, but still acknowledges the need to frame his discussion in relation to it.
12. Kenneth J. Arrow, Social Choice and Individual Values (New York: Wiley), 1951/1963
13. Amartya K. Sen, Collective Choice and Social Welfare (San Francisco: Holden-Day), 1970.
14. A review of the literature is beyond the scope of this article. William Riker sparked a debate by arguing that these problems challenge the meaningfulness of democracy
15. see Liberalism against Populism (San Francisco: W. H. Freeman, 1982).
16. William V. Gehrlein, "Condorcet's Paradox," Theory and Decision 15 (1983): 161-97. On the frequency of Condorcet cycles under some simple assumptions, see
17. Christian List and Philip Pettit, "Aggregating Sets of Judgments: An Impossibility Result," Economics and Philosophy 18 (2002): 89-110 See, among many other works
18. List and Pettit, "Aggregating Sets of Judgments: Two Impossibility Results Compared," Synthese 140 (2004): 207-35
19. Marc Pauly and Martin van Hees, "Logical Constraints on Judgement Aggregation," Journal of Philosophical Logic 35 (2006): 569-85
20. Franz Dietrich, "Judgment Aggregation: (Im)possibility Theorems," Journal of Economic Theory 126 (2006): 286-98
21. Dietrich, "A Generalised Model of Judgment Aggregation," Social Choice and Welfare 28 (2007): 529-65
22. Dietrich and List, "Arrow's Theorem in Judgment Aggregation," Social Choice and Welfare 29 (2007): 19-33
23. Klaus Nehring and Clemens Puppe, "Abstract Arrovian Aggregation," Journal of Economic Theory 145 (2010): 467-94
24. Elad Dokow and Ron Holzman, "Aggregation of Binary Evaluations," Journal of Economic Theory 145 (2010): 495-511.
25. Lewis A. Kornhauser and Lawrence G. Sager, "Unpacking the Court," Yale Law Journal 96 82-117 This literature draws on related work on the "doctrinal paradox" in law and economics, especially
26. Kornhauser and Sager, "The One and the Many: Adjudication in Collegial Courts," California Law Review 81 (1993): 1-59.
27. Robert Wilson, "On the Theory of Aggregation," Journal of Economic Theory 10 (1975): 89-99 The literature also draws on related work in abstract aggregation theory, especially
28. Ariel Rubinstein and Peter C. Fishburn, "Algebraic Aggregation Theory," Journal of Economic Theory 38 (1986): 63-77
29. Nehring and Puppe, "Strategy-Proof Social Choice on Single-Peaked Domains: Possibility, Impossibility and the Space Between," working paper (University of California, Davis), 2002
30. Pettit, "Deliberative Democracy and the Discursive Dilemma," Philosophical Issues (supplement to Nous) 11 (2001): 268-99 For contributions addressed to political philosophers, see, e.g.,
31. Bruce Chapman, "Rational Aggregation," Politics, Philosophy and Economics 1 (2002): 337-54
32. Kornhauser and Sager, "The Many as One: Integrity and Group Choice in Paradoxical Cases," Philosophy & Public Affairs 32 (2004): 249-76
33. List and Pettit, "On the Many as One: A Reply to Kornhauser and Sager," Philosophy & Public Affairs 33 (2005): 377-90
34. List, "The Discursive Dilemma and Public Reason," Ethics 116 (2006): 362-402.
35. List and Puppe, "Judgment Aggregation: A Survey," in The Handbook of Rational and Social Choice, For a survey, see ed. Paul Anand, Prasanta Pattanaik, and Clemens Puppe (Oxford: Oxford University Press), 2009, pp. 457-82.
36. List and Pettit, Group Agency: The Possibility, Design and Status of Corporate Agents For a discussion of the roles of intentional attitudes in individual and collective agency, see (Oxford: Oxford University Press), 2011.
37. The underlying model of agency goes back to David Hume, A Treatise of Human Nature, reprinted from the original and edited by L. A. Selby-Bigge (Oxford: Clarendon Press, 1739/1896).
38. Daniel Dennett, The Intentional Stance (Cambridge, Mass.: MIT Press), 1987.
39. List and Pettit, "Aggregating Sets of Judgments: An Impossibility Result" For different versions of this logic-based model of a decision problem, at increasing levels of generality, see
40. Dietrich, "A Generalised Model of Judgment Aggregation"
41. Dietrich and List, "The Aggregation of Propositional Attitudes: Towards a General Theory," Oxford Studies in Epistemology 3 (2010): 215-34.
42. Nehring and Puppe, "Abstract Arrovian Aggregation,"
43. Dokow and Holzman, "Aggregation of Binary Evaluations."
44. List and Pettit, "Aggregating Sets of Judgments: Two Impossibility Results Compared," This construction is formally given in
45. Dietrich and List, "Arrow's Theorem in Judgment Aggregation," but the idea of a propositional representation of preferences goes back to Georges-Théodule Guilbaud, "Theories of the General Interest, and the Logical Problem of Aggregation," in Readings in Mathematical Social Science, ed. Paul F. Lazarsfeld and Neil W. Henry (Cambridge, Mass.: MIT Press), 1966, pp. 262-307
46. even to Condorcet's Essay The present representation can be interpreted in various ways, which is implicit in the contrast between "preferred" and "preferable" in the formulation of ranking propositions; the details do not matter for present purposes.
47. Dietrich and List, "The Aggregation of Propositional Attitudes." The model can be further generalized to capture decision problems that involve the formation of nonbinary propositional attitudes, as discussed in
48. But since real-world democratic decisions typically take a discrete-especially binary-form (requiring the acceptance or rejection of certain propositions, or the ranking of certain options in an order of preference), I set the nonbinary case aside here.
49. For an English translation of, and commentary on, Borda's proposal, see McLean and Urken, Classics of Social Choice.
50. Iain S. McLean, Alistair McMillan, and Burt L. Monroe, eds., A Mathematical Approach to Proportional Representation: Duncan Black on Lewis Carroll (Dordrecht: Kluwer), 1996.
51. William Thomson, "On the Axiomatic Method and Its Recent Applications to Game Theory and Resource Allocation," Social Choice and Welfare 18 (2000): 327-86. For an excellent discussion of the axiomatic method in social choice theory, see
52. I thereby follow the technical literature on the aggregation of judgments and other propositional attitudes, as briefly reviewed in earlier notes.
53. Generally, if there are x admissible combinations of individual inputs and y admissible collective outputs, there are y x possible decision procedures. If each individual has z different choices, then x can be further expressed as z n, where n is the group size. In the examples just discussed, y = 2, z = 2, and n = 3 or n = 10.
54. This is the universal-domain requirement in the literature on judgment or attitude aggregation. In the special case of preferences, it reduces to Arrow's universal-domain condition.
55. Notice, further, that basic majoritarianism does not imply some of the other standard conditions commonly used to prove impossibility results in formal work on aggregation, such as "independence" or "systematicity." Independence requires that the collective attitude on each proposition depend only on individual attitudes on that proposition, not on individual attitudes on other conditions. Systematicity adds to this the requirement that the pattern of dependence be the same for all propositions.
56. Goodin and List, "Special Majorities Rationalized," British Journal of Political Science 36 (2006): 213-41 For discussions of such rules, see, e.g.,
57. Dietrich and List, "Judgment Aggregation by Quota Rules: Majority Voting Generalized," Journal of Theoretical Politics 19 (2007): 391-424
58. By contrast, weighted majority rules, under which different individuals have different voting weights, do not generally satisfy the present basic majoritarian requirement. Harry Brighouse and Marc Fleurbaey advocate such rules on the grounds of a particular proportionality principle
59. "Democracy and Proportionality," Journal of Political Philosophy 18 (2008): 137-55.
60. They suggest that, in certain collectivedecisions, each decision maker's voting weight should be proportional to his or her "stake" in the decision. Depending on the precise pattern of stakes, and on whether a simple or qualified version of weighted majority voting is used, the resulting decision procedure may well overrule the majority attitude-not, however, the attitude supported by more than half of the total voting weight. Although Brighouse and Fleurbaey's proposal may require a revision in the formulation of "basic majoritarianism," it is not generally immune to the kinds of technical difficulties illustrated by what I call the "democratic trilemma."
61. This is the collective-rationality requirement in the literature on judgment aggregation. Again, in the special case of preferences, it reduces to Arrow's ordering condition.
62. For present purposes, I set aside the distinct case of procedures for ranking distributions of certain goods or units of welfare in an order of social preference. The application of social choice theory to such problems of distributive justice is very important, but raises somewhat different challenges compared to the paradigmatic cases of democratic decision making (in elections, referenda, legislatures, committees, and the like).
63. John E. Roemer, Theories of Distributive Justice On the justice-theoretic side of social choice theory, see, e.g., (Cambridge, Mass.: Harvard University Press), 1996
64. Marc Fleurbaey, Fairness, Responsibility, and Welfare (New York: Oxford University Press), 2008.
65. Robert A. Dahl, "Procedural Democracy," in Philosophy, Politics and Society, 5th series, ed. Peter Laslett and James S. Fishkin (Oxford: Blackwell), 1979.
66. As formally stated here, this result is more general than the familiar observation that majority voting does not generally secure consistent collective attitudes, which has been shown at different levels of generality in the literature on judgment aggregation.
67. List and Pettit, "Aggregating Sets of Judgments: An Impossibility Result" For the versions of this standard result most closely related to the present point, see
68. Dietrich and List, "Judgment Aggregation by Quota Rules"
69. Nehring and Puppe, "The Structure of Strategy-Proof Social Choice-Part I: General Characterization and Possibility Results on Median Spaces," Journal of Economic Theory 135 (2007): 269-305
70. Nehring and Puppe, "Abstract Arrovian Aggregation."
71. Note that the present contribution is not so much the formal result, but rather its substantive interpretation.
72. Dietrich and List, "Judgment Aggregation by Quota Rules." This example was introduced in
73. Expressed in terms of the formal conditions for the democratic trilemma stated in the appendix, the present agenda has a minimally inconsistent subset of three propositions: the set consisting of "A is preferred/preferable to B,""B is preferred/preferable to C,""C is preferred/preferable to A." This set is inconsistent relative to the standard constraints on preferences, by violating transitivity, and minimally so, since the removal of any of its elements breaks the preference cycle and thereby restores consistency. Generally, if we wish to rank k options in an order of preference, the largest minimally inconsistent subset of the agenda contains k propositions, corresponding to a preference cycle of length k This shows that, like Condorcet's paradox, the democratic trilemma applies to a preference aggregation problem if and only if there are three or more options to be ranked. See also List and Pettit, "Aggregating Sets of Judgments: Two Impossibility Results Compared"; Dietrich and List, "Arrow's Theorem in Judgment Aggregation"; and Dietrich and List, "Judgment Aggregation by Quota Rules."
74. Duncan Black, "On the Rationale of Group Decision-Making," Journal of Political Economy 56 (1948): 23-34.
75. K.-I. Inada, "A Note on the Simple Majority Decision Rule," Econometrica 32 (1964): 525-31 Other key contributions include
76. Amartya K. Sen, "A Possibility Theorem on Majority Decisions," Econometrica 34 (1966): 491-99
77. Wulf Gaertner, Domain Conditions in Social Choice Theory For a survey of the literature and more recent results, see (Cambridge: Cambridge University Press), 2001
78. Dietrich and List, "Majority Voting on Restricted Domains," Journal of Economic Theory 145 (2010): 512-43.
79. List, "Two Concepts of Agreement," The Good Society 11 (2002): 72-79. On the notion of "metaconsensus" and the pattern of "unidimensional alignment" as discussed here, see
80. John Dryzek and Simon Niemeyer, "Reconciling Pluralism and Consensus as Political Ideals," American Journal of Political Science 50 (2006): 634-49. For some further, subsequent notions of "metaconsensus," see
81. Black, "On the Rationale of Group Decision-Making."
82. The significance of Black's result was emphasized even by the critic of populist democracy, William Riker, in Liberalism against Populism (at p. 128): "If, by reason of discussion, debate, civic education, and political socialization, voters have a common view of the political dimension (as evidenced by single-peakedness), then a transitive outcome is guaranteed."
83. Michael Walzer, Spheres of Justice Classic contributions include (New York: Basic), 1983
84. David Miller, On Nationality (Oxford: Oxford University Press), 1995.
85. Thomas Christiano, The Constitution of Equality: Democratic Authority and Its Limits For a related discussion, see (Oxford: Oxford University Press), 2008.
86. David Miller, "Deliberative Democracy and Social Choice," Political Studies 40 (1992): 54-67 [special issue]
87. Jack Knight and James Johnson, "Aggregation and Deliberation: On the Possibility of Democratic Legitimacy," Political Theory 22 (1994): 277-96
88. John Dryzek and Christian List, "Social Choice Theory and Deliberative Democracy: A Reconciliation," British Journal of Political Science 33 (2003): 1-28.
89. Dahl, "Procedural Democracy."
90. Christian List, Robert C. Luskin, James Fishkin, and Iain McLean, "Deliberation, Single-Peakedness, and the Possibility of Meaningful Democracy: Evidence from Deliberative Polls," working paper (London School of Economics), 2000/2006.
91. Pettit, "Deliberative Democracy and the Discursive Dilemma" For nontechnical discussions of this idea, see
92. List and Pettit, "Aggregating Sets of Judgments: An Impossibility Result"
93. Chapman, "Rational Aggregation."
94. List, "A Model of Path-Dependence in Decisions over Multiple Propositions," American Political Science Review 98 (2004): 495-513
95. Dietrich, "Aggregation Theory and the Relevance of Some Issues to Others," working paper (London School of Economics), 2006
96. Franz Dietrich and Philippe Mongin, "The Premised-Based Approach to Judgment Aggregation," Journal of Economic Theory 145 (2010): 562-82.
97. Jeremy Waldron, "The Core of the Case Against Judicial Review," Yale Law Journal 115 (2006): 1346-406.
98. John Rawls, A Theory of Justice The idea of "reflective equilibrium" goes back, of course, to (Cambridge, Mass.: Harvard University Press), 1971.
99. In a judgment-aggregation context, a proposal along the present lines is discussed in List and Pettit, Group Agency, chap. 3.
100. Sébastien Konieczny and Ramón Pino Pérez, "Merging Information under Constraints: A Logical Framework," Journal of Logic and Computation 12 (2002): 773-808
101. Gabriella Pigozzi, "Belief Merging and the Discursive Dilemma: An Argument-Based Account to Paradoxes of Judgment Aggregation," Synthese 152 (2006): 285-98
102. Michael K. Miller and Dan Osherson, "Methods for Distance-Based Judgment Aggregation," Social Choice and Welfare 32 (2009): 575-601.
103. In the special case of preference aggregation, the so-called Kemeny method is a well-known distance-based decision procedure.
104. On arguments for and against the Borda method, see, e.g., the debate between Mathias Risse, who advocates a variant of the Kemeny method (which, he argues, is Condorcetian in spirit), and Donald Saari, who advocates Borda's method.
105. Risse, "Arrow's Theorem, Indeterminacy, and Multiplicity Reconsidered," Ethics 111 (2001): 706-34
106. Saari, "Capturing the 'Will of the People,'" Ethics 113 (2003): 333-49
107. Risse, "Why the Count de Borda Cannot Beat the Marquis de Condorcet," Social Choice and Welfare 25 (2005): 95-113 followed by
108. Saari, "Which Is Better: The Condorcet or Borda Winner?" Social Choice and Welfare 26 (2006): 107-29.
109. It is well known that inconsistent attitudes make a decision maker-individual as well as collective-vulnerable to various forms of strategic exploitation by others, quite apart from the fact that, at least in classical logical terms, anything can be derived from an inconsistent set of commitments.
110. List and Pettit, "Aggregating Sets of Judgments: An Impossibility Result,"
111. List, "The Discursive Dilemma and Public Reason."
112. Pettit, "Deliberative Democracy and the Discursive Dilemma."
113. Cass Sunstein, Political Conflict and Legal Agreement, Tanner Lectures on Human Values See, in particular, (Harvard University), 1994
114. One Case at a Time: Judicial Minimalism on the Supreme Court (Cambridge, Mass.: Harvard University Press), 1999.
115. The acceptance threshold for any proposition must be above (k -1)/ k, where k is the size of the largest "minimal inconsistent" subset of the agenda (a measure of its "complexity").
116. Dietrich and List, "Judgment Aggregation by Quota Rules."
117. In the examples above, k = 3 and thus a decision procedure requiring more than two-thirds of the individuals for the acceptance of any proposition would guarantee consistent-albeit incomplete-collective attitudes.
118. Goodin and List, "Special Majorities Rationalized." Relatedly, on "symmetrical supermajority rules," see
119. On the notion of group agency, see List and Pettit, Group Agency.
120. Arrow, Social Choice and Individual Values.
121. Amartya K. Sen, "The Impossibility of a Paretian Liberal," Journal of Political Economy 78 (1970): 152-57.
122. This template is relevant not only to impossibility results, but also to possibility results where certain conditions characterize a nonempty class of decision procedures. Many such results can be interpreted in the present terms, too, by classifying the relevant conditions as input, responsiveness, and output conditions.
123. For a comprehensive review and helpful methodological discussion of the axiomatic method as it is used in a number of different areas of economic theory, see again Thomson, "On the Axiomatic Method and Its Recent Application to Game Theory and Resource Allocation."
124. That is, we keep weakening the desiderata until we reach a point at which any further weakening would render them mutually compatible. Note that a maximally weak formulation of the desiderata subject to the constraint that the incompatibility persists need not be unique.
125. For proofs that majority voting guarantees consistent collective attitudes if and only if the agenda has no minimally inconsistent subset of more than two propositions, see Dietrich and List, "Judgment Aggregation by Quota Rules," and Nehring and Puppe, "The Structure of Strategy-Proof Social Choice." For earlier related results, see Nehring and Puppe, "Strategy-Proof Social Choice on Single-Peaked Domains." Strictly speaking, without technical caveats, the "if and only if" claim requires an odd number of individuals.
126. Majority ties are possible only when the number of individuals is even. I set the technicalities raised by ties aside here and implicitly assume, for the sake of simplicity, an odd number of individuals.
127. Nehring and Puppe, "The Structure of Strategy-Proof Social Choice" For earlier discussions of this structure condition on an agenda (the "simplicity" or "median" property)
128. Dietrich and List, "Judgment Aggregation by Quota Rules"
129. Nehring and Puppe, "Abstract Arrovian Aggregation."
130. To avoid a trivial conflict between basic majoritarianism and collective completeness in the case of a majority tie, one may demand completeness only in the absence of a majority tie. The trilemma can then be shown to hold for all group sizes except two and, in case the largest minimally inconsistent subset of the agenda has exactly three elements, four.
131. Dietrich and List, "Judgment Aggregation by Quota Rules." This follows from a result in