Judgment aggregation a bibliography on the discursive dilemma, doctrinal paradox and decisions on multiple propositions |
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A
new problem of social choice has attracted the attention of scholars in
law, economics, political science, philosophy and computer science. How
can a group of individuals aggregate the group members' individual
judgments on some interconnected propositions into corresponding collective judgments on these
propositions? Such aggregation problems occur in many
different collective decision-making bodies, for example in committees,
legislatures, judiciaries and expert panels. This page provides a bibliography of online and published research on this paradox and on judgment aggregation more generally.
The "doctrinal paradox" illustrates the aggregation problem (Kornhauser and Sager 1986, 1993; Kornhauser 1992, the apparent first occurrence of the label "doctrinal paradox"; Chapman 1998). (Important earlier precursors in different frameworks are Guilbaud 1966, Wilson 1975, and Rubinstein and Fishburn 1986.) Suppose
that a three-member court has to make a judgment on whether a defendant is liable
for a breach of contract. According to legal doctrine, the defendant is liable
(proposition
All
three judges accept the rule In
earlier presentations of the problem under the name "doctrinal
paradox", the logical connection rule Propositionwise
majority voting thus produces an inconsistent collective set of judgments,
namely the set { For a recent discussion of the paradox by Kornhauser and Sager, see Kornhauser and Sager (2004, cited below); for a response, see List and Pettit (2005). For a discussion of the discursive dilemma from a social epistemology perspective, see Goldman (2004) and List (2005).
Premise-based
and conclusion-based procedures of decision-making have been proposed as
possible escape-routes from the paradox. These procedures interpret
propositions According
to the According
to the Thus the premise-based and conclusion-based procedures may produce different outcomes. For a discussion of the premise- and conclusion-based procedures, see Pettit (2001b) (a deliberative democracy and republican perspective), Bovens and Rabinowicz (2003, 2004) and List (2005) (an epistemic perspective, focusing on the truth-tracking capacities of the two procedures), Chapman (2002) (a common law perspective), Dietrich and List (2004a) (a discussion of the strategic incentives created by the two procedures). an impossibility theorem and more general developments It can be shown that the paradox is not just an artefact of majority voting, but that it illustrates a more general impossibility theorem. A
The sets of judgments of each individual are assumed to satisfy certain consistency conditions (completeness, consistency and deductive closure). For
the following first impossibility result, the Consider three simple conditions on an aggregation procedure (informally stated):
Systematicity. The collective judgment on each proposition depends only on individual judgments on that proposition and the same pattern of dependence holds for all propositions.
For extensions, generalizations and further impossibility results, see Pauly and van Hees (2003); Dietrich (2006); Gärdenfors (2006); Nehring and Puppe (2005a); Dietrich and List (2005b), (2005c), (2006); Dokow and Holzman (2005); Mongin (2006); Nehring (2005), (2006a). -
All of these papers consider independence conditions weaker than systematicity (dropping the second part of systematicity, which requires the same pattern of dependence to hold for all propositions), but typically require agendas of propositions with richer logical interconnections. For a critique of the systematicity condition, see Chapman (2002). -
Among other results, Pauly and van Hees show that the anonymity condition of the theorem can be relaxed to a non-dictatorship condition; their paper also includes the first impossibility theorem in the judgment aggregation literature in which systematicity is weakened to independence. -
Nehring and Puppe (2005a) prove several results on judgment aggregation drawing on related results on the aggregation of preferences over vectors of properties in property spaces; for a key characterization result, see Nehring and Puppe (2005b); a Paretian-rationalist problem is presented in Nehring (2005); a result on oligarchic aggregation rules in Nehring (2006a). -
Dietrich and List (2005b) prove Arrow's theorem on preference aggregation as a corollary of an impossibility theorem on judgment aggregation; for an earlier comparison with impossibility results on preference aggregation, see List and Pettit (2001/2004). In both papers, preference orderings are represented as sets of binary ranking propositions in predicate logic. Nehring (2003) derives an Arrow-like theorem as a corollary of a theorem in the property-space framework. -
Dokow and Holzman (2005) identify an algebraic condition on the structure of logical interconnections between propositions that is necessary and sufficient for an Arrow-style impossibility result; their paper also develops connections between the judgment aggregation framework and Wilson's (1975) as well as Rubinstein and Fishburn's (1986) frameworks. -
Mongin (2006) provides an impossibility result based on an independence condition restricted to atomic propositions. -
Dietrich (2006) introduces a family of weakened independence conditions capturing the idea that some (but not all) propositions are relevant to certain others and proves several possibility and impossibility results under these conditions..
Other developments include the following. -
Pauly and van Hees (2003) and van Hees (2004) prove results on the aggregation of judgments expressed in many-valued logics and extend some impossibility results to this setting. -
Dietrich and List (2004a) analyse strategic voting and strategy-proofness in judgment aggregation. The analysis is based on a non-preference-theoretic notion of (non-)manipulability, but this notion is also related to a preference-theoretic notion of strategy-proofness similar to the one in standard social-choice-theoretic work on the Gibbard-Satterthwaite theorem. -
Domain restrictions sufficient for avoiding majority inconsistencies in judgment aggregation are discussed in List (2003) (see also correction) and Dietrich and List (2007). -
For parallels with the computer science literature on merging knowledge bases, see Pigozzi (2005a), (2005b), and for parallels with distance-based social choice, see Eckert and Pigozzi (2005). -
For impossibility results on the assignment of (expert or liberal) rights to group members, see Dietrich and List (2004b). -
For a model of judgment aggregation in general logics (where propositions can be represented in several different logics, including propositional, predicate, modal and conditional logics), see Dietrich (2004). -
Quota rules (generalizing propositionwise majority voting) are discussed in Dietrich and List (2005a). -
Pauly (2005) analyses the problem of axiomatizing judgment aggregation procedures subject to the constraint that axioms must be expressed in a minimal logical language. -
Gärdenfors (2006) weakens the rationality conditions on collective judgments from full rationality to deductive closure and consistency. For extensions of these results, see Dietrich and List (2006).
Bonnefon,
Jean-François (2007)
"How do Individuals
Solve the Doctrinal Paradox in Collective Decisions? An Empirical
Investigation,"
Chapman,
B. (1998) "More Easily Done than Said: Rules, Reason and Rational
Social Choice," Chapman,
B. (2002) "Rational Choice and Categorical Reason," Ferejohn, J. (2001) "Statutes, Plans, Intentions: A Planning Theory of Legislation" (PDF) (source: http://www.law.nyu.edu/clppt/program2001/readings/index.html) Kornhauser,
L. A., and L. G. Sager (1986) "Unpacking the
Court," Kornhauser,
L. A. (1992) "Modelling Collegial Courts. II. Legal Doctrine," Kornhauser
L. A., and L. G. Sager (1993) "The One and the Many: Adjudication in
Collegial Courts," Kornhauser,
L. A., and L. G. Sager (2004) "Group Choice in Paradoxical Cases,"
List,
C., and P. Pettit (2005) "On the Many as One," Nash,
J. R. (2003) "A Context-Sensitive Voting Protocol Paradigm For
Multimember Courts,"
Baurmann, M., and G. Brennan (2005) "Majoritarian Inconsistency, Arrow Impossibility and the Comparative Interpretation: A Context-Based View," paper presented at the 2005 Public Choice conference (PDF) (source: http://www.pubchoicesoc.org/papers2005.html) Brennan
G. (2001) "Collective Coherence?" Chapman, B. (2001) "Public Reason, Social Choice, and Cooperation," paper presented at the Eighth Conference on Theoretical Aspects of Rationality and Knowledge, University of Siena, held at Certosa di Pontignano, Italy, July 2001 (PDF) (source: http://chass.utoronto.ca/clea/confpapers.htm) Chapman, B.
(2002)
"Rational Aggregation," Fallis, D. (2005) "Epistemic Value
Theory and Judgment Aggregation,"
Goldman, A. (2004) "Group Knowledge Versus Group Rationality: Two
Approaches to Social Epistemology," List, C.
(2001) "Two Concepts of
Agreement," List,
C. (2004) "The Discursive Dilemma and Public Reason," List,
C. (2005) "Group knowledge and group rationality: a judgment
aggregation perspective," List, C., and P. Pettit (2005) "Group Agency and Supervenience" (PDF) Pettit, P.
(2001a) "Akrasia,
Collective and Individual" Pettit, P.
(2001b) "Deliberative
Democracy and the Discursive Dilemma," Pettit, P. (2001c) "Groups with Minds of their Own" (PDF) (source: http://socpol.anu.edu.au/working.php3) Peritz, D. (2003) "The Discursive Dilemma Dissolved"
Cariani, F., M. Pauly and J. Snyder (2006) "Decision Framing in Judgment Aggregation" (PDF) Claussen, C. A., and Ø. Røisland (2005) "Collective Economic Decisions and the Discursive Paradox", Norges Bank Working paper (PDF) Dietrich,
F. (2004) "A generalised model of judgment aggregation," Dietrich, F. (2005) "The possibility of judgment aggregation on agendas with subjunctive implications" (PDF) Dietrich,
F. (2006) "Judgment aggregation: (im)possibility theorems," Dietrich, F. (2006) "Aggregation theory and the relevance of some issues to others" (PDF) Dietrich, F., and C. List (2004a) "Strategy-Proof Judgment Aggregation" (PDF) Dietrich,
F., and C. List (2004b) "A Liberal Paradox for Judgment Aggregation,"
Dietrich,
F., and C. List (2005a) "Judgment aggregation by quota rules," Dietrich,
F., and C. List (2005b) "Arrow's theorem in judgment aggregation,"
Dietrich, F., and C. List (2005c) "The impossibility of unbiased judgment aggregation" (PDF) Dietrich, F., and C. List (2006a) "Judgment aggregation on restricted domains" (PDF) Dietrich,
F., and C. List (2006b) "Judgment aggregation without full
rationality," Dietrich, F., and C. List (2007) "Judgment aggregation with consistency alone" (PDF) Dietrich,
F., and C. List (2007) "Judgment aggregation under constraints," in
Dietrich, F., and C. List (2007) "Majority voting on restricted domains" (PDF) Dietrich, F., and P. Mongin (2007) "The Premiss-Based Approach to Judgment Aggregation" (PDF) Dokow, E., and R. Holzman (2005) "Aggregation of Binary Evaluations" (PDF) Eckert, D., and G. Pigozzi (2005) "Belief merging, judgment aggregation and some links with social choice theory," in Belief Change in Rational Agents, J. Delgrande et al. (eds.), Dagstuhl Seminar Proceedings 05321, IBFI, Schloss Dagstuhl, Germany, 2005 (PDF) GarciaBermejo, Juan C. (2006) "Aggregating Judgments by the Majority Method" (PDF) Gärdenfors,
P. (2006) "An Arrow-like theorem for voting with logical
consequences," van
Hees, M. (2004) "The Limits of Epistemic Democracy," Levi,
I. (2004) "List and Pettit," List,
C. (2003) "A
Possibility Theorem on Decisions over Multiple Propositions," List,
C. (2004) "A Model of Path-Dependence in Decisions over Multiple
Propositions," List, C. (2006) "Which worlds are possible? A judgment aggregation problem" (PDF) List, C., and P. Pettit
(2002)
"Aggregating Sets of Judgments: An Impossibility Result," List, C., and P. Pettit
(2004)
"Aggregating Sets of Judgments: Two Impossibility Results
Compared," Mongin, Philippe (2006) "Factoring Out the Impossibility of Logical Aggregation" (PDF) Nehring,
K. (2003) "Arrow's theorem as a corollary," Nehring, K. (2005) "The Impossibility of a Paretian Rational" (PDF) Nehring, K. (2006a) "Oligarchies in Judgment Aggregation" (PDF) Nehring,
K. (2006b) "The Impossibility of a Paretian Rational: A
Bayesian Perspective," Nehring, K. and C. Puppe (2005a) "Consistent Judgement Aggregation: A Characterization" (PDF) (source: http://www.wior.uni-karlsruhe.de/LS_Puppe/Personal/Papers-Puppe/puppe_html) Nehring, K. and C. Puppe (2007) "Justifiable Group Choice" (PDF) Pauly, M. (2005) "Axiomatising Judgement Aggregation Procedures in a Minmial Logical Language" (PDF) Pauly,
M. and M. van Hees (2003) "Logical Constraints on Judgment
Aggregation," Pigozzi,
G. (2005a) "Collective Decision-Making without Paradoxes: A Fusion
Approach," Pigozzi, G. (2005b) "Should we send him to prison? Paradoxes of aggregation and belief merging," in We Will Show Them: Essays in Honour of Dov Gabbay, Vol. 2, S. Artemov et al. (eds.), College Publications: 529-542 (PDF) Zamora Bonilla, J. (2005) "Optimal Judgement Aggregation" (PDF)
Bovens,
L., and W. Rabinowicz (2003) "Democracy and Argument -
Tracking Truth in Complex Social Decisions," in A. van Aaken, C. List
and C. Luetge (eds.), Bovens,
L., and W. Rabinowicz (2004) "Democratic Answers to Complex
Questions - an Epistemic Perspective," List,
C. (2005) "The Probability of Inconsistencies in Complex Collective
Decisions,"
Anscombe,
G. E. M. (1976) "On Frustration of the Majority by Fulfillment of
the Majority’s Will," Blackburn, S. (2001) "Group Minds and Expressive Harm", Maryland Law Review 60: 467-491 Brams,
S. J., D. M. Kilgour and W. S. Zwicker (1997) "Voting on Referenda:
the Separability Problem and Possible Solutions," Brams,
S.J., D. M. Kilgour and W. S. Zwicker (1998) "The paradox of
multiple elections," Dietrich, F. (2004) "Opinion pooling under asymmetric information" (PDF) Dietrich, F. and C. List (2007) "Opinion pooling on general agendas" (PDF) (an appendix with additional results)
Grofman,
Bernard (1985) "Research Note: The Accuracy of Group Majorities for
Disjunctive and Conjunctive Decision Tasks", Guilbaud,
G. Th. (1966) "Theories of the General Interest, and the Logical
Problem of Aggregation," in P. F. Lazarsfeld and N. W. Henry (eds.), Hillinger,
C. (1971) "Voting on issues and on platforms," Kelly,
J. S. (1989) "The Ostrogorski Paradox," Levmore,
S. (2001) "Conjunction and Aggregation," Mazurkiewicz, M., and J. W. Mercik (2002) "Paradox of multiple elections - The probabilistic approach" (PDF) (source: http://polis.unipmn.it/epcs/papers/mercik.pdf) Nehring, K., and C. Puppe (2005b) "On the Possibility of Strategy-Proof Social Choice: Non-Dictatorship, Anonymity and Neutrality" (PDF) Rubinstein,
A., and P. Fishburn (1986) "Algebraic Aggregation Theory," Wilson,
R. (1975) "On the Theory of Aggregation,"
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Last modified 1 May 2008