Abstract
The question of how to maximize benefits from the accuracy of collective decisions by weighting votes has been examined for a single-issue agenda. This study generalizes the existing optimal weighting rule in the context of collective judgment on an agenda consisting of multiple logically interconnected issues. Specifically, it determines the best approach to weight each voter’s judgment on a proposition in order to estimate the states of premises behind the proposition, which maximize the expected collective benefit obtained from their correctness, when voters’ judgments for the proposition are available as a record, but their judgments for premises are not available. Although the optimal weight assigned to a vote for a single-issue agenda has been known to depend only on voters’ competences (i.e., probability of a voter making a correct decision), we found that the weight in the case of multiple connected issues further depends on the content of the voter’s judgment. This difference raises a new question. In the case of a single-issue agenda, if voters have overwhelmingly high competence, dictatorial or oligarchic situations arise, namely, the weights to those voters can be so large that the remaining voters’ decisions do not affect the collective decision. By contrast, in the case of multiple connected issues, we should define who would be dictatorial or oligarchic in terms of the contents of their decisions, not just their competence. We examine the conditions under which such cases are likely to arise.
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References
Alabert A, Farré M (2021) The doctrinal paradox: comparison of decision rules in a probabilistic framework. Soc Choice Welf 58:1–33
Austen-Smith D, Banks JS (1996) Information aggregation, rationality, and the condorcet jury theorem. Am Polit Sci Rev 90(1):34–45
Baharad E, Goldberger J, Koppel M, Nitzan S (2011) Distilling the wisdom of crowds: weighted aggregation of decisions on multiple issues. Auton Agent Multiagent Syst 22(1):31–42
Baharad E, Goldberger J, Koppel M, Nitzan S (2012) Beyond condorcet: optimal aggregation rules using voting records. Theory Decis 72(1):113–130
Ben-Yashar R, Danziger L (2011) Symmetric and asymmetric committees. J Math Econ 47(4–5):440–447
Ben-Yashar R, Danziger L (2014) On the optimal composition of committees. Soc Choice Welf 43(4):973–980
Ben-Yashar R, Nitzan S (2001) The invalidity of the condorcet jury theorem under endogenous decisional skills. Econ Gov 2(3):243–249
Ben-Yashar R, Paroush J (2001) Optimal decision rules for fixed-size committees in polychotomous choice situations. Soc Choice Welf 18(4):737–746
Berg S (1993) Condorcet’s jury theorem, dependency among jurors. Soc Choice Welf 10(1):87–95
Black D (1958) The theory of committees and elections. Kluwer Academic Press, Amsterdam
Bodanza G, Freidin E, Linares S, Delbianco F (2020) Modulation of the leniency bias in the discursive dilemma. Int J Psychol 55(1):67–75
Boland PJ (1989) Majority systems and the condorcet jury theorem. J R Stat Soc Ser D (The Statistician) 38(3):181–189
Boland PJ, Proschan F, Tong YL (1989) Modelling dependence in simple and indirect majority systems. J Appl Probab 26(1):81–88
Bonnefon JF (2007) How do individuals solve the doctrinal paradox in collective decisions? an empirical investigation. Psychol Sci 18(9):753–755
Bonnefon JF (2010) Behavioral evidence for framing effects in the resolution of the doctrinal paradox. Soc Choice Welf 34(4):631–641
Bovens L, Rabinowicz W (2006) Democratic answers to complex questions-an epistemic perspective. Synthese 150(1):131–153
Grossi D, Pigozzi G (2014) Judgment aggregation: a primer. Synth Lect Artif Intell Mach Learn 8(2):1–151
Guha B (2018) Secret ballots and costly information gathering: the jury size problem revisited. Int Rev Law Econ 54:58–67
Kornhauser LA, Sager LG (1993) The one and the many: adjudication in collegial courts. Calif L Rev 81:1
Ladha KK (1992) The condorcet jury theorem, free speech, and correlated votes. Am J Polit Sci 36:617–634
List C (2004) On the significance of the absolute margin. Br J Philos Sci 55(3):521–544
List C (2004) A model of path-dependence in decisions over multiple propositions. Am Polit Sci Rev 98(3):495–513
List C (2005) The probability of inconsistencies in complex collective decisions. Soc Choice Welf 24(1):3–32
List C, Goodin RE (2001) Epistemic democracy: generalizing the condorcet jury theorem. J Polit Philos 9(3):277–306
List C, Pettit P (2002) Aggregating sets of judgments: an impossibility result. Econ Philos 18(1):89–110
List C, Pettit P (2004) Aggregating sets of judgments: two impossibility results compared. Synthese 140(1):207–235
List C, Pettit P (2011) Group agency: the possibility, design, and status of corporate agents. Oxford University Press, Oxford
List C, Puppe C (2009) Judgment aggregation: a survey. In: List C, Puppe C (eds) Handbook of rational and social choice. Oxford University Press, Oxford
McCannon BC, Walker P (2016) Endogenous competence and a limit to the condorcet jury theorem. Public Choice 169(1–2):1–18
McLean I, Urken A (1995) Classics of social choice. University of Michigan Press, Ann Arbor, Michigan
Mukhopadhaya K (2003) Jury size and the free rider problem. J Law Econ Organ 19(1):24–44
Nitzan S, Paroush J (1982) Optimal decision rules in uncertain dichotomous choice situations. Int Econ Rev 23:289–297
Nitzan S, Paroush J (1984) A general theorem and eight corollaries in search of correct decision. Theory Decis 17(3):211–220
Owen G, Grofman B, Feld SL (1989) Proving a distribution-free generalization of the condorcet jury theorem. Math Soc Sci 17(1):1–16
Paroush J (1997) Stay away from fair coins: a condorcet jury theorem. Soc Choice Welf 15(1):15–20
Pettit P (2001) Deliberative democracy and the discursive dilemma. Philos Issue 11:268–299
Sekiguchi T (2016) Optimal group composition for efficient division of labor. Theory Decis 81(4):601–618
Sekiguchi T (2019) Preferences over procedures and outcomes in judgment aggregation: an experimental study. Theory Decis 86(2):239–258
Sekiguchi T, Ohtsuki H (2015) Effective group size of majority vote accuracy in sequential decision-making. Jpn J Ind Appl Math 32(3):595–614
Shapley L, Grofman B (1984) Optimizing group judgmental accuracy in the presence of interdependencies. Public Choice 43(3):329–343
Tomiyama Y (1991) Decomposition of the group members into two-subgroups based on the correctness probability of collective choice: two-decomposition theorem of the complete homegeneous group. Sociol Theory Method 6(2):69–84
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The author thanks two anonymous reviewers for their valuable comments.
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This work was supported by the Grants-in-Aid for Scientific Research from the Japan Society for the Promotion of Science (JSPS) to TS (KAKENHI grant number: 18K18588).
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Sekiguchi, T. Voting Records as Assessors of Premises Behind Collective Decisions. Group Decis Negot 32, 257–275 (2023). https://doi.org/10.1007/s10726-022-09807-9
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DOI: https://doi.org/10.1007/s10726-022-09807-9