×

zbMATH — the first resource for mathematics

The limits of epistemic democracy. (English) Zbl 1180.91251
Summary: The so-called doctrinal paradox reveals that a jury that decides by majority on the truth of a set of propositions, may come to a conclusion that is at odds with a legal doctrine to which they all subscribe. The doctrinal paradox, and its subsequent generalization by List and Pettit (Econ Philos 18:89 - 110, 2002), reveal the logical difficulties of epistemic democracy. This paper presents several generalizations of the paradox that are formulated with the use of many-valued logic. The results show that allowing the individual or the collective judgements to be formulated in terms of degrees of beliefs does not ensure the possibility of collective epistemic decision making.

MSC:
91F10 History, political science
91B12 Voting theory
PDF BibTeX Cite
Full Text: DOI
References:
[1] Cohen J (1986) An epistemic conception of democracy. Ethics 97:26–38
[2] Coleman J, Ferejohn J (1986) Democracy and social choice. Ethics 97:6–25
[3] Dietrich F (2006) Judgment aggregation: (im)possibility theorems. J Econ Theory 126:286–298 · Zbl 1108.91024
[4] Dietrich F, List Chr (2004) A liberal paradox for judgment aggegation. Working paper
[5] Gärdenfors P (2006) A representation theorem for voting with logical consequences. Econ Philos 22:181–190
[6] Kornhauser L, Sager L (1993) The one and the many: adjudication in collegial courts. Calif Law Rev 81:1–59
[7] List Chr (2005) The probability of inconsistencies in complex collective decisions. Soc Choice Welfare 24:3–32 · Zbl 1100.91020
[8] List Chr, Pettit Ph (2002) Aggregating sets of judgments: an impossibility result. Econ Philos 18:89–110
[9] List Chr, Pettit Ph (2004) Aggregating sets of judgments: two impossibility results compared. Synthese 140:207–235 · Zbl 1205.03009
[10] Nehring K, Puppe C (2004) Consistent judgement aggregation: a characterization. Working paper
[11] Pauly M, van Hees M (2006) Logical constraints on judgement aggregation. J Philos Logic (forthcoming) · Zbl 1108.03009
[12] Pettit Ph (2001) Deliberative democracy and discursive dilemma. Philos Issues 11:268–299
[13] Post E (1921) Introduction to a general theory of elementary propositions. Am J Math 43:163–185 · JFM 48.1122.01
[14] Rescher N (1969) Many-valued logic. McGraw-Hill, New York · Zbl 0248.02023
[15] Urquhart A (2001). Basic many-valued logic. In: Gabbay DM, Guenther F (eds). Handbook of philosophical logic, 2nd edn, vol. 2 Kluwer, Dordrecht pp. 249–295 · Zbl 1003.03523
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.