Abstract
The two-dimensional jury model, which is the core of this paper, demonstrates the two, partly conflicting, dimensions in Condorcet’s work and life. There is the dimension of enlightenment, reflected in Condorcet’s jury theorem, i.e., the belief that there is some truth can be approximated in collective decision-making. On the other hand, there is creed that individual preferences are the building blocks of the society with the consequence of inevitable conflicts in aggregating them. This paper combines the idea of winning a maximum of votes in a voting game with utility maximization that derives from the winning proposition. The model assumes a first mover, the plaintiff, and a second mover, the counsel of the defendant. Typically, these agents represent parties that have conflicting interests. Here they face an arbitration court in the form of jury that consists of three voters such that no single voter has a majority of votes. The agents are interested in both gaining the support of a majority of jury members and seeing their preferred alternative selected as outcome. It will be demonstrated that equilibrium decision-making can be derived for this model.
I would like to thank Hannu Nurmi for very helpful comments.
Parts of this paper, especially the model discussed in Sects. 3–5, are borrowed from Holler and Napel (2007) and Holler (2010).
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Notes
- 1.
- 2.
Ladha (1993) introduces symmetrically dependent votes and demonstrates that Condorcet’s main result holds: a majority of voters is more likely than any single voter to choose the better of two alternatives. Berg (1993) discusses correlation by assuming that a juror’s competence depends on preceding votes.
- 3.
See Black (1963, pp. 64ff.) for this judgement and the arguments.
- 4.
Later, the relationship of voting and Rousseau’s common will was excessively discussed. See Grofman and Feld (1988) and the literature given in this article.
- 5.
Kaniovski (2010) demonstrates that an enlargement with positive correlation can be detrimental up to a certain size, beyond which it becomes beneficial.
- 6.
See Faccarello (2016) and Behnke (2011). However, Rothschild (2001, p. 198) observes that “Condorcet's political and philosophical opinions changed substantially in the course of his public life…He became considerably more skeptical, in particular…about the prospects for education in enlightenment…”.
- 7.
There is no ordering of u, v, and w such that the preferences of all voters are single-peaked. Thus, the preferences are nonsingle-peaked (see Black 1948).
- 8.
The variable m represents the standard vote maximizing objective that public choice theory assumes for political agents, while p is a close relative to the utility maximization suggested in Wittman (1973) that becomes relevant if the incumbent (i.e. the proposer) faces cyclical majorities and thus cannot win an election.
- 9.
These preferences result from applying the dominance relation, but do not consider trade-offs between m and p. For example, in g’s perspective u dominates v as a response to a’s choice of u (denoted by u* in Fig. 2). However, winning for sure (m = 1) with w, that is ceteris paribus the least desirable policy for D, may potentially be preferred to responding with u resulting in outcome u (indicated in bold in Fig. 2) but only m = 1/2.
- 10.
Laver and Shepsle (1990) analyze a two-dimensional voting model with discrete alternatives, rather similar to the model presented here, however with single-peakedness in each dimension. They show that, in general, the core is not empty—therefore stable outcomes are likely.
- 11.
See Nurmi (2006, p. 131) for illustration and discussion.
- 12.
Saari’s concept of a “ranking wheel” allows for identifying the preference profile that is characterized by a majority cycle, i.e., a voting paradox (see Saari 2011). For the case of three alternatives there are two (types of) profiles that imply a voting paradox.
- 13.
There are however voting procedures that give a ranking of the alternatives that can be interpreted as a social welfare function (e.g., Borda count). Needless to say that such social welfare functions do not satisfy Arrow’s axioms and conditions as stated above.
- 14.
“Investor-state dispute settlement”, version of February 9, 2016.
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Holler, M.J. (2016). Marquis de Condorcet and the Two-dimensional Jury Model. In: Marciano, A., Ramello, G. (eds) Law and Economics in Europe and the U.S.. The European Heritage in Economics and the Social Sciences, vol 18. Springer, Cham. https://doi.org/10.1007/978-3-319-47471-7_9
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