The Classical Athenians developed two formal arbitration procedures. They assigned low stakes disputes to a panel of arbitrators, while high stakes cases were handled by a single arbitrator. Given the information aggregation benefit of collective decision making, one would have expected more individuals to be assigned to more important cases. I develop a theoretical model to provide an explanation for their design. Recognizing that arbitrator competence is endogenous, effort put into making a good decision takes time and effort. In larger groups free riding is a concern. Consequently, there exists environments where the free-riding loss is magnified in higher stakes disputes to the point where the socially optimal panel size is inversely related to the stakes involved.
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I date the Classical Period by the political structure. Thus, the period begins with Cleisthenes’, the “father of Athenian democracy”, creation of the constitution in 508 B.C. after the removal of the tyrant, to 322 B.C. with the death of Alexander the Great and the rise of the monarchies of the Successors. See McCannon (2011) for a social choice analysis of jury composition and structure in Classical Athens. Also, see MacDowell (1978) for his seminal volume cataloging Athenian legal procedures and Aristotle's Constitution of Athens for details. The introduction of public arbitrators likely occurred in the mid-sixth century A.D. during the Peisistratos’ rule prior to the Classical period.
The Athenians did have cost-saving rules. For example, trials could last no longer than 1 day and time limits were put on speeches/testimony. Slave labor was used in the courts as well. The existence of these efforts suggests the time and costs were an issue the Athenians developed institutions to deal with.
See Carugati et al. (2015) for a discussion of the ability of the Athenians to maintain social order without using formal, centralized institutions.
See Fleck and Hanssen (2012) for a discussion of the lack of expertise in the Athenian legal system. They briefly discuss arbitration in Classical Athens, but talk about the informal mechanism of selecting a private mediator, rather than using the formal system described here.
In a surviving court case, an appeal of an arbitration decision is preserved (Against Meidias, XXII). In it, proper procedures are claimed to be violated and the jurors of the trial court were asked to rectify the conflict.
These are strong assumptions, but are common in the literature. For an overview and discussion see McCannon (2015).
Again, this is a simplifying assumption made for convenience. The main result can be extended if differences in the competence technology is introduced.
Obviously, n is an integer. I employ the notation for ease of presentation. An increase in the number of people, holding constant each person's competence, improves the group's improves accuracy.
Therefore, my modeling approach is closer to Buchanan and Tullock (1962) who also consider collective decision making. They investigate the optimal voting threshold, which balances the internal costs and the external costs. I, instead, focus on the number of people making the decision.
For example, if dρ/dε → − ∞ as ε → 0, then the Intermediate Value Theorem guarantees an equilibrium. See McCannon and Walker (2016) for a theoretical model exploring collective decision making when competence is endogenous.
It is, of course, possible that the LHS of (4) is increasing, since it combines a positive and negative term. The results require that the mechanism is on the downward sloping portion of the curve. In the context of arbitration this assumption is defensible. Elderly citizens were utilized as arbitrators. Adding more of them has a low opportunity cost. Juries, on the other hand, that use prime aged, productive citizens can be expected to have a high marginal cost.
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McCannon, B.C. Arbitration in classical Athens. Const Polit Econ 29, 413–423 (2018). https://doi.org/10.1007/s10602-018-9267-0
- Condorcet Jury Theorem
- Free riding
- Group size