10 September 2010, Computational Social Choice Seminar, Eva S. Hendriks
Condorcet's Jury Theorem (Condorcet 1785, hereafter: CJT) estimates the accuracy of outcomes of juries. Juries can be seen as committees voting on binary choices. In this paper a Generalized Condorcet's Jury Theorem (GCJT) is introduced, discussing committees voting on any type of decision, be it binary, discrete, continuous or otherwise. In a framework where an optimal decision exists, but is unknown at the time of voting, committee members base their voting on the signals they receive. In this paper it is shown that it is optimal for voters to reveal their true signals, and that they will take a decision that is equal to the UMVU estimator of the optimal decision, regardless of the distribution of the signals.
With the formalization of the CJT into the GCJT, the fact emerges that, in the literature, information is not always used efficiently. The GCJT, by using all available information efficiently, reverses some results in the literature, for example it is shown how indirect democracy does not create a loss of accuracy of the decision, contrary to beliefs based on Boland (1989).
The value of this GCJT in legal policy lies in the formalization of democratic processes it enables. It creates the possibility to extend the common CJT analyses to other cases. The applications of the GCJT within the democratic framework are endless. This paper only discuses a few of them, amongst others that the GCJT can be used to determine the accuracy of democratic decisions based on the number of participants in the democratic decision process. It provides a way to quantify the value of democratic processes in their accuracy, and with that enables cost/benefit analyses with respect to committee sizes. The GCJT also discloses the foundations of the expressive function of law.
This is joint work with Giuseppe Dari-Mattiacci and Maarten Havinga.