Abstract
The Condorcet Jury Theorem (CJT), together with a large and growing literature of ancillary results, suggests two conclusions regarding collective wisdom. First, large committees outperform small committees, other things equal. Second, heterogeneous committees can, under the right circumstances, outperform homogeneous ones, again other things equal. But this literature has done little to bring these two conclusions together. This paper employs simulations to compare the respective contributions of size and difference to optimal committee performance. It demonstrates that the contributions depend dramatically upon bias. In the presence of low bias, committee composition matters little. In the presence of high bias, it can matter a great deal; optimal committee performance, however, does not vary dramatically between low- and high-bias committees.
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Notes
- 1.
- 2.
Stone [28] considers only the absolute magnitude of the loss, and so treats \(e_a\) and \(e_b\) as positive. Here we treat these expressions as losses, and so assume \(e_a\), \(e_b < 0\).
- 3.
See also [8], which demonstrated that a committee whose members have different prior beliefs regarding the correct option is equivalent to a committee whose members have the same prior beliefs but different attitudes towards risk.
- 4.
- 5.
- 6.
This condition is minimal but not negligible. If it were not satisfied, then an X-member would be more likely to select a when b is correct than when a is correct!.
- 7.
- 8.
If \(e_a = e_b\), then \(E(u) = e_a [\pi (1-C_a)+(1-\pi )(1-C_b)] = e_a (1-C)\). Because \(e_a < 0\), this means that we can find a maximum of E(u) by maximizing C.
- 9.
For a more detailed defence of this claim, see [27].
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Acknowledgements
Earlier versions of this paper were presented at the 6th Munich-Sydney-Tilburg Conference on Models and Decisions, Munich, April 10–12, 2013, and at the 3rd Annual Conference of the European Political Science Association, Barcelona, June 20–22, 2013. We would like to thank participants at both events for helpful comments and suggestions.
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Stone, P.C., Kagotani, K. (2017). The Wisdom of the Multitude: Diversity Versus Size. In: Urbaniak, R., Payette, G. (eds) Applications of Formal Philosophy. Logic, Argumentation & Reasoning, vol 14. Springer, Cham. https://doi.org/10.1007/978-3-319-58507-9_4
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