Abstract
What if the decision makers have different degrees of expertise and the aim is to maximize the probability of a correct decision? (The first three sub-sections are largely based on Nurmi, Voting procedures under uncertainty. Springer, Berlin-Heidelberg, pp 49–59, 2002) This possibility has been considered for a long time. We shall describe the main results in this field of inquiry where the degrees of competence play a crucial role. We begin with a classic result that is based on the assumption that the individual decision competences are equal and representable by the probability that the decision made by the individual is correct. The issue of where the competence probability comes from is left open. We also discuss epistemic paradoxes, i.e. peculiarities encountered when aggregating premises of an argument separately from the conclusions.
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Notes
- 1.
Nitzan and Paroush (1982) express the theorem in natural logarithms, i.e. logarithms to base \(e = lim_{n \rightarrow \infty }( 1+ (1/n))^n = 2.718 \ldots \), while Shapley and Grofman (1984) use Briggs’ logarithms or logarithms to base 10. These are equivalent in the present setting, since \(ln \ x/ln \ y = lg \ x /lg \ y\) for all real numbers x and y.
- 2.
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de Almeida, A.T., Morais, D.C., Nurmi, H. (2019). Qualified Majorities and Expert Choice. In: Systems, Procedures and Voting Rules in Context . Advances in Group Decision and Negotiation, vol 9. Springer, Cham. https://doi.org/10.1007/978-3-030-30955-8_9
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