De Finettian consensus (Q1592994)

The authors refer to a result of de Finetti, going back to the year 1953 (i.e. the possibility of constructing a real function \(\varphi\) in such a way that \(\varphi(X)\) and \(\varphi(Y)\), where \(X\) and \(Y\) are random quantities with continuous distribution functions \(F\) and \(G\), respectively, have both the same distribution function \(H)\), in order to introduce an alternative way to describe the `opinion' of a group of experts about a continuous random quantity through the construction of a finite union of intervals where the opinions of the experts coincide (with respect to that random quantity). They discuss also, in this context, a continuous version of the well-known Allais' paradox.