DeFinettian consensus

It is always possible to construct a real function phi, given random quanti ties X and Y with continuous distribution functions F and G, respectively, in such a way that phi(X) and phi(Y), also random quantities, have both the same distribution function, say H. This result of De Finetti introduces an alternative way to somehow describe the `opinion' of a group of experts ab out a continuous random quantity by the construction of Fields of coinciden ce of opinions (FCO). A Field of coincidence of opinions is a finite union of intervals where the opinions of the experts coincide with respect to tha t quantity of interest. We speculate on (dis)advantages of Fields of Opinio n compared to usual 'probability' measures of a group and on their relation with a continuous version of the well-known Allais' paradox.