Webs, iteration groups, and equivalent changes in probabilities

Abstract

Yew-Kwang Ng [12] listed several “reasonable properties” for equivalent changes of probabilities and other proportions. He produced a family of functions satisfying all properties and asked whether there exist essentially different ones. We show that this is the case, by constructing uncountably many families of functions satisfying all properties. We show also that there are no other solutions. Our method establishes connections with webs (nets) and iteration groups. This may be of interest both in itself and for applications.