Coherence in the aggregate: A betting method for belief functions on many-valued events

• We investigate a generalised betting method and isolate its general form of coherence.
• We provide an operational semantics for belief and plausibility functions.
• We investigate generalised uncertainty measures on MV-algebras.

Betting methods, of which de Finetti's Dutch Book is by far the most well-known, are uncertainty modelling devices which accomplish a twofold aim. Whilst providing an (operational) interpretation of the relevant measure of uncertainty, they also provide a formal definition of coherence. The main purpose of this paper is to put forward a betting method for belief functions on MV-algebras of many-valued events which allows us to isolate the corresponding coherence criterion, which we term coherence in the aggregate. Our framework generalises the classical Dutch Book method.