Admissibility of possibility functions and other non-probability functions in Lindley´s extension of the DeFinetti-Savage uncertainty game

D.V. Lindley´s contention probability is essentially the only admissible uncertainty function within a rational context is reexamined. The entire problem is restated within a rigorous game-theoretic setting. The author clarifies Lindley´s extension of the `Dutch book´ argument for probability and related functions over the choice of other possible uncertainty functions. It is argued that Lindley´s conclusions concerning the inadmissibility of possibility functions and Dempster-Shafer functions were patently incorrect in general