Choquet operators and belief functions

This paper investigates characterizations of a class of belief functions. Our main contributions are threefold. First, using the notion of invariant weights, we characterize the Choquet operator with respect to belief functions along the lines of Schmeidler [26]. Second, we directly derive a class of belief functions on a state space and a collection of events that determines whether the Möbius inversion is strictly positive or zero. Third, we show that the derived collection is simple-complete. Our characterization results yield a wide variety of applications to economics, a multiperiod decision model, an inequality aversion model, and Leontief preferences.