for example, we could assume the decision maker is an expected utility maximizer with initial wealth "w" whose utility function, formula_28, is chosen to satisfy <math>e(u(w+b)|a=a) for at least some values of "a" (that is, holding onto formula_24 is strictly preferred to switching to "b" for some "a"). although this is not true for all utility functions, it would be true if formula_28 had an upper bound, formula_31, as "w" increased toward infinity (a common assumption in mathematical economics and decision theory). michael r. powers (2015) provides necessary and sufficient conditions for the utility function to resolve the paradox, and notes that neither formula_32 nor formula_33 is required.