  Employing a generalized definition of Pratt (1964) and Arrow's (1965, 1971)
probability premium, we introduce a new concept of attitude towards
probability. We illustrate in a problem of risk sharing that whether attitude
towards probability is a first-order or second-order phenomenon has important
economic applications. By developing a local approximation to the probability
premium, we show that the canonical rank-dependent utility model usually
exhibits attitude towards probability of first order, whereas under the dual
theory with smooth probability weighting functions attitude towards probability
is a second-order trait.
