The utility function for perceived gains has two key properties: an upward slope, and concavity. (i) The upward slope implies that the person feels that more is better: a larger amount received yields greater utility, and for risky bets the person would prefer a bet which is first-order stochastically dominant over an alternative bet (that is, if the probability mass of the second bet is pushed to the right to form the first bet, then the first bet is preferred). (ii) The concavity of the utility function implies that the person is risk averse: a sure amount would always be preferred over a risky bet having the same expected value; moreover, for risky bets the person would prefer a bet which is a mean-preserving contraction of an alternative bet (that is, if some of the probability mass of the first bet is spread out without altering the mean to form the second bet, then the first bet is preferred).