Suppose that, when evaluating two alternatives x and y by means of a parametric utility function, low values of the parameter indicate a preference for x and high values indicate a preference for y. We say that a stochastic choice model is monotone whenever the probability of choosing x is decreasing in the preference parameter. We show that the standard use of random utility models in the context of risk and time preferences may sharply violate this monotonicity property, and argue that their use in preference estimation may be problematic. In particular, they may pose identification problems and yield biased estimations. We then establish that the alternative random parameter models, in contrast, are always monotone. We show in an empirical application that standard risk-aversion assessments may be severely biased.