I examine the shape of the probability weighting function (PWF) in a model of decision making that allows for optimism/pessimism over probability distributions and for loss averse/loss tolerant stochastic reference dependence. By imposing psychologically intuitive restrictions, I can give a preference interpretation to commonly observed shapes of PWF. In particular, I establish a deep connection between two of the most established phenomena in decision making: loss aversion and the inverse-S PWF: the former is a precondition for the latter. An extension of the model to allow distinct PWFs in the gain and loss domains predicts a domain-specific switching of preferences over probability distributions.