We examine the effect of variability in model parameters on the predictions of expected utility theory and cumulative prospect theory, two of the most influential choice models in decision making research. We find that zero-mean and symmetrically distributed noise in the underlying parameters of these models can systematically distort choice probabilities, leading to false conclusions. Likewise, differences in choice proportions across decision makers might be due to differences in the amount of noise affecting underlying parameters rather than to differences in actual parameter values. Our results suggest that care and caution are needed when trying to infer the underlying preferences of decision makers, or the effects of psychological, biological, economic, and demographic variables on these preferences.