Researchers applying predictive political economic models to speci_x001c_c real world policy problems typically face at least two di_x001e_cult challenges. First, they have very limited information on which to assign parameters to the mappings from policies to outcomes to utilities. Second, they have very little basis for declaring that any given political economic model will adequately represent the political process in question. This paper presents methodology, which we call Probabilistic Political Viability (PPV,) that applies tools of political economy to make probabilistic predictions about the viability of various political alternatives in real world settings. This methodology is applied toto the debate over the future of California's Sacramento-San Joaquin Delta using a simulation approach. We study the properties of our models under a wide range of plausible parameter speci_x001c_cations and then assess the likelihood that any particular policy option will be politically viable, based on the fraction of our universe of parameter values for which the option meets a viability criterion. Using this model, we _x001c_rst present evidence that there are some alternatives that would be politically viable, provided that all stakeholder groups trusted that these alternatives would be implemented in accordance with declared guidelines. We then incorporate institutional mistrust into our model and discuss how the political viability of these alternatives changes as institutional mistrust increases. Broadly speaking, mistrust in our context regards the suspicions of other stakeholders that urban and agricultural users will exploit the capacity of any alternative conveyance structure fully, regardless of any agreements to limit water exports in total, or to limit the use of the conveyance structure in order to maintain throughDelta _x001d_ows. Given institutional mistrust, none of the policy alternatives under consideration are politically viable.