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We study the decentralization of liquor policies in the Post-Prohibition Era, which is the most famous natural experiment ever conducted with respect to policy decentralization in the U.S. Our empirical analysis exploits a unique feature of this policy change, namely that we observe votes of citizens in public referenda as well as roll call votes of the state legislators affecting the same policy. Our analysis is based on a probabilistic voting model. We show how to identify and estimate a model with a multi-dimensional policy space. These estimates then allow us to map the policy space into an alcohol consumption space. We find that this mapping is highly non-linear. Hence, differences in estimated bliss points in the ideological policy space tend to exaggerate differences in preferences over alcohol consumption. Nevertheless, decentralized policies offer the opportunity to account for heterogeneity in preferences and increase welfare. The optimal decentralized policy increases aggregate welfare by up to 79 percent compared to the optimal uniform policy