Why did socialists win elections in some countries in Europe, and fascists in others, during the interwar period? Many political historians have viewed ''distributive class politics'' as the appropriate characterization of this period and place, but heretofore, formal politico-economic analysis has not been employed to study the question. Here, a new conception of political competition between parties, which yields Nash equilibria when the policy space is multi-dimensional, is harnessed to the task. Each party proposes a class distribution of income, chosen from a (multi-dimensional) issue simplex. The theory, proposed by G. Luebbert, that active class conflict between the landed peasantry and landless laborers was the necessary and sufficient condition of fascist victory is modeled, and is largely, but not conclusively, confirmed.