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This paper pushes forward political research from across disciplines seeking to understand the linkages between public opinion and social policy in democracies. It considers the thermostatic and the increasing returns perspectives as pointing toward a potentially stable set of effects running between opinion and policy. Both theoretical perspectives argue that opinion and policy are reciprocally causal, feeding back on one another. This is a general argument found in opinion-policy literatures. However, much empirical research claims to model 'feedback' effects when actually using separate unidirectional models of opinion and policy. Only a small body of research addresses opinion-policy endogeneity directly. In this paper I consider an opinion-policy system with simultaneous feedback and without lags. I argue that there is a theoretical equilibrium in the relationship of opinion and policy underlying the otherwise cyclical processes that link them. Given that available cross-national data are cross-sectional and provide limited degrees of freedom, an ideal theoretical model must be somewhat constrained in order to arrive at empirically meaningful results. In this challenging and exploratory undertaking I hope to open up the possibility of a general system of effects between public opinion and social policy and how to model them in future research. I focus on social welfare policy as it is highly salient to public interests and a costly area of government budgets, making it an area of contentious policymaking. Social policy is also a major part of the thermostatic model of opinion and policy, which was recently extended to the cross-national comparative context (Wlezien & Soroka, 2012) providing a critical predecessor to this paper because identification of equilibrium between public opinion and social policy in any given society is greatly enhanced through comparison with other societies. This counterfactual approach helps to identify opinion-policy patterns that may not change much within societies, but can be seen as taking on discrete trajectories between societies. [ABSTRACT FROM AUTHOR]