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We apply a recent game-theoretic model of joint action prediction to the congressional setting. The model, known as the ideal point model with social interactions, has been shown to be effective in modeling the strategic interactions of Senators. In this project, we apply the ideal point models with social interactions to different spheres of legislation. We first use a machine learning algorithm to learn ideal point models with social interactions for individual spheres using congressional roll call data and subject codes of bills. After that, for a given polarity value of a bill, we compute the set of Nash equilibria. We use the set of Nash equilibria predictions to compute a set of most influential senators. Our analysis is based on these three components--the learned models, the sets of Nash equilibria, and the sets of most influential senators. We systematically study how the ideal points of senators change based on the spheres of legislation. We also study how most influential senators, that is a group of senators that can influence others to achieve a desirable outcome, change depending on the polarity of the desirable outcome as well as the spheres of legislation. Furthermore, we take a closer look at the intra-party and inter-party interactions for different spheres of legislation and how these interactions change depending on whether or not we model the contextual parameters. Finally, we show how probabilistic graphical models can be used to extend the computational framework.
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