This paper employs a novel method for the empirical analysis of political discourse and develops a model that demonstrates dynamics comparable with the empirical data. Applying a set of binary text classifiers based on convolutional neural networks, we label statements in the political programs of the Democratic and the Republican Party in the United States. Extending the framework of the Colonel Blotto game by a stochastic activation structure, we show that, under a simple learning rule, the simulated game exhibits dynamics that resemble the empirical data.