Before revision:  We perform unsupervised clustering with Gaussian Mixture Model method on this dataset , and we find the cluster center found under a two-cluster restriction is close to the party centers, which are estimated using the mean position of the individuals self-identified with the parties . We conclude that the major US parties are representative of the US population under the constraint that the political system is limited to two parties .
After revision:  We perform unsupervised clustering with Gaussian Mixture Model method on this dataset , and we find the cluster center found under a two-cluster restriction is close to the party centers, which are estimated using the mean position of the individuals self-identified with the parties ) is similar to that of the centrist cluster, and the Republican Party's position is between the two clusters .