I don't know why you say conservative minority. I'd argue that it benefits whoever the majority is.

In Quebec, Canada, it's the liberal party. A blend of progressives and conservatives, but it seems to me they are more progressive than not. Imagine voting for conservatives here during the federal elections, when you know that the province just doesn't like conversatives that much. They only have a chance when the liberals get the people very mad.

In the USA, I think there're plenty of conservatives still, I wouldn't call them a minority.