I'm sure that in general people describing themsleves as "conservatives" in most countries would insist that they were "moderates", rather than taking pride in declaring that they were extreme in their views.

Isn't that true in the USA?

Surely the central tenet of any kind of "conservative", whether Republicans in the States, or old-fashioned Communists in Russia, is a distrust of change, and an insistance that any change has to be proved necessary before it is introduced.
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Pretty well all political parties do tend to be controlled by people who do not actually reflect the people who vote for them too well. I think many people around the world take comfort from that thought, when they look at the current administration in the USA. I mean, it wouldn't be very pleasant to think that most Americans really were like that...