I like how you're trying to clear up some things, but I don't know if you fully understand the two parties. Democrats are generally viewed as libertarian, supporting more freedom and less government. Some of your points don't directly apply to the parties or are misapplied.
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Oh I see your thinking now. Democrats and republicans aren't exactly named for those reasons. Reguardless of who is in power we are always (supposedly) a representative democracy, or republic. The founding fathers never wanted pure democracy because they didn't like majority rule (since they were elite and feared the masses). So when I am talking about democrats/ republicans I'm not talking about the government itself (we will never change in that way , atleast for now)