defining Libertarian, Democrat, and Republican

Let's start with Websters...

lib⋅er⋅tar⋅i⋅an

Websters does a nice job with its first definition: "a person who advocates liberty, especially with regard to thought or conduct". In the context of politics and policy, this reduces nicely to advocacy of a strong, but (quite) limited government-- to protect liberty from encroachment by others. Thus, liberty is defended and defined negatively (what others and govt should not do to you) and positively (what one should be allowed to do). Of course, there are differences between Libs, but these are rather modest.

Websters does not define Libertarian in the context of a political party. I'd say that's an oversight on one hand; on the other hand, it is certainly appropriate to see Libertarian as philosophical more than political.
The Websters definitions of dem⋅o⋅crat and re⋅pub⋅li⋅can focus on the derivative of each name from the concepts of democracy and republic. These connections may have been more than a nickname at some point. But today, the allusions are nonsensical in trying to define the two.

Websters does mention each in connection with its political party affiliation. And this too is quite proper. Each has little philosophical underpinning-- at least what would be consistent throughout each party. Both are political far more than philosophical.

This is not to imply that philosophy is irrelevant to each. In fact, there are subsets within each which have relatively well-defined philosophies (e.g., evangelicals and environmentalists). But these are far from consistent within the parties. The result is a big-tent political unit with various sorts of democrats/republicans-- or their cousins, the various types of liberals and conservatives-- within each.

So, for all of your Democrats and Republicans out there:
Would you like to take a shot at defining your movement?
Any thoughts on the sub-groups within?