Okay. I live in a country with some 25 active political parties ranging from conservative Christian to libertarian to UFO nuts and even a pirate party, who unfortunately did not support my plan to let criminals be keelhauled.
It's impossible to make a category system in which everyone feels they can fit, unless you make a few billion categories. Now for certain paradox computer game I'm currently modding on I'm working on I'm making a cube like three axis divide: Economic, social/civil and political/governmental.
Now using these axis three very distinct oppositions arrive.
1 free market / planned economy ( with interventionism, state run capitalism, controlled market, being some of the steps in between)
2 social reactioranism / free choice (conservatives and progressives being in between these)
3 full state control / no government (with various yet unnamed steps in between)
Now even with these distinctions I have not captured all the issues but I believe most are confined within.
A few examples of political ideologies placed along these lines.
Communists (planned economy, social conservatism, full state control)
Socialists (state run capitalism, social progressive, heavy state control)
Social democrats/labour (interventionism, social progressive, medium State control)
Liberal democrats (guided free market, social progressive, limited state control.)
Religious democrats ( guided free market, social conservatism, heavy state control)
Liberals ( free market, social progressive, limited state control)
Anarcho liberals (free market, free choice, no state control)
Libertarians ( free market, social conservative, no state control)
Anarcho socialists (planned economy, social progressive, no state control)
Reactionaries (protectionism, social reactionarism, heavy state control)
Fascism (protectionism, social reactionarism, heavy state control)
National socialism (state capitalism, social reactionarism, full state control)
Theocratic (state run capitalism, social conservatism, full state control)
Neo populism (which ever get's votes, which ever get's votes, which ever get's votes)
And these are just the examples I've researched so far. Guessing there are a few more. I'm currently working out a four axis system, to include religious tolerance, but There's still no 4 dimensional display mechanism.