The left/right is economic policy.
Left is about taxing people and spending that on public good, and the right is about not taxing people and letting the private sector handle the public goods.
The up/down is authoritarian/libertarian.
Authoritarian is all about large government and lots of control. Libertarian is about personal freedom and minimal government interference.
All the way right and all the way authoritarian is fascism (Nazi Germany). All the way left and all the way authoritarian is a socialist dictatorship (USSR, China, North Korea). All the way right and all the way libertarian is anarchy, no government at all. All the way left and all the way libertarian is communism as Karl Marx envisioned it.
The key is finding a balance in government, and most people will find themselves somewhere near the center, but will vote to an extreme to avoid the other side gaining ground.
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