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At the higher echelons psychos shake hands, on the lower echelons psychos split and manage conflict. That is, they search for conflicts, pour oil on the fire, then suggest future directions.

It's a bit more nuanced than this. First there is the "uniparty" which is part of both left and right. These are wings of the same bird. Outside the uniparty, the left and right are very different. Sometimes the left is more (socially) libertarian and sometimes the right is more (fiscally) libertarian, but if one side is libertarian, the other side is authoritarian. The uniparty sides with the authoritarian side to crush the libertarians element. In rare cases, libertarians take over the bulk of one side and push the uniparty 80% out. At that point, there is a clear choice, even if imperfect.