I've been sitting on this for awhile, this train of thought was initiated by reading over the comments in a rather old Economist blog post on a completely different topic, but I figure it's a topic worth posting about. However, I do think a bit of throat clearing is in order. I don't really believe that individual's political beliefs can be located along a line. But I do believe there are constant threads of political belief that tie together the aristocratic and democratic factions of Aristotle with modern Republicans and Democrats.
Specifically, it's the belief that some individuals are better endowed than others with controlling the ship of state vs. the belief that the important thing is that everyone that a decision involves should have a say (or as the disability community puts it, "nothing about us without us," which I see as the essence of left wing politics). I realize that doesn't form anything resembling a line, I believe this is an essential element in each side talking past each other. But I do think this can reasonably be used to compare Aristotle's, or Thucydides', democratic vs oligarchic party, with the optimates vs populares of the Roman Republic, with the Mensheviks vs Bolsheviks, or with the modern Republican and Democratic parties.
Something that needs to be noted is that this is about political orientation, it has nothing to do with people's economic beliefs; that's an entirely distinct way to group ideas that doesn't work with a right vs. left analysis.* Once this is accepted the classification works well enough to describe regimes, though it will upset those who use a more muddied conception of left vs. right to do things like classify the Soviet Union as left-wing (it was a radical regime, but it was far more elitist than Aristotle's oligarchic party which makes it really weird to put it on the left wing of the political spectrum, obviously where it is on the economic spectrum is irrelevant to its political classification).
It also needs to be noted that this does not necessarily make regimes more democratic. Many more left oriented regimes, particularly in ancient Greece and with Caesar's populares but also many Latin American regimes, resulted in dictatorships. Some of these eventually shifted right, remember Augustus started on the side of the optimates, others however simply collapsed after the death of a popular dictator who never formed an elite to facilitate the rightward shift. Generally stated, however, the political orientation is that of elitists vs. populists, in a modern context identifying characteristics are things like wanting to limit the franchise to people who are good citizens or embedded in their communities vs. those that think everyone should have a voice, even if they are downtrodden and despicable.
*I realize using right vs. left to communicate economic ideas is common even among well educated people. However, it results in nonsense like saying they're so far right that they're left. This just doesn't work, the Bolsheviks, for instance, compare with the Nazi regime because both had political beliefs regarding the need for an elite to dominate society, to an extent that could be called extremely far right. Both were radical parties and both implemented many similar economic policies, though to protect radically different social segments. But ultimately they were both rather similar in their political orientation as classified by Aristotle, even if radically different in many other ways of classifying societies.