> Perhaps the pattern arises because societies with pre-
  > existing tendencies to authoritarianism and corruption
  > are more likely to give rise to communist regimes

Seems more likely that whenever someone wants to rise to power as a despot, it's a lot easier when you are claiming to be communist/a workers' paradise/a government for the people, even if that description is in name only. E.g.:

    Why do you want to over-throw $despot? You must be
    an enemy of 'the people.'