And while I am talking about newly democratic countries...
In applied economics, particularly since the experience of Eastern Europe and Russia in the 1990s, there has been a great emphasis on robust institutions being required for a transition to a capitalist economic system from a state-run economic system. "Institutions" here is a broad term, including organisations like government regulatory bodies and consumer rights bodies, but also attitudes and relations of people.
No doubt some political theorists have proposed necessary requirements for a transition from an authoritarian system to a democratic one in the light of recent experience. Some of them seem likely to overlap with the institutional demands of capitalism, such as good knowledge of the operation of the system by a wide number of participants, and protection against capture by a small number of individuals.
One requirement in the economic case is probably low or moderate degrees of economic risk. Rationally, some Eastern Europeans were unwilling to participate in some capitalist markets in the presence of extreme risk in those markets or in the macroeconomy. It would be interesting to know whether perceived political risk leads to increased conservatism in newly democratised countries, or complete withdrawal from the political process.