Ezekiel comments on "Progress" - Less Wrong
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In this context, it would mean that those countries that aren't currently democratic will almost certainly adopt democracy at some point in the future.
And stay there? Or visit it as part of, for instance, a random walk?
And stay there, except for occasional digressions.
In other words, assuming I understand the claim: as time approaches infinity, so the probability of a randomly selected country being democratic approaches 1.