In a finite population that repeatedly lets one uniformly chosen individual copy a uniformly chosen distinct individual, the fraction of either type is a bounded martingale. Conditional probabilities of an increase and decrease coincide. Absorption at one of the two unanimous states occurs almost surely, since from every state there is a uniformly positive probability of reaching unanimity in a fixed finite block of updates. Bounded convergence implies that the probability of eventual unanimity of one type equals its initial fraction.
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