Summary: Finally, we explore the collective behaviors of manipulative voters. Assume every voter can change their vote for an infinite number of times. They formulate strategies based on their observations on the preference of the population. The observations, which contain noise, are generated by some distribution conditioned on the current vote status. We show that the plurality rule almost always elects the instant run-off winner, while Borda count almost always elects the Condorcet winner (when one exists) as the number of voters grow.