Abstract We study the social choice problem where a group of n voters report their preferences over alternatives and a voting rule is used to select an alternative. We show that when the preferences of voters are positively correlated according to the Kendall-Tau distance, the probability that any scoring rule is not ex post incentive compatible (EPIC) goes to zero exponentially fast with the number of voters, pimproving over the previously known rate of 1/ n for independent preferences. Motivated by rank-order models from machine learning, we introduce two examples of positively-correlated models, namely Conditional Mallows and Conditional Plackett-Luce. Conditional Mallows satisfies Kendall-Tau correlation and fits our positive result. We also prove that Conditional Plackett-Luce becomes EPIC exponentially quickly.