Maybe a better heuristic is to consider whether your degree of assurance in your position is more or less than your average degree of assurance over all topics on which you might encounter disagreements. Hopefully there would be less of a bias on this question of whether you are more confident than usual. Then, if everyone adopted the policy of believing themselves if they are unusually confident, and believing the other person if they are less confident than usual, average accuracy would increase.
Maybe a better heuristic is to consider whether your degree of assurance in your position is more or less than your average degree of assurance over all topics on which you might encounter disagreements. Hopefully there would be less of a bias on this question of whether you are more confident than usual. Then, if everyone adopted the policy of believing themselves if they are unusually confident, and believing the other person if they are less confident than usual, average accuracy would increase.