Your intuition is in fact correct. Balanski and Laraki have shown that a median based rating system, in the limit where all voters are rational and their utilit

Your intuition is in fact correct. Balanski and Laraki have shown that a median based rating system, in the limit where all voters are rational and their utilities are maximized by electing their desired candidate, that the winner is always a Condorcet winner. This is one of the reasons that Majority Judgement (their name for this system) has so much going for it.