this is quite simple. you're making more difficult than it needs to be. I think you would agree that arrows impossibility theorem concludes that given more than two choices, there is no fair way to democratically select the winner. so practically speaking, in how many presidential elections were there only two individuals in the entire country that were seeking the position?
my loose analogy was meant to show that even though the final election -- if it was to come down to two candidates, which is never the case -- is fair. the process by which those two candidates were selected must have been unfair according to the theorem. In the same way that just treatment of an individual at a particular point in time, does not negate the unjust treatment at a prior point; a fair election does not make the final result fair if the selection of those candidates was unfair.
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