Arrow suggests that, if voters provide a rank ordering of candidates on the ballot paper, then the death of one candidate should be handled by simply ignoring them and counting up the rest of the votes as if they'd never existed. For the presence of a dead candidate to affect the choice between two live ones would violate what he calls the Independence of Irrelevant Alternatives.
Since many electoral systems only ask people to declare their first preference, so this isn't always feasible. More importantly, I don't think Arrow ever tells us what to do when the dead guy wins...
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