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Marcus, I understand that what is usually meant by "monotonicity" is what Woodall calls "Mono-raise". " Mono-raise: a candidate x should not be harmed if x is raised on some ballots without changing the orders of the other candidates." On the other hand, what you refer to here is not Mono-raise but is instead what Woodall calls "Mono-add-top". SD chooses candidate A. Act II: If "DE 19" is changed to "DE 10" then SD chooses candidate D."Mono-add-top: a candidate x should not be harmed if further ballots are added that have x top (and are otherwise arbitrary)." You have just done the operation back-to-front. Woodall writes that we can't have all three of his Plurality property, Condorcet(Net) and Mono-add-top. Mono-add-top is met by IRV, but is failed by all fashionable and (IMHO) reasonable Condorcet methods. Chris Benham |
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