Talk:Distributed Score Voting: Difference between revisions
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: Every voting method that passes the majority criterion fails IIA, see the Wikipedia article. What you're talking about sounds like [[ISDA]], which by the way is mutually incompatible with IIA, since ISDA implies the majority criterion. . [[User:BetterVotingAdvocacy|BetterVotingAdvocacy]] ([[User talk:BetterVotingAdvocacy|talk]]) 00:45, 9 February 2020 (UTC)
:: You're right, in the Smith set I have to apply extra rules to reduce it in order to satisfy the IIA; specifically I have to reduce the possible condorcet paradox to a group of only 3 best candidates in a cyclical path; I'm looking for a definition for this but for now the maximum I have found is Smith set. [[User:Aldo Tragni|Aldo Tragni]] ([[User talk:Aldo Tragni|talk]]) 13:59, 9 February 2020 (UTC)
::: You forgot to sign your post, btw. But look, here's an example of how every voting method that always elects the majority's 1st choice has to fail IIA:
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::: 35 C>A>B
::: Your voting method guaranteeably elects one of these candidates. Now, if we eliminate one of the losing candidates, we find that there's another candidate who is a majority's 1st choice (if A wins, eliminate B who lost, and now C wins. If B wins, eliminate C and A wins. If C wins, eliminate A and B wins), and so they must win, violating IIA. It is a very specific criterion, and I think you're possibly discussing something completely new. But unfortunately, the only reasonable voting methods I'm aware of that pass IIA are Approval and Score Voting, and that too only under contrived conditions. https://en.wikipedia.org/wiki/Independence_of_irrelevant_alternatives#Criticism_of_IIA [[User:BetterVotingAdvocacy|BetterVotingAdvocacy]] ([[User talk:BetterVotingAdvocacy|talk]]) 13:24, 9 February 2020 (UTC)
:::: I didn't have time to correct my previous answer. The IIA that is satisfied concerns the set, that is:
:::: IIA: A is preferred to B. If I add C a less appreciated candidate than A and B, then A continues to be preferred over B.
:::: IIA-set: X is a set containing all the preferred candidates over B. If I add C a less appreciated candidate than the candidates in X and B, then all candidates in X continue to be preferred over B.
:::: - B is outside the Smith set: Smith set = X and the candidate added A would lose both against B and X leaving B (and A) outside the Smith set.
:::: - B is inside the Smith set: adding A could not get B out of the Smith set; at most A could enter the Smith set. In the Smith set the score voting is applied to choose the winner, in which the IIA is satisfied.
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