Talk:Distributed Score Voting: Difference between revisions
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: Woodall states that DAC passes participation in his article "Monotonicity and Single-Seat Election Rules". [[User:Kristomun|Kristomun]] ([[User talk:Kristomun|talk]]) 09:56, 8 February 2020 (UTC)
:: I'd guess the reasoning for why consistency and participation are equivalent is that if you have a group of voters before and after adding in a voter, participation requires that voter not to get a worse result from voting, while consistency considers the voter a second "group" of voters who, when their vote fuses with the first group, shouldn't change the winner if they personally voted for the winner as their 1st choice. [[User:BetterVotingAdvocacy|BetterVotingAdvocacy]] ([[User talk:BetterVotingAdvocacy|talk]]) 16:10, 9 February 2020 (UTC)
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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 (IIA*), that is:
:::: IIA: A is preferred to B. If I add C, then A continues to be preferred over B.
:::: IIA*: X is a set containing all the preferred candidates over B. If I add C a less appreciated candidate (in head-to-head) 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 C would lose both against B and X leaving B (and C) outside the Smith set.
:::: - B is inside the Smith set: adding C could not get B out of the Smith set; at most C could enter the Smith set. In the Smith set the score voting is applied to choose the winner [[User:Aldo Tragni|Aldo Tragni]] ([[User talk:Aldo Tragni|talk]]) 14:00, 9 February 2020 (UTC)
::::: That is, as best as I can tell, ISDA (Independence of Smith-dominated Alternatives). https://en.wikipedia.org/wiki/Independence_of_Smith-dominated_alternatives. Also, just as a note, if the "eliminate the worst, redistribute points" procedure is done to the candidates within the Smith Set, that seems equivalent to [[Smith//IRV]], while if you're correct about this being Score Voting in the Smith Set, then it's equivalent to [[Smith//Score]]. [[User:BetterVotingAdvocacy|BetterVotingAdvocacy]] ([[User talk:BetterVotingAdvocacy|talk]]) 16:10, 9 February 2020 (UTC)
:::::: Yes, basically it's one [[Smith//Score]] that adds a couple of rules to handle the multi-winner case. [[User:Aldo Tragni|Aldo Tragni]] ([[User talk:Aldo Tragni|talk]]) 19:33, 9 February 2020 (UTC)
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