Talk:Arrow's impossibility theorem: Difference between revisions
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:::: [[User:Kristomun|Kristomun]] To be clear a relative scale is when you put your favourite(s) to MAX_SCORE and everybody you do not like to 0, right? And your claim is that there is an extension of Arrow's theorem which would apply to [[Score voting]] if that was true. I would think this is always true so I would be very interested in such a proof. Do you have a reference? --[[User:Dr. Edmonds|Dr. Edmonds]] ([[User talk:Dr. Edmonds|talk]]) 22:27, 20 March 2020 (UTC)
::::: I think Kristomun is talking about something like a 3-candidate Condorcet cycle, where no matter who Score elects, if one candidate drops out, then if voters normalize between the two remaining candidates, then you get majority rule. [[User:BetterVotingAdvocacy|BetterVotingAdvocacy]] ([[User talk:BetterVotingAdvocacy|talk]]) 22:47, 20 March 2020 (UTC)
:::::: Pretty much. By "relative scale" I mean in the sense of Balinski and Laraki: an absolute scale is where the grades (or ratings) mean the same thing for everybody, a relative one is where what ratings you provide depend on what candidates are running. I don't know of a published proof, but it seems obvious, just follow [[User:BetterVotingAdvocacy]]'s suggestion: you set up an election where there's a Condorcet cycle and no matter who wins, if another candidate drops out then winner loses the resulting majority election. [[User:Kristomun|Kristomun]] ([[User talk:Kristomun|talk]]) 23:25, 20 March 2020 (UTC)
::::::: OK I understand. This is the sort of thing that systems like [[Distributed Voting]] try to get around. I have a bit of a rant on this [https://forum.electionscience.org/t/utilitarian-vs-majoritarian-in-single-winner/602 here]. Score has a built in assumption that candidates will not be added and removed. In any case, I do not think this is really related to Arrow's theorem directly so can we all agree that Arrow's theorem does not apply to score? This other stuff is interesting though. Perhaps somebody wants to add some explanation to the [[Voting paradox]] page. All the theorems are tied together in some way and they are all important. I did not know till vary recently that [[Balinski–Young theorem]] extends to multi-member systems. It implies that all Monroe type systems fail something like participation. Furthermore, there are Multimember systems where the score does have a much more absolute scale. The most obvious is [[Sequentially Spent Score]]. --[[User:Dr. Edmonds|Dr. Edmonds]] ([[User talk:Dr. Edmonds|talk]]) 01:53, 21 March 2020 (UTC)
:::::::: Quote from Dr. Edmonds: "Score has a built in assumption that candidates will not be added and removed." With such an assumption, it may be possible to make many ranked methods evade Arrow's Theorem as well. [[User:BetterVotingAdvocacy|BetterVotingAdvocacy]] ([[User talk:BetterVotingAdvocacy|talk]]) 02:07, 21 March 2020 (UTC)
::::::::: Well if you can formalize and prove that then there is a Nobel Prize in it for you. Social choice theory generally assumes that the choices come as part of the problem. This is one criticism of the whole field. We are going pretty far off topic. Lets move this to a forum. --[[User:Dr. Edmonds|Dr. Edmonds]] ([[User talk:Dr. Edmonds|talk]]) 05:22, 21 March 2020 (UTC)
:::::::::: Yes, let's take it to the election-methods list, then we can refer to the thread from here. I'd just say, in conclusion, that I think it's possible to phrase this in an Arrovian context, and that E-M style voting theory is already outside of social choice if what you're saying is true (consider e.g. Tideman's independence of clones criterion). [[User:Kristomun|Kristomun]] ([[User talk:Kristomun|talk]]) 10:29, 21 March 2020 (UTC)
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