Talk:Ranked voting: Difference between revisions
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::::: It sounds like you're saying that in each pairwise comparison, the voter must maintain the same cardinal preference for a candidate i.e. if my preference is A>B>C and I score, on a scale of 0 to 5, A:5 B:0 in the A vs B matchup, then I can't score B:5 C:0 in the B vs C matchup. What I was talking about was generalized in the sense that you could do that, meaning (as far as I can tell) that the preferences obtained might not be combinable into a rated or a ranked ballot. [[User:BetterVotingAdvocacy|BetterVotingAdvocacy]] ([[User talk:BetterVotingAdvocacy|talk]]) 17:55, 13 April 2020 (UTC)
:::::: [[User:BetterVotingAdvocacy|BetterVotingAdvocacy]] No, that is what I was getting at with the closure of the group. Lets say the group operation is addition (this way we do not need to deal with infinities like we would with multiplication) so if A:5 B:0 in the A vs B matchup and B:5 C:0 in the B vs C matchup then we need at least a scale of 10 if we wish to put them all on the same score ballot. ie A:10,B:5,C0. I am not really sure what you are driving at here. My point was that the group operation exists in Cardinal systems but does not in ordinal systems so they are very different mathematical objects. This is what makes it impossible for you to give the A:0 C:5 in the A vs C matchup. The cardinal system has some mathematics implicit hiding under it. This is why we can push it all to a single score ballot without loss of generality but pairwise rank and a single ranked ballot cannot really be unified. We do not really need to go down the number theory rabbit hole here. We can on the CES forum if you would like the best books on this are [https://www.amazon.com/dp/0070542341 Rudin] and [https://www.amazon.com/dp/0134689496 Royden] but I have not read them in a few decades. The point is that this is not new theory we are talking about. This has been unchanging theory for ages. Ordinal and Cardinal numbers are different. Conflating them is not going to help us in any way. --[[User:Dr. Edmonds|Dr. Edmonds]] ([[User talk:Dr. Edmonds|talk]]) 20:43, 13 April 2020 (UTC)
: I think we conflate many things when we talk about [[election method]]s. This community seems to break up the tabulation strategies for electoral methods into two big categories: ordinal and cardinal. We also have two categories of ballots: ranked and rated. The two categories are orthogonal; that is, it's entirely possible to tabulate an election conducted with rated ballots using an ordinal method. In fact, that was my strategy with [[Electowidget]]. Moreover [[STAR voting]] is a hybrid of ordinal and cardinal tabulation methods. So to answer [[User:BetterVotingAdvocacy|BVA]]'s question: I believe that it would be difficult to tabulate ranked ballots using cardinal methods, though I suppose that's what the [[Borda count]] is. -- [[User:RobLa|RobLa]] ([[User talk:RobLa|talk]]) 05:16, 13 April 2020 (UTC)
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