# Talk:Cardinal voting systems

## Merge with "Category:Cardinal voting methods"

Should this just be merged into Category:Cardinal voting methods? — Psephomancy (talk) 05:28, 27 January 2019 (UTC)

## Recent edits

"Score voting has the lowest Bayesian Regret among all common single-winner election methods"

Should always clarify that BR/SUE/VSE are measurements, and that evaluation of methods depends on the assumptions made in the simulations. In other words, distinguish Smith's BR simulations from BR itself, and Quinn's/Merrill's VSE/SUE simulations from VSE/SUE itself. I could run BR simulations with different voter distributions that give different results, for instance.

"Simply put, voting in the range [0,1] or [0,100] or even [-42,7] is irrelevant."

This isn't true in the real world, because of the psychological impact of negative numbers. See https://halshs.archives-ouvertes.fr/halshs-01618039/document etc

Also I think it's good to use the term "Score voting" for real-world systems with discrete score levels, and "Range voting" for mathematical simulations with real numbers from 0 to 1, as in the references on https://en.wikipedia.org/wiki/Cardinal_voting#Variants.

— Psephomancy (talk) 17:46, 5 December 2019 (UTC)

## Favorite betrayal and cardinal methods

(There is never incentive for favorite betrayal by giving a higher score to a candidate who is liked less.), (Furthermore, all cardinal methods satisfy the participation criterion.), and, can Smith//Score or Condorcet//Score be considered cardinal methods?

Some of the points made about cardinal methods on this page seem to ignore STAR Voting. Wikipedia says that STAR fails the participation criterion, and the STAR Voting website has an article mentioning that STAR fails Favorite Betrayal. So maybe a distinction should be made between "classical/pure cardinal" methods, such as Approval and Score, and "semi-cardinal" methods like STAR. I think this rangevoting article also has examples featuring other criterion failures that don't occur in Approval or Score.

Also, I'd like to ask if Smith//Score or Condorcet//Score can reasonably be added to this page as cardinal (or semi-cardinal?) methods. Both methods use cardinal information when there is no weak Condorcet winner. BetterVotingAdvocacy (talk) 21:40, 15 December 2019 (UTC)

- Hmm, STAR is a hybrid of cardinal and ordinal utility, no? — Psephomancy (talk) 03:02, 7 January 2020 (UTC)

- Yes, but several of the statements on the page are inaccurate when talking about any cardinal method other than Approval or Score. BetterVotingAdvocacy (talk) 06:45, 27 January 2020 (UTC)

## Arrow and cardinal methods

User:RobLa and User:Dr. Edmonds, I think this edit (https://electowiki.org/w/index.php?title=Cardinal_voting_systems&curid=77&diff=8724&oldid=8653) is likely to be controversial, so I'd like to discuss it with both of you. This is the part that is at stake:

`Unlike ordinal voting, Arrow's Impossibility Theorem does not apply to pure cardinal methods. Furthermore, all pure cardinal methods satisfy the participation criterion.`

RobLa, I'd say that this is not controversial? If cardinal methods' failure of the universality criterion is an issue, we can simply say "Arrow's Impossibility Theorem doesn't apply to cardinal methods when ignoring the universality criterion (see that page for further discussion)." and leave it at that. In addition, it has been proven that cardinal methods pass the participation criterion, so I'm not sure why that has to be taken out. At most, the quote should be moved further down the article (say, to the "Notes" section); I suggest that as a general editing practice, rather than only here. BetterVotingAdvocacy (talk) 22:36, 16 March 2020 (UTC)

- User:RobLa I do not see how this could be considered controversial. Arrow did not consider Cardinal methods in his proof. Further work proved that extensions to Cardinal methods work as described. --Dr. Edmonds (talk) 02:45, 17 March 2020 (UTC)

- User:BetterVotingAdvocacy and User:Dr. Edmonds, I think a
*variant*of the text I removed could be added lower in the page. I truly believe that the intro has become too long, and the article has a lot of other problems that I'd like to fix when I get the chance (e.g. section titles really shouldn't be hyperlinks). The intro section to an article really should only be (at most) 2-3 short paragraphs that summarize the remainder of the article. I copied and adapted a section of the "Arrow's impossibility theorem" article, which I think gives this the issue its due. You can also see my comments over on Talk:Arrow's impossibility theorem where I've documented the EM list conversation about Arrow and cardinal methods. -- RobLa (talk) 06:07, 17 March 2020 (UTC)

- User:BetterVotingAdvocacy and User:Dr. Edmonds, I think a

- RobLa The information you removed is important and should be in the page. There are several similar proofs/paradoxes which are important to not conflate. The Voting paradox lists them. Perhaps somebody with deep knowledge on this can do a full comparison. --Dr. Edmonds (talk) 18:08, 17 March 2020 (UTC)