Talk:Weighted positional method

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Baldwin and Nanson

"It follows that the only Condorcet-compliant sequential runoff method based on a weighted positional method is Baldwin"

Nanson's method doesn't count? — Psephomancy (talk) 15:28, 18 February 2020 (UTC)

By "sequential" I mean that it eliminates one candidate at a time. Nanson eliminates every candidate with a below-average Borda score, and so may take more than one at once. Kristomun (talk) 15:53, 18 February 2020 (UTC)

Just as a technical note, IRV is often done with batch elimination, though only when this is mathematically guaranteed to give the same winner(s) as one-at-a-time elimination. BetterVotingAdvocacy (talk) 15:00, 27 February 2020 (UTC)

Borda and Condorcet Winner ranking

The Borda count is the only weighted positional method that never ranks the Condorcet winner last.

Since Nanson and Baldwin pass Smith, can we rephrase this as "never ranks every member of the Smith set last"? BetterVotingAdvocacy (talk) 07:20, 27 February 2020 (UTC)

No, because those aren't weighted positional methods. They are elimination methods with weighted positional methods as the base. Same difference as IRV (or Carey) vs FPTP.

As for the second implied question, any method that never ranks the CW last may be used along with one-at-a-time elimination to pass Smith, even if the base methods may rank Smith set members last. This because once all but one Smith set member is eliminated, the remaining one is the CW by definition and so won't be eliminated.Kristomun (talk) 10:01, 27 February 2020 (UTC)

For Nanson, you also need to prove that eliminating below-average Borda count members won't erase the whole Smith set in one go, so that's slightly more complicated. Kristomun (talk) 10:06, 27 February 2020 (UTC)

Category

Can we make a category for IRV, Coombs, Baldwin, and similar methods? "Sequential runoff methods" or "sequential elimination methods" or something? — Psephomancy (talk) 15:49, 27 February 2020 (UTC)

I've just created Sequential loser-elimination method and Category:Sequential loser-elimination methods. Kristomun (talk) 20:22, 28 February 2020 (UTC)

Connection between weighted positional and Range failures

User:Closed Limelike Curves: While I think that some relative criteria failures of Range can be derived by looking at similar criteria for weighted positional methods, doing so might be quite complex. E.g. the later-no-help problem isn't a problem if we say "failures that exist in at least one weighted positional method for some completion mechanism chosen to make the criterion pass as easily as possible"; because then Summed-Ranks is the Borda analog that passes LNHelp. But I can't see at the moment how to phrase that for an encyclopedia entry. So I'll just go with that the relation holds for absolute criteria (e.g. Condorcet, Condorcet loser, majority, mutual majority, etc.), which should be correct. Kristomun (talk) 23:29, 25 August 2024 (UTC)

I'm not sure that's correct either; if we defined a criterion like "always elects the utilitarian winner", then every weighted positional method fails while score passes. I'm not quite sure what the correct claim here would actually be, although you're right to bring up that they're related (both being point-summing rules). —Closed Limelike Curves (talk) 02:44, 28 August 2024 (UTC)

Does Score pass? Suppose some voters vote approval-style (for any of a number of reasons, not necessarily strategic). Then the "always elects the utilitarian winner" property could well fail. Even if we insist on von Neumann-Morgenstern consistency, normalization can still make the property fail. Kristomun (talk) 15:53, 28 August 2024 (UTC)