Talk:Weighted positional method

"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)

 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)