Talk:Center squeeze: Difference between revisions
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: Presumably, Center should also be elected if any of the candidates is cloned in a way that does not introduce a Condorcet cycle among the cloned candidates. This could exclude methods that check a fixed number of candidates to otherwise obtain Condorcet compliance, but it would also be more difficult to test. [[User:Kristomun|Kristomun]] ([[User talk:Kristomun|talk]]) 14:41, 18 December 2023 (UTC)
:: Good thinking. I will try more variations in the vote counts and comment on the results. Also, will have a look at your cloning scenario. Thanks for the feedback. [[User:RalphInOttawa|RalphInOttawa]] ([[User talk:RalphInOttawa|talk]]) 19:10, 19 December 2023 (UTC)
::: I'm interested in a formal definition of a "center squeeze" criterion as well, [[User:RalphInOttawa|RalphInOttawa]]. Some reasonable definitions:
:::: 1. Candidates can fall outside of their region on a Yee diagram. (I think this is the best definition.)
:::: 2. Candidates may have an empty set on a Yee diagram.
:::: 3. Satisfying the traditional definition of candidate-later-no-harm (i.e. later preferences have no impact on the election, so there's no consensus-seeking).
::: --[[User:Closed Limelike Curves|Closed Limelike Curves]] ([[User talk:Closed Limelike Curves|talk]]) 21:20, 18 February 2024 (UTC)
:::: You could formalize the "elects C in every [[Left, Center, Right]] election" condition (e.g. for all positive x, y, z_1, z_2, v so that v = x+y+z_1+z_2, x+y > v/2, x < v/2, y < v/2, the method must elect C for the election "x: L>C>R, y: R>C>L, z_1: C>L>R, z_2: C>R>L"). But I don't think that would be very transparent a criterion.
:::: Ultimately, the problem is that center squeeze is loosely defined as "strong wing candidates mustn't exclude the candidate more voters are closer to". Its importance didn't come from theory, but from examples of methods failing it and producing intuitively wrong results. It's thus much harder to find an elegant theoretical phrasing of just what it means.
:::: LNHarm doesn't need to imply center squeeze, though: see for instance [[MMPO]]. [[User:Kristomun|Kristomun]] ([[User talk:Kristomun|talk]]) 18:24, 21 February 2024 (UTC)
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