Talk:Ranked Pairs: Difference between revisions
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== Any Landau-independent variants? ==
What the title says. Right now, RP seems to be the "best available" Condorcet system (it's a top-shelf method alongside STAR). Can we make it even better? What's the strongest possible independence
: [[Independence of covered alternatives]] (IoCA; Landau-independence) is unfortunately incompatible with monotonicity. [[River]] passes a criterion somewhere between ISDA and IoCA called "independence of strongly dominated alternatives". That criterion also implies IPDA. So there might be some space between strongly dominated and IoCA that would still give you monotonicity, but I don't know what it would be. If you want the max amount of "independence from X" of any known method, River is probably better than RP.
: From another direction, it might be possible to create a Ranked Pairs version that does everything RP does but also elects from the uncovered set, even if it's not independent of covered candidates. Such a method has been discussed on EM under the name "short ranked pairs", but hasn't been fully fleshed out or implemented by anyone to my knowledge. [[User:Kristomun|Kristomun]] ([[User talk:Kristomun|talk]]) 13:08, 22 February 2024 (UTC)
:: Oof :( Oh well, independence of strongly-dominated alternatives is still pretty good! Does River satisfy LIIA? (Assuming you order the result by running the election without the winner.) --[[User:Closed Limelike Curves|Closed Limelike Curves]] ([[User talk:Closed Limelike Curves|talk]]) 22:55, 22 February 2024 (UTC)
::: I ''think'' so, but I never got a satisfactory proof on EM. You might want to contact [https://www.pik-potsdam.de/members/heitzig Jobst Heitzig] and ask. [[User:Kristomun|Kristomun]] ([[User talk:Kristomun|talk]]) 13:58, 23 February 2024 (UTC)
:::: Found answers to both my questions: 1. LIIA follows from independence of last-place alternatives and the construction of the River ordering, which means removing first-place candidates leads to the 2nd-place candidate winning. 2. The maximally-independent form of RP seems to be [[Stable voting]], but as you said, it violates monotonicity :( --[[User:Closed Limelike Curves|Closed Limelike Curves]] ([[User talk:Closed Limelike Curves|talk]]) 04:26, 1 March 2024 (UTC)
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