# Talk:Ranked Pairs

## Speeding up calculation

I'd like to see if there's a way the calculation can be sped up even further. I think the key is that if we have, for example, a candidate with 1 pairwise defeat and no pairwise ties, and early on in the RP procedure this candidate's only defeat is ignored, then we automatically know they're the winner. So I'd like to suggest the following procedure: calculate the number of pairwise defeats for each candidate, and then run RP until at least one candidate has no defeats. If that candidate has pairwise ties, keep running RP, otherwise that candidate is the winner. BetterVotingAdvocacy (talk) 00:19, 28 February 2020 (UTC)

## 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 criterion we could get; Landau seems achievable. What about Dutta? --Closed Limelike Curves (talk) 19:29, 21 February 2024 (UTC)

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. 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.) --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 Jobst Heitzig and ask. 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 :( --Closed Limelike Curves (talk) 04:26, 1 March 2024 (UTC)