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Revision as of 23:59, 15 February 2024

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→‎Practically different from RP?
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: They have the same broad logic of locking in successive defeats unless prohibited by a condition based on the defeats already locked in. For Ranked Pairs, the condition is "we can't make a cycle". For River, it is "we can't make a cycle or have a candidate be defeated twice". Algorithmically, this doesn't seem to be much of a difference, but it does make some difference in the results.
:: -* Ranked Pairs fails IPDA and independence of strongly dominated alternatives, River passes both.
:: -* Ranked Pairs returns a full social ordering (who came in first, second, etc.), River only returns a winning set. (I think sequentially running River and eliminating the winner to get first place, second place, etc. produces an order that passes LIIA, but I don't have a proof.)
:: -* Ranked Pairs' complexity is O(n^3). River's is O(n^2).
: Although the differences in properties and behavior are IMHO significant enough to make River a separate method, I wouldn't imagine it to have its own article on Wikipedia, since the procedure itself is so similar. But I don't know for sure what Wikipedia's convention is in these matters. [[User:Kristomun|Kristomun]] ([[User talk:Kristomun|talk]]) 21:43, 14 February 2024 (UTC)
:: Interesting, thanks! Are there any advantages to RP, or is River+ pretty much just an improvement (by reducing sensitivity to very weak candidates)? I'm struggling to think of possible downsides to this modification, relative to MAM or MMV. --[[User:Closed Limelike Curves|Closed Limelike Curves]] ([[User talk:Closed Limelike Curves|talk]]) 23:59, 15 February 2024 (UTC)
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