Talk:River

Practically different from RP?

The article makes it sound like this method is very similar to RP. Is this different enough from RP to merit its own article on Wikipedia, or should it be considered as a minor variant? --Closed Limelike Curves (talk) 18:41, 14 February 2024 (UTC)

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. 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. --Closed Limelike Curves (talk) 23:59, 15 February 2024 (UTC)