I made this exact same mistake a couple days ago, while trying to simplify
the Wikipedia article :)

I ultimately settled on this description:

1. Sort margins by how close they are to being tied.
2. Go down the list, and cross out any pairwise matchups that would result
   in a cycle.
3. (Optional) For River, also cross out "redundant" (duplicate) defeats of
   the same candidate.

The advantage of River mostly seems to be that it's less vulnerable to
irrelevant alternatives. Stable voting is another refinement on RP that's
even better at this; it seems like it prioritizes crossing out pairs that
would lead to an IIA violation. But I haven't worked out a simple
explanation of it, and I'm not sure I even quite understand what it's doing
yet.

Stable voting and split cycle are methods from the same academics (Holliday and Pacuit) that tend to behave somewhat similarly but they're not the same.

Split cycle is the one closest in spirit to ranked pairs, but it achieves its improvement in participation by sacrificing resoluteness. Not many methods can produce multiple potential winners even when both 1) there are no head to head ties and 2) the margins between candidates are all unique, but split cycle sometimes manages even in that case.

The only ways of describing stable voting I've seen are recursive (looking at subsets of the candidates). I don't know if its properties are as well understood, but my impression is that it's much, much less likely to produce multiple winners than split cycle is.

On 2/29/24 16:39, Closed Limelike Curves wrote: