[EM] 2 oddities. Use for Borda(=<). Clarification.

[Joshua Boehme]

If I remember correctly (I couldn't find my notes from when I was playing around with it back in the day), one of Split Cycle's major differences from RP is its tendency to end up with multiple winners much more often, even when not strictly necessary. Suppose edge A>B is part of two different but at least partially overlapping cycles and is the weakest in cycle 1 but not the weakest in cycle 2. Split Cycle breaks both A>B and the weakest edge in cycle 2, even though the latter isn't necessary. I think that redundancy ended up being necessary... if you only split the minimal number of edges, it lost some of its interesting properties.

Also, RP breaks edges by reversing them, while Split Cycle breaks them by turning them into head-to-head ties.

In a way, it's a little bit of a cheat on the algorithm's part. Algorithms that have overly expansive sets of potential winners can more easily satisfy things like participation and monotonicity, at the expensive of producing more ties and outsourcing some of the work to the tiebreaking mechanism


On 1/14/24 16:45, Michael Ossipoff wrote:

> 1.
> 
> An author, in an academic journal paper, proposed the following method:
> 
> Drop the weakest defeat in each cycle.
> 
> [end of definition]
> 
> As goes without saying,  there’s then always an unbeaten candidate.  …& as
> goes without saying, s/he wins.
> 
> Speaking for myself, that sounds like a briefer wording of Ranked-Pairs
> (RP).
> 
> But the author says it’s better than RP, & that it meets strong no-show
> criteria that no other Condorcet method meets.
> 
> I don’t know how it differs from RP, other than briefer wording.