[EM] AFB Ranked Pairs Attempt

[Kevin Venzke]

Hi Gustav,

Le lundi 20 avril 2026 à 13:00:19 UTC−5, Gustav Thorzen via Election-Methods <election-methods at lists.electorama.com> a écrit :
> That is quite the counterexample,
> but mind if I ask why you did not mention the monotonicity failure
> for the reversed version where we go from C winning to B winning
> by lowering B?

I wasn't checking the reversed method, so it wasn't on my mind. From your original
post I wasn't totally sure whether you thought the reversed method was still
monotone, but it surely isn't, because it penalizes candidates for getting more
votes in their losing contests.

The reversed method of the new suggestion has a similar issue: Being penalized for
getting more votes when on the winning side.

> So at this point I decided to play around with similar versions to the proposed method,
> since my guess that sorting by greater or equal would be the key.
> specifically I found replacing the scoring of each entry from
> v(Winner > Loser) + v(Winner = Loser) to strictly v(Winner > Loser),
> while keeping sorting largest first to lowest last in place,
> makes things a little more hopefull

This territory is a little better explored, but I think four candidates are needed
for some of the demonstrations.

The issue is not how you count the defeat strengths, but that the locking mechanism
permits chaotic effects. I tried to warn about this earlier, but I didn't mention
locking per se, maybe.

Favorite betrayal:

0.411: C=A>B>D  ->  A>B>C=D  (i.e. C is betrayed)
0.377: D>A>C>B
0.158: B>D>C>A
0.052: A>D>C>B

Win moves from D to A.
(First the B>D win is rejected, then D>A is.)

Later-no-harm:

0.377: C>A>B>D
0.277: D>A>B=C  ->  D>A>C>B  (i.e. add lower preference for C)
0.199: A>B>D>C
0.145: B>D>C>A

Win moves from A to C.
(First the C>A win is rejected, then D>C is.)

Later-no-help:

0.350: B>A>C=D  ->  B>A>D>C  (i.e add lower preference for D)
0.331: D>C>B>A
0.240: C>A>D>B
0.077: A>B=D=C

Win moves from C to B.
(First C has no majority losses; then it does, to D, and C places last in the ranking.)

Again, hopefully no errors.

A pattern is that which defeats get rejected or locked seems to lack a clear
connection to how we modified the ballots. This makes it extremely difficult to
offer guarantees about the effects of vote changes.

> So thanks for the great conter examples,
> this will save my much otherwise wasted time and effort.

I hope I could help, all in all.

Kevin
votingmethods.net