[EM] Oops (re resistant set extension)

Kristofer Munsterhjelm km_elmet at t-online.de
Wed Dec 20 13:51:59 PST 2023


I missed an obvious counterexample for the first preference-based extension.

34: A>B>C
33: B>C>A
33: C>A>B

Now (A,B) ~> C since 34 + 33 > 50,
{B, C} ~> A since 33 + 33 > 50
and {C, A} ~> B since 33 + 34 > 50

hence a cycle.

So that relation (with that threshold) is unsuitable. If the first 
preference extension is to be salvaged, the threshold can't be 1/(k-|S|+1).

-km


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