[EM] The rationale under the "winning votes" defeat strength measure

[Kristofer Munsterhjelm]

On 2025-07-01 21:51, robert bristow-johnson via Election-Methods wrote:

>> and even a universally-ranked-last candidate can win.
> 
> There has to be at least one ballot with that candidate ranked
> higher  (and one is only sufficient if the vote with the two extreme candidates
> is exactly evenly split).

I've got the guy plonked, so his message didn't grace my inbox, but I 
think he's referring to arguments in the style of Warren Smith's DH3.

One should be careful here, because Warren never proved that *every* 
Condorcet method fails DH3. (And indeed, that is false. Smith,IRV 
passes, for instance.) Similarly, he never proved that every pairwise 
margins method fails DH3, either. So this statement, if it does indeed 
refer to DH3, needs proof - and if it's a blanket statement about every 
margins method, it needs a proof that covers every one of them.

-km