[EM] A few more Bucklin variants, because why not?

[Kristofer Munsterhjelm]

On 2024-09-28 13:06, Etjon Basha wrote:
> Thanks Kristofer,
> 
> On why the CW must be in the Serious Candidate Set: once explained in 
> those terms, it really seems quite intuitive indeed, and I should have 
> thought a bit harder before posting.
> 
> I also think that explanation is sufficient to model the observed 
> relationship between the Smith and SC Sets: using your argument, setting 
> the approval cut-off at a Smith Set member will elect some Smith Set 
> member. Setting to the cutoff at some non-member may elect any 
> candidate, inside or outside the Smith Set.

It almost is. You'd also have to show that no cycle can appear, so that 
the Smith set members don't exclude each other from the SC set by having 
another Smith set member win when the approval cutoff is placed just 
below their rank.

I'm pretty sure that the relation is acyclical, so that that can't 
happen: my thoughts are something like that one of the Smith set members 
has more votes closer to the top than the other Smith set members have, 
and therefore will win his own contest. But I haven't proven it in any 
formally rigorous way :-)

-km