[EM] Method X

[Kristofer Munsterhjelm]

On 8/2/23 07:07, Forest Simmons wrote:
> Thanks for opening up new vistas!
> 
> How about restricting method X to Smith?
> 
> Or using some other method to pare down the field to manageable size?

It's even more strange if I do so. Here's Smith//X:

Burial, no compromise:  4262    0.0875496
Compromise, no burial:  9268    0.190382
Burial and compromise:  1933    0.0397075
Two-sided:              8103    0.166451
Other coalition strats: 0       0
==========================================
Manipulable elections:  23566   0.48409

See how there's no "Other"? So it too most likely is monotone! Just how 
is that possible? Schwartz//X is monotone too.

(I don't think the difference between manipulability here and for 
Smith,IRV is significant, as much as it would be fun to say I've not 
just met but beat IRV :-)

I tried to check Landau//X. It had plenty of Other strats, which is not 
unexpected given your proof about independence of covered alternatives 
plus first preference tiebreak implying nonmonotonicity... but I think 
my implementation of Landau is suspect, so I'm not including it here.

I could try other variants like "whenever someone is eliminated, 
everybody he beats pairwise must also be eliminated". If that were done 
on a global ordering (like IRV), that should give us Landau (and 
Banks?), but I don't know if our method construction guidelines still 
hold when the elimination order is different for different candidates. 
This is rather uncharted territory!

-km