[EM] Resistant set results

[Kristofer Munsterhjelm]

On 2023-12-09 18:47, Joshua Boehme wrote:
> 
> Apologies if this is a naive question, but based on that definition is 
> the resistant set affected by clones? Consider...
> 
> 4 A>B
> 3 B
> 
> A ~(AB)~> B and not vice versa, so A ~> B
> 
> Now add A', a clone of A...
> 
> 2 A'>A>B
> 2 A>A'>B
> 3 B
> 
> A~(AA'B)~>B isn't true, so A ~> B no longer holds
> 
> 
> Allowing tied rankings doesn't solve it, since A and A' could be from 
> different wings of one major party -- so voters have true preferences 
> between them -- while B is from another major party.

Yes. The set as a whole can be affected by cloning. But a method can 
still elect from it and pass clone independence.

In a later post, I want to show that both IRV and IFPP elect from the 
resistant set. The former is cloneproof while the latter is not.

Methods of the type "resistant,X" will probably not be cloneproof as 
such, so I don't claim they're good methods. They do, however, all seem 
to resist strategy. Since this kind of strategy resistance seemed to be 
such a rare property, that's what I've been focusing on.

-km