[EM] Resistant set results

[Kristofer Munsterhjelm]

On 2023-12-09 19:24, Kristofer Munsterhjelm wrote:
> 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.

Just wanted to say: there is a good implied point that it doesn't make 
sense for strategy resistance to be weakened just because clones happen. 
Perhaps there is a subset of the resistant set that is cloneproof as a 
set and (e.g.) is straightforwardly monotone or captures even more of 
the strategy resistance of something like IRV.

I've been thinking vaguely along the lines of solid coalitions 
disqualifying candidates if the members, considered as one candidate, 
pass the 1/k criteria. Nothing concrete yet, though.

-km