[EM] The resistant set

[Kristofer Munsterhjelm]

On 8/16/23 19:18, Filip Ejlak wrote:
> If we have a cycle scenario
> 
> 7: A>B>C
> 7: B>C>A
> 6: C>A>B
> 
> then the resistant set is {A}, so A is the winner. But if we change one 
> BCA voter to an ABC voter (mono-raising A), then the resistant set is 
> {A, C} - and now every majoritarian method will choose C. So 
> Resistant//? or Smith//Resistant//? will be non-monotonic, no matter 
> what the "?" method is, right?

That's a good point, and means that IRDA (independence of 
resistant-dominated candidates) and majority implies nonmonotonicity.

I'm not entirely sure which outcome is the wrong one. If I had to guess, 
I'd say it's the pre-raising outcome, given my suspicion that the 
resistant set is sufficient but not necessarily, er, necessary.

-km