[EM] Resistant, monotonicity, and UD

[Kristofer Munsterhjelm]

On 2024-02-21 19:05, Kristofer Munsterhjelm wrote:
> Here's a thought about how to get resistant set compliance and 
> unrestricted domain. If it works, then that's a new combination: no 
> other method that I know of has all three. And it would show that 
> monotonicity is not incompatible with Resistant, despite IRV making it 
> seem like they are.

Replying to myself because I think this is busted. The problem is that 
the induction step doesn't hold - it's possible for B's disqualification 
path to contain A, and then A can't simply prepend his own 
disqualification of B and automatically get a longer path than B. Hence 
the resistant set compliance proof fails.[1]

I suspect that the monotonicity proof also fails; unless I'm missing 
something, it could be possible that raising A could establish A ~(x)~> 
E for some subelection x, and so allow B's path to grow from, say,

B ==> ... ==> A

to

B ==> ... ==> A ==> E

without affecting the length of A's path.

I have some ideas for other monotone methods, but I really need to test 
them. If they turn out not to work, I have an idea of how I can use 
integer programming to find a template for monotone four candidate 
elections that pass resistant and monotonicity, and hopefully learn from 
or try to generalize from that.

There's just a lot of work between here and there.

-km

[1] A simple patch is to require that for each step of the path, the 
current head node is not disqualified by any candidate lower down the 
path, on the current path set and all subsets of it. But that doesn't 
fix the monotonicity problem.