[EM] Friendly Voting: Some Criteria Compliance Proof Sketches

[Kristofer Munsterhjelm]

On 10/16/22 03:08, Forest Simmons wrote:
> Suppose de granted each candidate one free bullet ballot .... that would 
> keep non-Smith candidates from being in the tied-for-win set ... but it 
> creates a non-scaling problem.
> 
> However, if we grant each candidate a gratuitous bullet ballot with 
> positive weight epsilon, and shrink epsilon until further shrinkage 
> stops changing the winner, then the method becomes scale invariant.

Yeah, I thought about that. Basically you can add an epsilon to every 
candidate's first preference count and then let epsilon go to zero. This 
is equivalent to counting sum over friends A: fpA - sum over defeaters 
C: fpC as a two-vector whose first element is just the sum and the 
second is the number of friends minus the number of defeaters, and then 
using leximax.

The problem is that this fails clone independence. Suppose A and B are 
tied even given the tiebreaker above, and let C be some friend of A 
who's not a friend of B. Clone C, then A wins.

-km