[EM] Decloned Copeland Borda Hybrid

[Kristofer Munsterhjelm]

On 08.04.2022 19:15, Forest Simmons wrote:
> Kevin,
> 
> I'm glad you caught that. It looks like we have to go back to explícit
> designations of anti-favorites to avoid this "accidental" lowering of B
> on a set of ballots resulting from intentional raising of C on other
> ballots.
> 
> The other option would be to count truncated votes fractionally in the
> anti-favorite tallies. But that would be messy in hand computations.

There's a third option, I think, which involves counting both B and C.

E.g. in my three-candidate method enumeration, the IRV scoring function is

f(A) = -fpC, f(B) = -fpA, f(C) = -fpB

This is nonmonotone because raising A can lower B's first preferences
and thus increase f(C), making C win instead of A. But introducing an
fpA term

f(A) = fpA - fpC

makes sure that A's score always increases when A is moved first,
canceling out any potential improvement to C's score.

Your method seems similar enough (based on last preferences rather than
first ones) that a similar kind of fix could be employed. But perhaps
you've already anticipated that by your description:

> Elect the candidate with the greatest difference between the number of
> ballots on which it (itself) is the designated favorite and the number
> of ballots on which it is pairwise defeated by the designated favorite. 

I'm not sure, I thought I should mention it anyway :-)

-km