[EM] Single-candidate DMTBR idea

[Kristofer Munsterhjelm]

On 3/11/22 6:04 AM, Kevin Venzke wrote:
> Hi Kristofer,
> 
>> On 3/11/22 12:33 AM, Kristofer Munsterhjelm wrote:
>> Does it also apply to the generalization where you just take the two
>> candidates with the most first preferences? I'm not sure.
> 
> In the three-candidate case, electing the pairwise winner between the top two
> candidates is basically IRV.
> 
> Without the 1/3 limit it could happen that the FPW gets more votes and changes
> who the second place candidate is. He might not beat the new one.
> 
> This is interesting though. The "obvious" way to expand IFPP to many candidates
> is to eliminate candidates with a below-average vote count. But it seems like
> the 1/3 rule was the important thing, as it's what enforces that always either
> one or two candidates are eligible to win, and these candidates can't be harmed
> by getting more votes.

Yes, that also explains where the "third" in dominant mutual third comes 
from. Like with Droop proportionatliy, it's the smallest quota so that 
only two candidates can exceed it. And that would also suggest that (at 
least by this approach), third is the best we can do; there's no, say, 
dominant mutual quarter for Condorcet.

> Tricky, to reduce a scenario to this state without breaking mono-raise.

We could of course just stitch something together, e.g. if there're 
exactly two candidates above 1/3 fpp, elect the candidate who pairwise 
beats the other, otherwise just elect the Plurality winner. This should 
be monotone because raising A doesn't harm A when A has >1/3 fpp, and 
raising B to >1/3 fpp gives him a second chance against A (if B beats A 
pairwise).

It's not very elegant: the seams are very obvious. But perhaps elegance 
can come later... or perhaps it will be induced by turning DMT candidate 
BR into full DMTBR.

-km