[EM] Single-candidate DMTBR idea

[Kristofer Munsterhjelm]

On 3/11/22 12:33 AM, Kristofer Munsterhjelm wrote:
> If there are two candidates with more than 1/3 fpp, elect the one that 
> pairwise beats the other. If there is only one candidate with more than 
> 1/3 fpp, elect that candidate. And if there are none, do something else 
> that doesn't violate monotonicity given the rules above.

I was thinking, perhaps this isn't monotone after all. The usual 
nonmonotonicity problem (e.g. in IRV) has the pattern that you're in an 
ABCA cycle, then some BAC voters rank A higher so that B drops below C 
in first preferences, and then A is defeated by C in the second round.

But suppose A and B both have > 1/3 first preferences. Then upranking A 
on a BAC ballot has no effect if B stays above 1/3 first preferences, 
and if it pushes B below the threshold, then A wins outright as the sole 
candidate with more than 1/3 fpp. Upranking A can't give C more first 
preferences, and three candidates can't all have more than 1/3 of the 
first preferences.

So is monotonicity preserved after all? If so, that's a nice trick!

Does it also apply to the generalization where you just take the two 
candidates with the most first preferences? I'm not sure.

-km