[EM] Single-candidate DMTBR idea
km_elmet at t-online.de
Thu Mar 10 15:55:09 PST 2022
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
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.
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