[EM] Benham-DAC/DSC

[Kevin Venzke]

Hi Kristofer,

Le dimanche 12 juin 2022, 06:35:17 UTC−5, Kristofer Munsterhjelm <km_elmet at t-online.de> a écrit :
> Here's a modification to DAC and DSC inspired by Benham's method:
> 
> Intersect coalition sets as in DAC and DSC. But before intersecting with
> a set, check if the current set contains a candidate who beats everybody
> else in it pairwise. If so, elect this candidate.
> 
> It's clearly Condorcet (the initial set is the set of all candidates).
> It's probably not DMTBR (because DAC and DSC aren't.) Is it Smith? For a
> Smith failure to happen, the set at some stage needs to have more than
> one Smith candidate, and then they all get eliminated by the next
> intersection. I don't know if that's impossible - or possible.

Neither variant seems to satisfy DMTBR. I think DAC itself can only fail
DMTCBR if you'd say that Bucklin can.

The DSC variant violates Smith because the strongest coalition excluding at
least one candidate is often a singleton containing the plurality winner. This
could be the Condorcet loser.

For the DAC variant I haven't been able to find a Condorcet loser failure,
although I'm not sure logically why there couldn't be one. It's probably less
likely that a set with few candidates could have a lot of strength relative to
sets with more, making it less common to see multiple disqualifications in the
same step.

The DAC version seems to be a lot like DMC or approval-elimination Condorcet.

Kevin