[EM] Sorted Approval Margins (plus two other Condorcet methods)

[Forest Simmons]

If I had to narrow it down to three for public proposal, I would probably
choose the same three. DMC would be right up there too ... in the form of
approval based Benham ... eliminate low approval candidates until an
undefeated candidate remains.

We called the chain building method
Uncovered Approval or unc(approval). Thanks for dusting it off!

For those not familiar with "chains" ...in the election methods context a
chain is a transitive beatpath ... so each member of the beatpath is beaten
by each of its predecessors ... not only by its immediate predecessor.




On Sun, Aug 6, 2023, 2:59 PM C.Benham <cbenham at adam.com.au> wrote:

>
> I think Condorcet methods that don't allow voters to enter an approval
> threshold have to choose between trying to
> minimise Compromise incentive or trying to reduce Defection incentive.
>
> The methods I like in this category allow voters to rank however many
> candidates they like and also approve all but
> one or only one or any number in between of the candidates (consistent
> with their rankings). Equal-ranking is allowed.
>
> Default approval goes only to candidates ranked below no other candidate.
>
> I suggest that voters can just mark one of the candidates as the lowest
> ranked one they approve (i.e. only that candidate
> and those ranked higher or equal to it are approved).
>
> But other ways of doing it could be fine.
>
> Regarding which algorithm, I very much like Forest's  Sorted Approval
> Margins.
>

Or more commonly, "Approval Sorted Margins"

[A rose by any other name ...]

>
> I also like another method of his, the exact name of which I've
> forgotten (something about "Chain" building or climbing):
>
> *Begin the chain with the most approved candidate.  Then add the most
> approved candidate that covers that candidate.
> Then add the most approved candidate that covers all the candidates
> already in the chain.
>
> Keep doing that as many times as possible, and then elect the last added
> candidate*.
>
> I think nearly always this will elect the same candidate as
> Smith//Approval, but is more elegant and ensures that the
> winner is Uncovered.
>
> For a practicable Condorcet method that uses plain ranked ballots
> (equal-ranking and truncation allowed), I like
> Smith//Ranked below none minus ranked above none.
>
> *Eliminate all the candidates not in the Smith set. Give each remaining
> candidate a score equal to the number of ballots
> on which it is ranked (among remaining candidates) below no other
> candidate minus the number of ballots on which it
> is ranked (among remaining candidates) above no other candidate.
>
> Elect the candidate with the highest score."
>
> Given how rare top cycles will likely be, I think this is probably good
> enough.
>
> Obviously it meets Plurality.  It fails both Minimal Defense and Chicken
> Dilemma, but never both at once :)
>
> It looks fair and gives a pretty-enough winner.  I'll be back later with
> some examples.
>
> Chris Benham
>
>
>
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