[EM] "Double Defeat, Hare" poll candidate

[Chris Benham]

> I would like to nominate  Double Defeat, Hare.
>
> *Voters strictly rank from the top however many candidates they wish and
> also may specify an approval cutoff.
>
> Default approval is only goes to top-ranked candidates.
>
> All candidates that are pairwise beaten by a more approved candidate are
> disqualified.
>
> If that leaves more than one qualified (i.e. not disqualified)
> candidate, commence eliminations according to Hare
> rules until only one qualified candidate remains.*
>
> This is a compromise between Hare and Condorcet which will probably not
> please the fundamentalist supporters of either,
> because it doesn't meet the Condorcet criterion and is more complicated
> than Hare and fails Later-no-Harm and Later-no-Help.
>
> But it addresses the concern some have about electing a weak low social
> utility Condorcet winner, and I think it might simulate
> well.

I think that methods that allow voters to both rank the candidates and 
specify an approval threshold/cutoff
should never elect a candidate that is pairwise beaten by a more 
approved candidate.

I coined this criterion as "Double Defeat" and it occurred to me that it 
could be a disqualification device that
is part of a method.

Some people are wary of Condorcet electing a "weak centrist" candidate, 
for example

49 A>>>C>B
48 B>>>C>A
03 C>A>>>B

Assuming all voters get the same utility from electing their favourites, 
the Hare (and FPP and presumably Approval)
winner is the highest Social Utility candidate A.

With those sincere preferences, the ranking-with-specified-approval 
ballots would be

49 A|>C
48 B|>C
03 C>A|

Here the Double Defeat rule doesn't interfere with Hare.  B is 
disqualified because B is pairwise beaten by the more approved A.

So then, following Hare rules C is eliminated leaving A as the only 
qualified candidate and so winner.

The C>A voters have no real complaint other than "The method should meet 
the Condorcet criterion" and any complaint from
the B>C voters is answered by "To get a result you prefer you didn't 
have to order-reverse, you could have had A disqualified by
approving C".

The method is similar in spirit to an "Approval-enhanced Hare" that 
arose from discussion I had here a few months ago with Forest,
but which I forgot about and didn't rediscover until after nominations 
for the poll had closed:

*Elect the most approved member of the set comprising the Hare winner 
and all the candidates with a beat-path to the Hare winner.*

49 A (sincere might be A>B)
24 B (sincere might be B>C)
27 C>B

A classic example that has been interpreted as Hare and Margins by 
electing A failing Minimal Defense and avoidably causing the C voters to 
regret
not Compromising, and alternatively by electing B the C>B voters having 
been taken advantage of by the B voters using a Defection strategy, a 
failure
of the Chicken Dilemma criterion.

In this example it is true that in all the methods that meet Double 
Defeat it is up to the C>B voters to decide which is more important for 
them:
preventing the election of their greater evil A, or preventing being 
taken advantage of by Defecting B voters.

Chris B.


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