[Election-Methods] Improved Approval Runoff

[Chris Benham]

Peter Barath wrote:

>And what about the method (I don't know the name) in which
>the least approved candidate is eliminated until there is
>a Condorcet-winner?
>
That is called "Definite Majority Choice". It has some alternative 
algorithms.

http://wiki.electorama.com/wiki/Definite_Majority_Choice

>Does it also fail FBC?
>

Yes. All methods that meet the Condorcet criterion fail FBC. Condorcet 
is incompatible
with FBC. Kevin's "adjustment" of Condorcet//Approval to meet FBC causes 
it to no
longer strictly meet the Condorcet criterion.

>Did somebody
>analyse the strategy incentives then?
>
Yes, it has been discussed a lot at EM. It used to be my favourite.

31: A>>B
32: B>>C
37: C>>A

Leaving aside the approval cutoffs, methods that don't elect C here must 
fail mono-raise.
With these rankings and also C being the most approved candidate, for me 
a method needs
a good excuse for not electing C.

DMC and also "Approval-Weighted Pairwise" both elect C.

http://wiki.electorama.com/wiki/Cardinal_pairwise

I like  "Approval-Sorted Margins".

http://wiki.electorama.com/wiki/Approval_Sorted_Margins

I also like using that method to find the lowest-ordered candidate, 
eliminate that candidate, and then
repeat the process until one remains, each time interpreting ballots 
that make no approval distinction
among remaining candidates as approving all except those they rank 
(among the remaining candidates)
bottom or equal-bottom. (I think that is also good for plain ranked 
ballots that allow truncation but not
an explicit approval cutoff.)

An algorithm that is equivalent or nearly equivalent to ASM is to use 
one of  Beatpath, River or Ranked Pairs
measuring the 'defeat strength' by the difference between the two 
candidates' approval scores. I proposed this
a while ago as  "Approval Margins".

Chris Benham


>>By the way, electing from the Condorcet top tier using approval
>>would be called Smith//Approval or Schwartz//Approval depending on
>>which top tier is used. I don't typically consider these methods
>>because they are more complicated than Condorcet//Approval and
>>can't be adjusted to satisfy FBC.
>>    
>>
>
>And what about the method (I don't know the name) in which
>the least approved candidate is eliminated until there is
>a Condorcet-winner? Does it also fail FBC? Did somebody
>analyse the strategy incentives then?
>
>(And here I don't think of a method in which all ranked
>candidates are considered as approved, but a whole preference
>order with a cutoff mark somewhere between.)
>
>Peter Barath
>
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