[Election-Methods] Improved Approval Runoff (small correction)

[Chris Benham]

Chris Benham wrote:

> 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. 

The last line is wrong. I meant to write

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

They both elect B. Sorry if  I caused any confusion.

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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>>  
>>
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