[EM] two "new" hybrid approval-ranking methods by Brams & Sanver

[Chris Benham]

David and interested others,

Dgamble997 at aol.com wrote:

> http://www.nyu.edu/gsas/dept/politics/faculty/brams/approval_preference.pdf
>  
> I was surprised to find that the PAV (preference approval voting) 
> method described is identical to something called Ranked Approval that 
> I posted to this list 18 months ago.

I now notice  that a small difference is  that  Brams-Sanver PAV  allows 
the voters to enter an explicit approval cutoff so they can rank above 
bottom candidates they don't approve,
whereas  Gamble RA doesn't.

> Take the following example under Ranked Approval/preference approval 
> voting:
>  
> 41: A
> 44: B>A
> 5: C>B
> 10: C
>  
> A is the only candidate approved by a majority of voters and therefore 
> the winner.
>  
> If the 44 B>A voters approve only B the votes are now:
>  
> 41: A
> 44: B
> 5: C>B
> 10: C
>  
> and B is the winner as the most approved candidate.

DMC  elects B both times. 

Like  DMC, these methods meet  Mono-raise (and  
"approval-monotonicity")  and  Definite Majority (i.e. they elect from 
the set of candidates not pairwise-beaten by a more
approved candidate); but unlike DMC  they fail  Condorcet  and  the 
Independence from Irrelevant Ballots criterion (with no countervailing  
advantage that I know of).


Chris  Benham


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