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

Sun, 11 Dec 2005 10:50:36 -0800

David and interested others,

[EMAIL PROTECTED] wrote:
 
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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