[EM] Re: Definite Majority Choice, AWP, AM

[Chris Benham]

Forest, Jobst, Ted and others,

At one point I proposed something very like DMC, which
I referred to as "Condorcet completed by Approval
Elimination".
When I first proposed Approval Margins (AM), I wrote
that I was scratching the other method because I'd
discovered that it was vulnerable to (a form of) 
Pushover strategy. In the example I gave, this was 
combined  (mixed up) with Burying.I thought "Pushover"
was just raising some "weak" alternative in an
elimination method, hoping to give some preferred
candidate an easier-to-beat opponent in the final
runoff. Checking the definition at Blake Cretney's
website, I see that it (now) specifies ranking
a candidate above your favourite.

Adapting the earlier example that included Burying,
here is a demonstration that DMC fails  "Approval
Later-no-Help" and what  I thought  was  "Approval
Pushover".

"Sincere" preferences:
49: A>>C>B
06: B>A>>C
12: B
06: B>C>>A
27: C>B>>A

A>C>B>A.  Approvals:  A55,  B51,  C33. 
DMC (and AM and AWP)  elects B.

Now suppose the A voters decide to approve C:
49: A>C>>B
06: B>A>>C
12: B
06: B>C>>A
27: C>B>>A

A>C>B>A.  Approvals:  A55,  B51,  C82.
Now DMC elects A.   (AM  and  AWP elect C.)

The effect of  the action has been to change P from 
{AB} to {AC}.

(Recall that in AM, in a 3-candidate cycle the winner
is always one of the approval top-two.Approval
runner-up can only win if
(1) s/he pairwise beats the AW, and (2) if  approval
runner-up's approval score is closer to the AW's than
to approval last's.)

I  am sure, and might get around to demonstrating in a
future post, that (at least in the 3-candidate
situation) AM meets Approval Later-no-Help.

(To be clear, what I mean by "Approval Later-no-Help"
is  "without any change in the rankings, approving
another candidate shouldn't help any already approved
candidate."


Chris Benham





















So I no longer support Condorcet completed by
Compressing Ranks, or Condorcet completed by Approval
Elimination. I think they are unneccessarily drastic.
I scratched the Approval
Elimination method when I discovered that it is
vulnerable to Pushover strategy.


http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-July/013416.html



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