[EM] Re: AWP versus DMC and AM

[Araucaria Araucana]

On 28 Apr 2005 at 00:54 UTC-0700, Chris Benham wrote:
> James,
> Here is an example of yours that we've been
> discussing.
>
> Preferences
> 26: A>>C>B
> 22: A>>B>C
> 19: C>B>>A
> 06: C>>B>A
> 22: B>C>>A
> 05: B>>A>C
>
> Direction of defeats
> A>C 52-48
> C>B 51-49
> B>A 52-48
>
> Approvals: A48,  B46,  C47.
>

Interesting example.  But you forgot to consider approval cutoff
strategies:

What happens if the 22 B>C>>A voters move the approval cutoff upward,
to get

   22: B>>C>A

You get

    Approvals: A48, B46, C25.

Consider the pairwise array with approval on the diagonal:

            A  B  C
         A  48 48 52
         B  52 46 49
         C  48 51 25

B is now the DMC (and MRAV/AM) winner.

Even if the 19: C>B>>A voters moved their cutoff up as well, B would
still win.

This illustrates a Later-no-harm violation of the approval cutoff in
DMC/AM: B- and C-preferring voters actually get the better effect of
defeating A if they do NOT approve each other.

B would also have been elected if the "6: C>>B>A" voters had moved
their cutoff below B.

As with all of these hypothetical examples, I should point out that
the margins are extremely slim, smaller than could be predicted by any
standard poll.

-- 
araucaria dot araucana at gmail dot com