[EM] The good counter-example

[Adam Tarr]

I think you got it this time.  I'm glad I made my (ultimately false) claim, 
because now I have a better sense of when it is not the case.  It would be 
nice to understand it even better, though.

Stephane Rouillon wrote:

>2: A
>2: A >B >C
>2: B >A >C
>1: B >C >A
>4: C
>
>With winning votes A (6) > C (5), then
>                               B (5) > C (4), then
>                               A (4) > B (3).
>Note that A is the Condorcet Winner.
>Margins as relative margins would produce the same result
>with a different order.
>
>The B >A >C voters (2) decide to believe Bart Ingles and truncate their
>ballots to produce insincere votes,  namely B ballots:
>2: A
>2: A >B >C
>2: B    (truncated!)
>1: B >C >A
>4: C
>
>With winning votes the pairwise comparisons become:
>B (5) > C(4) and C(5) > A(4), then
>A(4) > B(3) is dismissed.
>Bart wins...
>Note that relative margins would preserve Adam's victory.
>With margins it depends on the tie-breaker...
>
>Do you surrender, this time?

I do agree it seems that truncation helps in this case.  One question I 
have is, why does it help?  It seems that the benefit of truncation here 
depends on extensive truncation already present in the ballots.  Can anyone 
make a little more sense out of it?  Mike, I remember you stating something 
about this a while back but I'm not sure.

Just to see if it makes things clearer, here's the same election listed 
above turned into a percentage breakdown:

36% George
9% Al>George>Ralph
18% Al>Ralph>George
18% Ralph>Al>George
19% Ralph

Ralph (one of the outside candidates, from the appearance of the votes) is 
the Condorcet winner.  If the Al>Ralph>George voters just vote Al, then Al 
wins.

Maybe the fact that the supporters of the Condorcet loser (George) don't 
bother with a second choice has something to do with it?  Those voters seem 
like the ones with the most reason to support a second choice, yet they do 
not.  Maybe this example works because the Condorcet winner being beaten us 
on the edge of the spectrum here, rather than in the middle?  I'm trying to 
come up with a succinct reason why the truncation helps here.

Blake just chimed in with another example, but it has seven or eight 
factions rather than five, so I'm not going to try to get inside that 
one.  As an aside, Blake, haven't you said in the past that you would 
recommend that voters in winning votes methods should randomly complete 
their ballots it they have no sincere lower preference?  This would seem to 
be bad advice for the Al supporters above.  Honestly, this argument of 
yours was one of the reasons I made the claim in the first place; it seemed 
to logically follow from your argument.  I'd guess your response would be 
that random completion would not _consistently_ hurt your candidate, even 
if some of the votes were counter-productive.

-Adam


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