[EM] Citation for immunity to strategic voting?
Andrew Myers
andru at cs.cornell.edu
Tue Sep 13 10:07:09 PDT 2005
On Tue, Sep 13, 2005 at 09:45:12AM +0200, Jobst Heitzig wrote:
>
> Dear Andrew and Stephane!
>
> Andrew wrote:
> > Actually even this weaker claim (as I understand it) is wrong. Consider the
> > following election with 100 voters:
> >
> > 23 A>B>C
> > 25 A>C>B
> > 3 B>A>C
> > 26 B>C>A
> > 3 C>A>B
> > 20 C>B>A
> >
> > Therefore we have A preferred to B 51-49, A preferred to C 51-49, and B
> > preferred to C 52-48. So A is a strong Condorcet winner. But consider what
> > happens when the 3 B>A>C voters decide to bury A, changing their ballots
> > to B>C>A. Then a cycle results:
> >
> > A vs. B: 51-49
> > B vs. C: 52-48
> > C vs. A: 52-48
> >
> > According to all wv methods, we drop the weaker A vs. B preference, and B wins.
>
> In DMC, those who prefer A to B can easily protect the A>B defeat by placing their approval cutoff between these two candidates:
>
> 23 A>>B>C
> 25 A>>C>B
> 03 B>A>C, whatever approval cutoff
> 26 B>C>A, whatever approval cutoff
> 03 C>A>>B
> 20 C>B>A, whatever approval cutoff
>
> Same cycle A>B>C>A, approval scores A>50>B, hence B is doubly defeated by A and thus loses in DMC. In view of this counterstrategy, it makes no sense for the B voters to bury A.
>
> Yours, Jobst
But note that this depends on the C voters placing *their* approval cutoff
lower. And the election's close enough that they may not know whether to defend
A against B or C against B. Defense seems pretty difficult to me.
Here are a couple of (more extreme) examples to think about that produce the
same cycle and strategic vulnerability:
48 A>B>C
3 B>A>C
1 B>C>A
3 C>A>B
45 C>B>A
3 A>B>C
45 A>C>B
3 B>A>C
46 B>C>A
3 C>A>B
In the first case, B is able to swing the election even though only 4 voters
have B as a first choice. In the second case, the presence of C enables B
to swing the election even though the 3% who prefer C like A more than B.
-- Andrew
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