[EM] Citation for immunity to strategic voting?

Jobst Heitzig heitzig-j at web.de
Tue Sep 13 00:45:12 PDT 2005

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
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