[EM] Citation for immunity to strategic voting?

stephane.rouillon at sympatico.ca stephane.rouillon at sympatico.ca
Tue Sep 13 07:07:06 PDT 2005

Sorry if I was not clear enough.
All the comments I made were relevant only
to truncation strategies...
As you just showed, order reversal (burying for
the intimates) can get even a strong Condorcet winner.

Two analysis could help go further in that direction:
- Is there some level that makes a Condorcet winner
immune to burying strategy ?
- What is the method that brings the less esperance 
(gain probability) when using truncation or burying strategies?

My guess would be that a stronger Condorcet winner (66% of
winning votes) is immune to any strategy. Please feel free
to show I am wrong... For the second analysis, I have not
found any track toward a result yet.

PS: Mike Ossipoff provides some proof for the 50% barrier
immunity against truncation on some website.
For the 66%, it is the result of my own analysis, and I do not
have a formal proof.  I do not know of any book containing
such information.  The last claim about no method protecting
a weak Condorcet winner is obvious to me in the sense that
any change of mind can bring different majorities, both leading
to a legitimate winner. Again, I have no formal proof.
Sorry for the lack of thourougness.

> De: Andrew Myers <andru at cs.cornell.edu>
> Date: 2005/09/13 mar. AM 12:19:55 GMT-04:00
> À: Stephane Rouillon <stephane.rouillon at sympatico.ca>
> Cc: election-methods-electorama.com at electorama.com
> Objet: Re: [EM] Citation for immunity to strategic voting?
> On Sun, Sep 11, 2005 at 04:47:19PM -0400, Andrew Myers wrote:
> > On Mon, Sep 05, 2005 at 05:55:01PM -0400, Stephane Rouillon wrote:
> > > Actually as many people will tell you,
> > > this claim is wrong.
> > > 
> > > I see that Rob already gave you a counter example.
> > > 
> > > Maybe you would like to know that using winning vote as
> > > criteria to make pairwise comparison instead of margins
> > > can make your claim true for strong Condorcet winners
> > > (ones which have a more than 50% majority against every
> > > other candidate).
> 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.
> -- Andrew

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