[EM] Challenge2 - give an example where MFBC is violated for Condorcet methods

[Jameson Quinn]

That I'm aware of, favorite betrayal is almost always a tool to help someone
besides your favorite. Think of plurality: you vote the "lesser evil".

Only in a non-monotonic method could it be otherwise. The only non-monotonic
methods worth even mentioning are runoff methods.

Jameson

2011/6/6 Peter Zbornik <pzbornik at gmail.com>

> Dear all,
>
> two clarifications.
> With "favorite" i mean the "sincere favorite" below.
>
> A correction of an unfinished sentence (addition in CAPITALS):
> MFBC and MSFBC say basically, that if some of the voters who have A as
> a first preference (i.e. vote A>(OR =)...[the other candidates]) in an
> election where A does not win, change preferences between A and the
> other candidates so, that A is less prefered than before (example  A>B
> turns to B>A, A=B turns to B>A, A>B turns to A=B) and the preference
> between the other candidates (excluding A) do not change (i.e. it is
> not allowed for B>C  to turn B=C or C>B) THEN CANDIDATE A CANNOT WIN
> EITHER.
>
> Basically, you cannot make your losing (sincere) favorite win by
> ranking him lower, if he didn't win before.
>
> Best regards
> Peter Zborník
>
> On Mon, Jun 6, 2011 at 8:42 PM, Peter Zbornik <pzbornik at gmail.com> wrote:
> > Dear Markus Schulze and all others,
> >
> > Thanks for the example.
> > I messed things up a bit with a bad definition, my appologies.
> > What I would like to see was a violation of a weaker criterion (that
> > is clear from the example specification).
> >
> > What I would like then to see a proof of violation, is a less general
> > l variant of FBC (changes to FBC in capitals):
> > 1. MFBC: A voting method satisfies the Modified Favorite Betrayal
> > Criterion (MFBC) if there do not exist situations where a voter is
> > only able to obtain A WIN FOR HIS OR HER FAVORITE by insincerely
> > listing another candidate ahead of his or her sincere favorite WHILE
> > THE PREFERENCES BETWEEN THE OTHER CANDIDATES REMAIN UNCHANGED.
> >
> > and conversly
> >
> > 2. MSFBC: A voting method satisfies the Modified Strong Favorite
> > Betrayal Criterion (SFBC) if there do not exist situations where a
> > voter is only able to obtain a A WIN FOR HIS OR HER FAVORITE by
> > insincerely listing another candidate ahead of or equal to his or her
> > sincere favorite WHILE THE PREFERENCES BETWEEN THE OTHER CANDIDATES
> > REMAIN UNCHANGED.
> >
> > MFBC and MSFBC say basically, that if some of the voters who have A as
> > a first preference (i.e. vote A>...[the other candidates]) in an
> > election where A does not win, change preferences between A and the
> > other candidates so, that A is less prefered than before (example  A>B
> > turns to B>A, A=B turns to B>A, A>B turns to A=B) and the preferences
> > between the other candidates (excluding A) do not change (i.e. it is
> > not allowed for B>C  to turn B=C or C>B).
> >
> > I wanted to say (but didn't do very clearly) is that MFBC and MSFBC
> > hold for all Condorcet (Shulze reference) elections.
> >
> > Sorry for that and thanks for the example.
> >
> > So I lost challenge one due to a messy specification, that counts too.
> >
> > So challenge 2 is to prove MFBC and MSFBC are violated for Condorcet
> > elections with or without generalized symmetric completion.
> >
> > Maybe the result that MFBC and MSFBC hold is trivial, or stems from
> > some other result, like consistency.
> >
> > Best regards
> > Peter Zborník
> >
> > On Mon, Jun 6, 2011 at 7:30 PM, Markus Schulze
> > <markus.schulze at alumni.tu-berlin.de> wrote:
> >>
> http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-May/015945.html
> >>
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