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

[Peter Zbornik]

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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