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

[Peter Zbornik]

Hi Kevin,

I agree, FBC is a problem for all Condorcet elections and generalized
symmetric completion does not help.
I think something should be written about the FBC on Wikipedia (but
with an other name as someone (Jonathan Lundell?) proposed on this
list, in order to avoid "emotional" connotations with the word
"betrayal").
Thanks to the kind explanations and examples on this list I now get a
grip of the problem :o)
I am a bit slow starter (was like ten years since I studied maths.
I'd say that FBC (and LNH) is quite a big problem for Condorcet
methods, at least for someone (like me) who think sincere voting
should be the norm.
It seems that there is a risk, that Condorcet methods are reduced to
plurality-like methods due to voting strategies that exploit the fact
that FBC and LNH do not hold.

I think equal rankings is not a problem with generalized symmetric
completion, which basically means that you account for the empty
ballot by adding a null candidate.
If equalities resolve 0.5 vote then in the pairwise comparison the
votes always sum up to 100% of the votes cast, which I think is nice.
Without the null candidate ("none of the above") neither margins nor
winning votes sum up to 100% for truncated ballots.
I do not understand when and why equalities should be a problem for
any method using generalized symmetric completion.

I think generalized symmetrical completion is a good thing, basically
it unifies margins and winning votes, makes the methods less
complicated, accomodates the blank vote and satisfies Woodall's
plurality criterion.

But as Juho and Kristoffer mentioned and I later formalized, there are
other ways to introduce cut-offs externally.

Basically, generalized symmetrical completion is just a fancy name for
making the (partially) blank vote count by including the null
candidate ("none of the above") in the election system.

Best regards
Peter Zborník



On Tue, Jun 7, 2011 at 2:43 AM, Kevin Venzke <stepjak at yahoo.fr> wrote:
> Hi Peter,
>
> This is how I look for (and usually define) FBC failures: Lowering a
> candidate from the top position should not move the win from somebody
> not ranked top to somebody who was ranked top. (It could be the lowered
> candidate, but that's a bigger concern.)
>
> I don't know about your method, but with the standard symmetrically-
> completed Schulze etc. you have the theoretical conflict that symmetric-
> completion wants to make it less useful to use equal ranking ("tell a
> half-truth") while what FBC is saying you won't have to do any worse than
> tell a half-truth, regarding your true favorite. So if SC succeeds in
> dissuading people from casting equal rankings, the only way it could
> satisfy FBC is by offering an even better guarantee.
>
> I don't know about your modified criteria, either, but standard weak FBC
> is very hard to satisfy.
>
> Kevin Venzke
>
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