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

[Kristofer Munsterhjelm]

Peter Zbornik wrote:
> 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 burial is a more likely problem than FBC. As has been mentioned 
before, FBC is a problem when there is a cycle, but burial is a problem 
in certain cases where there's a Condorcet winner (depends on the 
magnitude and coordination of the strategy). Perhaps FBC is a greater 
problem than burial in the Condorcet-IRV hybrids, though.

As for LNHarm, I'd say that breaking LNHarm is reasonable. If you vote 
"your side extremist > centrist > other side extremist", then it's 
reasonable that the centrist vote harms your extremist because he's 
better for society as a whole. Now, there's a chance that that would 
make true extremists simply truncate after "your side extremist", but 
then you lose nothing with respect to having a method that passes LNHarm.