[EM] Margins fails FBC, with 3 candidates

[MIKE OSSIPOFF]

I was saying that I determined that both wv and Margins can´t fail FBC, with 
3 candidates, if the B voters in my scenario vote A in 2nd place. That´s 
true, unless I made an error in the determination.

Well, with wv, if the B voters truncate, don´t vote for anyone but B, then 
the C voters don´t have to do anything other than rank sincerely to save B.

With that scenario, with Margins, I couldn´t find a contradiction between 
the inequalities that must be satisfied in order for the C1 voters to be 
unable to save B by ranking B equal to C, but able to save B by ranking B 
over C.

In fact, the Margins WDSC failure example that I posted a few days ago is 
also a Margins FBC failure example, because the C voters can´t save B by 
ranking B equal to C, but can save B by ranking B over C. They can get their 
best outcome, B, only by voting B over their favorite.

So Margins fails FBC, and has an FBC failure example with 3 candidates.

Unless I made an error, there´s no wv FBC failure example with 3 candidates.

Maybe wv doesn´t fail FBC, but it really seems to me that someone once sent 
to me an example in which wv failed FBC. Maybe that example wasn´t valid for 
some reason, and wv passes FBC. I don´t know. Can anyone post a 
demonstration that FBC doesn´t fail FBC, or an example in which wv fails 
FBC?

Of course, if it takes a fair amount of work finding a wv FBC failure 
example, then, for all practical purposes, it´s really as if wv passed FBC, 
even if it doesn´t.

Likewise PC and GSFC & SDSC. PC passes SFC & WDSC, but hasn´t been shown to 
pass or fail GSFC or SDSC.

The fact that these things haven´t been demonstated is very different from 
saying that there´s a situation in FBC or GSFC doesn´t give a clear answer 
about whether a method passes. What I´m saying is only that, in every 
situation tested so far, PC passes GSFC, and in every situation tested so 
far, all the wv methods pass FBC.

Some criterion compliance/noncompliance determinations are just difficult. 
That doesn´t mean there´s something wrong with the criteria. It would be 
unreasonable to expect all methods to conveniently and easily show a failure 
example, or be shown to not have a failure example. Expecially, if there 
isn´t a failure example, showing that there isn´t one could be quite 
difficult, even if possible, for some methods. And not just for my criteria.

Mike Ossipoff

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