[EM] A definition for your criteria system

Michael Ossipoff mikeo2106 at msn.com
Wed Mar 21 11:01:12 PDT 2007

Chris quoted my definition of FARCS:

>Michael Ossipoff wrote:
> > FARCS stands for Fictitiously Assumed Rankings Criteria System.
> >
> > Because no FARCS advocate on EM has defined FARCS, I’m going to define
> > it in this posting.
> >
> > Definition of FARCS, consisting of instructions for writing a
> > criterion failure example in the FARCS system:
> >
> > 1. Specify a set of voter rankings that complies with the criterion’s
> > premise’s stipulations about rankings.
> >
> > 2. Specify each voter’s actual vote (using the actual balloting system
> > of the method being tested) in such a way that s/he doesn’t vote X
> > over Y when your ranking for that voter ranks Y over X.
> >
> > 3. If you can thereby specify actual votes that give a result that
> > doesn’t comply with the criterion’s requirement, then you have written
> > a successful failure example.
> >
> > [end of FARCS definition]
>Regarding (1), I'm not sure exactly what "the criterion’s premise’s
>stipulations about rankings" means.

I reply:

A criterion’s premise is the part that states the conditions under which the 
criterion applies. It’s the “if” part of the criterion. (The “,then…should…” 
part of the criterion is the criterion’s “requirement”).

If a criterion is intended to be used with FARCS, then its stipulations 
about voting will be about rankings.

Chris continues:

>Your point (2) is inadequate, because it could be that the voter intends
>to strictly rank some candidates while the actual
>used method allows but not compels the voter to equal-rank them. By this
>definition it could be possible to create a
>"criterion failure example" by having "actual votes" with equal-ranking
>where the voter intended strict ranking, even though
>the the used method would have allowed the intended strict ranking.

Good point. Condorcet’s method would fail Condorcet’s Criterion, would it 

So, how would you avoid that? You’d change (2) so that the failure-example 
writer isn’t allowed to modify the “intended” rankings if the tested method 
is a rank method. Of course if the tested method is a nonrank method, then 
the “intended” ballots must be modified, because the two balloting systems 
don’t match. Then, the  failure example writer is free to modify the 
intended rankings in any way that is consistent with the intended rankings, 
and may contrive a modification that results in failure of the criterion.

And that’s because, for the nonrank method, the balloting systems don’t 
match. Because, if the method is a rank method, the balloting systems match, 
it isn’t necessary to modify the intended ballots. And you say we shouldn’t 
let the example writer do so, because you want to make Condorcet meet 
Condorcet’s Critrerion.

Do you see the contrived nature of that choice? Do you see how  FARCS favors 
a method whose balloting system matches FARCS’ privileged balloting system?

Thanks for pointing that out.

Mike Ossipoff

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