[EM] Should we say a criterion implicitly doesnt apply to a method?

[MIKE OSSIPOFF]

There could be some disagreement over whether a certain kind of criterion 
applies to Plurality. Such as this defective Condorcet Criterion definition, 
which I call a "ham-sandwich" criterion because earlier I said that a ham 
sandwich would pass it if it's application weren't limited to voting 
systems.

For all candidates Y, if more voters rank X over Y than rank Y over X, then 
X should win.

[end of Ham-Sandwich  CC definition]

My position yesterday was that Plurality passes that criterion, 
meaninglessly. I said that because it seemed unwarranted to customize the 
meaning of passing a criterion just to protect that defective criterion from 
giving a meaningless answer. I felt that to do so would be to give 
unwarranted recognition to ham-sandwich criteria.

Of course it could be argued that avoiding a meaningless answer is 
desirable, and that since ham-sandwich criteria are to be found written in 
many places, it's worth having definitions that avoid having to say that 
Plurality (meaninglessly) passes them.

So how about this approach?:

This first statement goes without saying, but I'll say it anyway:

A criterion explicitly doesn't apply to a method or class of methods if that 
criterion's definition explicitly says that the cariterion doesn't apply to 
that method or class of methods.

A criterion implicitly doesn't apply to a method  if it can be shown that no 
example with that method can comply with that criterion's premise, and if 
that criterion's definition doesn't explicitly say that the criterion 
doesn't apply to that method or to some class of methods to which that 
method belongs.

If a criterion explicitly or implicitly doesn't apply to a method, then that 
method neither passes nor fails that criterion.

[end of suggested definitions about criteria explicitly and implicitly not 
applyng to methods]

Mike Ossipoff

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