[EM] Should we say a criterion implicitly doesnt apply to a method?
nkklrp at hotmail.com
Mon May 9 22:51:03 PDT 2005
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
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
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]
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