[EM] More comments on approaches to preference

[MIKE OSSIPOFF]

Comments on approach 1a:

To clarify what I meant by approach 1a, it's as if the writer of a criterion 
failure example preceded his statement of his scenario or example with the 
following introductory  paragraph:

"If what is said in the following paragraph (I'll call it the scenario 
paragraph)  were a true statement, then, as you can judge for yourself, the 
premise of the criterion would be met, and, as I'll show, if [some 
particular voting system] is used, the requirement of the criterion is not 
met."

(here would follow the scenario paragraph)

What I've just said in the introductory  paragraph could be a true 
statement, even if part of what  is said in the scenario paragraph that 
follows it has imprecise meaning, unknown meaning, or no meaning. That's 
because in the quoted paragraph I said "_If_ what is said in the following 
paragraph were a true statement." So, whether everything in the scenario 
paragreaph  means anything and could be true, is irrelevant. The quoted 
paragraph merely talks about _if_ what follows were true.

So, if the scenario paragraph says that a majority of the voters prefer X to 
Y, and since WDSC says that if a majority prefer X to Y then WDSC's 
requirement must be met, and if, when that voting system is used in the 
situation described  in the scenario paragraph, the majority said in that 
paragraph to prefer X to Y have no way to meet WDSC's requirement, then it 
can be said that the method fails the criterion, even without a definition 
for "prefer",  for the reasons described above. Whatever "prefer" means, the 
scenario paragraph says those voters prefer X to Y, and WDSC says that if a 
majorilty prefer X to Y, then they must be able to meet WDSC's requirement.

Of course the writer of an example could actually word it by starting with a 
paragraph like that introductory  paragraph, to clarify the point that I'm 
making here. But of course the introductory paragraph isn't needed, because 
the things that it asserts, when true, are just as true without being 
asserted in that paragraph.

The preceding is intended to clarify approach 1a, which argues that 
well-defined criteria could use the word "prefer" even if it had imprecise 
meaning, unknown meaning, or no meaning.

Comments on approach 1b:

To show that "prefer" has a meaning, whether or not that meaning is 
precisely-defined, I'll use that word here:

Markus and some others may prefer that "prefer" not be used in definitions 
of criteria, but expressing that preference isn't the same as showing that 
such criteria are ambiguous, unclearly-defined, or not well-defined.

I define criteria in terms of preference because that avoids the problems 
that I've described that some criteria would otherwise have. But it would be 
great if someone posted definitions equivalent to my criteria, without using 
the word "prefer". The only legimate objections to the use of "prefer" in 
criterion definitions are aesthetic objections. I prefer the aesthetic 
objections to the problems that some criteria would have without the use of 
"prefer".

Markus, you keep saying that definitions equivalent to mine, but which don't 
use "prefer" are or should be possible. Can you or can you not post one?

Mike Ossipoff

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