[EM] Re: A majority rule definition based on the Smith set

[MIKE OSSIPOFF]

Kevin--

James had said:

>Definition of strong majority rule criterion: If voters cast ballots
>sincerely, and the voting method in question always chooses a member of
>the sincere Smith set, the method passes the strong majority rule
>criterion. Otherwise, the method fails the strong majority rule criterion.

You replied:

You don't need to suppose that ballots are cast sincerely, since there is
no way to fill out ballots such that they couldn't possibly be sincere.

I reply:

Sure there is. If a ballot is not sincere, then it couldn't possibly 
sincere. That's because it can't be both sincere and not sincere. For that 
reason, if you fill out a ballot in such a way that it is not sincere, then 
you've filled it out in such a way that (given your preferences) it couldn't 
possibly be sincere.

Of course if you meant "couldn't" to mean "couldn't, if you had different 
preferences", then it would indeed be difficult or impossible to ever fill 
out a ballot that couldn't possibly be sincere.

But none of this is relevant to James posting of my Smith Criterion, because 
it doesn't say "a ballot that couldn't possibly be sincere". It stipulates 
sincere voting, and I've posted a definition of sincere voting.

You continue:

If
a method fails Smith for any set of ballots, it must fail your criterion.

I reply:

You mean "Mike's criterion".

And yes, that criterion is the Smith Criterion. My preference version of the 
Smith Criterion.

But though that's an exact word-for-word rendition of my Smith Criterion, 
there have been more than one Smith Criterion defined. For instance, Blake's 
Smith Criterion (if it's as it was when I last checked it) explicitly 
stipulates that it applies only to rank methods. That makes it very 
different from my Smith Criterion, which has no such limitation of 
applicability.

Sometimes the Smith Criterion is stated in such a way that Plurality passes 
it.

So it wouldn't be true to say that all Smith Criterion versions are the 
same.

You continue:

So this criterion isn't different from the "Smith criterion."

I reply:

That depends on which Smith Criterion you're referring to. Yes, what James 
posted is a word-for-word rendition of my Smith Criterion. No, it is 
definitely different from Blake's Smith Criterion, if Blake's Smith 
Criterion is as it was when I last checked it.

Mike Ossipoff

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