Calc. Smith set

[Mike Ossipoff]

Bruce Anderson writes:
> 
> On Apr 19,  1:07am, Mike Ossipoff wrote:
> > If "Any alternative is a member of the Smith set if it beats or
> > ties a member of the Smith set" is vague, then could you tell us
> > more than 1 meaning that it could have. If not, then it's you who
> > are being vague.
> >-- End of excerpt from Mike Ossipoff
> 
> As a declarative sentence, the quote above is not vague.  As a declarative 
> sentence, it's accurate, precise, and concise -- I couldn't have said it better 
> myself.  However, as an instruction in a procedure, it's vague -- it doesn't 
> clearly indicate what action the procedure should take at this point.  To 
> repeat, the context is:
> 

That sentence wassn't represented as an instruction. An instruction
immediatelly followed my list of numbered paragraphs. I said something
to the effect of: "So admit to the Smith alternatives that qualiffy
according to the above rules until there aren't any that qualify."


> On Apr 16,  4:55am, Mike Ossipoff wrote:
> > Subject: Smith procedure briefly stated
> > I'd like to state, more briefly & clearly, the procedure that I suggested
> > for determining the Smith set:
> > 
> > 1. Order the alternatives according to how many alternatives they're
> > beaten by.
> > 
> > 2. The alternative beaten by fewest alternatives is a member of the Smith set
> > (as are any several that tie for that distinction).
> > 
> > 3. Any alternative is a member of the Smith set if it beats or ties
> > a member of the Smith set, or if it's beaten by no more alternatives
> > than is a member of the Smith set.
> > 
> > So admit alternatives to the Smith set according to these rules till
> > there are no more that qualify.
> >-- End of excerpt from Mike Ossipoff
> 
> The potential problem here is as follows.  Candidate i might not beat or tie any 
> member of the current Smith set, so i would not be admitted.  But then the next 
> candidate in the order, say j, might be admitted, and i might beat j.  So a 
> proper algorithm might have to go back and reconsider all previously rejected 

I di> candidates every time a new candidate was admitted.  I think that this is quite 
> a lot to have to read into the "state[ed] more briefly & clearly" procedure 
> above, which is why I called it vague.
> 
I didn't say that the instruction that you quoted was an "algorithm",
so we needn't judge whether or not it is a "proper algorithm".

It isn't clear what you mean by the vague phrase "a lot to have to
read into..." Don't read into it anything other than what it says.
My listed numbered rules clearly & unequivocally state what qualifies
an alternative for the Smith set. Immediately after those numbered rules
I say to admit alternatives to the Smith set according to those rules
till there are no more than qualify.

There's nothing to read in. Just follow the instructions. At the later
time when alternative i qualifies, the rules as I stated them 
call for admitting i to the Smith set--nothing to read in. You know
that as well as I do, Bruce.

And no, the rules that you quoted aren't an algorithm because they
don't tell the order in which to do things, because the order doesn't
matter, except that some orders are speedier than others. So I later
posted to this list an instruction list that _does_ specify the order
for doing things, and which does qualify as an "algorithm", even though
it's written in English, the language that I prefer for discussion
in this list.


> On Apr 19,  1:07am, Mike Ossipoff wrote:
> > You said that "Any alternative is a member of the Smith set if it's
> > beaten by no more alternatives than is some member of the Smith set"
> > is "...a tautology at best". What does that mean? 
> >-- End of excerpt from Mike Ossipoff
> 
> Since any alternative is beaten by no more alternatives than it (itself) is 
> beaten by, this statement seems to me to be logically equivalent to the 
> statement that "any alternative is a member of the Smith set if it's
> a member of the Smith set".  That's a pretty good example of a tautology.

Yes, but it's your tautology, not mine, since it's you who said that.

Sure, once an alternative is already established as a member to the
Smith set, someone whose only purpose is to waste our time could say
"Since alternative X is a member of the Smith set, and since X isn't
beaten by more alternatives than X, therefore X is a member of the
Smith set". And the statement would be true, but I don't know what
idiot would spend time demonstrating that X is a member of the
Smith set after that's already established. After X has been
declared as a member of the Smith set, I don't mind if you demonstrate
that it is, because it isn't beaten by more alternatives than itself.
But it would be pretty stupid to spend time admiting to the Smith
set alternatives already known to be in it, and I didn't say to
do that.

The statement that an alternative is a member of the Smith set
if it isn't beaten by more alternatives than some member of the
Smith set is a useful way of admitting new alternatives to the
Smith set. In the rules written by me, which you quoted &
disagreed with, I could have said, after the numbered paragraphs
, that one should only admit to the Smith set alternatives which
have not already been admitted to it, but it didn't seem necessary
since only an idiot would spend time repeatedly admitting the same
alternative to the Smith set because it isn't beaten by more alternatives
than itself.

Besides, it seems to me that one _can't_ admit to the Smith set
an alternative that's already in it, because admiting something
implies that it hasn't been admitted there yet, unless it has
been admited & then expelled, in which case it could then be
re-admitted. I couldn't admit you to a movie theater if you're
already in the movie theater, Bruce.

Only someone whose only purpose is to waste our time could raise
such an objection.

Do we have to keep debating the prettiest way to word the instructions
for determining the Smith set?

Anyway, in the algorithm that I posted aferwards, since it's intended
as an instruction that tells exactly what to do at each point in the
procedure, I do make it clear that alternatives not previously
known to be in the Smith set are the ones to be tested for membership.
Because that's intended as an algorithm.

> 
> Bruce
> 
> 
> 
> 
> .-
> 


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