[EM] Part 2 of Many things wrong with Richard's claims

[MIKE OSSIPOFF]

This discussion began when Richard said that it isn't true that my
Pij definition and Bart's have the same meaning.

But, even if we accept Richard's apparent notion about Bart's wording,
and the conclusions that Richard draws from that notion, the only
difference between my Pij definition and Bart's is when there's no
tie--a situation of no interest for strategy. Bart's Pij and mine
would result in the same Approval strategy.

For that reason alone, Richard's claim that Bart's definition
and mine are the same is questionable. They (maybe) differ in a way that's 
academic, but, for determining one's voting strategy, they're the
same.

They differ in that one of them is the one that Richard found those
paradoxical conclusions with. And which one was that? Bart's.

So now, since that's the only difference, which one does Richard say
is the better of the two? The one with which he found his paradoxical
conclusions.

But now let's take a closer look at what Bart actually said:

"Pij is the probability, given that there's a tie, that the tie is
between i & j."

Richard seems to believe that Bart said:

"Pij is the probability that, given a tie, it's between i & j."

But that isn't the same thing. What follows "that" is what the
probability is about. The "given..." clause is not in the "that..."
clause. The "given..." clause doesn't refer to what the probability
is the probability of. The "given..." clause is part of the sentence's
main clause. It modifies the statement about Pij being the probability
that...

It modifies the verb "is" in "Pij is the probability that..."

In other words, Bart's wording means this:

If there's a tie, then Pij is the probability that it's between i & j."

Certainly Richard's misreading of Bart's wording is understandable.

When Bart's wording is taken literally, none of the alleged problems
that Richard brought up can exist.

Now, one more thing. Aside from everything that I've said so far,
we've been using the present tense when stating Bart's definition.
But, even if Bart's definition were worded as Richard mistakenly
believed, wouldn't it mean this?:

"Pij is the probability that if there will be a tie, it will be between
i & j."

Not much difference, true. But it makes Richard's objection less
convincing. No one can say that there won't be a tie (whereas, if
we speak of it in the present, someone can point out that there
isn't a tie). And the future tense is more proper for that definition.

So the convincingness of Richard's objection is further reduced when
the definition is stated in the future tense, and there's still less
reason to accept the absurd contradiction that Richard uses that
objection to justify.

The application of ideas about conditional probability has been
controversial. I didn't expect that I'd enounter that here, but I
guess it was inevitable.

Mike Ossipoff

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