[EM] Many things wrong with Richard's claims

[MIKE OSSIPOFF]

Richard wrote:
> > Still accepting Richard's notion of how Bart's Pij definition is worded
> > (I'll get to that later), I took it to have a different meaning.
> > To me it meant "In the event that there should be a tie, it would be
> > between i & j."
> >
> > In other words, I took it as a general statement, one that doesn't
> > become paradoxical and meaningless nonsense if there's no tie.
> >
> > That's why, yesterday I worded it: "If there is/were a tie, it is/would
> > be between i & j.  (use the verb before the "/" if there is a tie, and
> > the verb after the "/" if there isn't a tie).
>
>The subjunctive form doesn't help here. That form is used to describe
>things outside the universe of discourse.

...and you're saying that the universe of discourse has to be the
outcome of that one election.

>So you can't really apply
>logical analysis to a subjunctive statement.

Not if there's an agreed-upon rule that you can't, or that logic
has to speak only about one particular event. Maybe you're saying
that a statement about elections in general is forbidden by logic.
We needn't get into that, because Bart's quote of Merrill's Pij
definition was the original issue. I don't suppose it matters,
for that purpose, about the subjunctive in logic.

> >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."
>
>Oddly enough, I'm really not interested in any Pij as defined
>by the second statement, if we understand the "given" phrase
>to belong to the second half.

But that's the interpretation that you were talking about, when
justifying your claim that Bart's definition of Pij, and my definition
of it, can define different probabilities.

>If you are trying to say that the probability of the conditional is
>not equal to the conditional probability, you'll get no argument
>from me. But the probability of the conditional is irrelevant to
>strategy, as far as I can tell.

If Bart had written it as the probability of the conditional, the use
of the Pij that would define would lead to the same Approval strategies
as those that the correct interpretation of Bart's definition
leads to. Maybe you meant that it's irrelevant to strategy which
of two ways the definition is worded.


>
> >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.
>
>Sounds more like you misread what I'm saying. I've been saying
>all along that we should use the conditional probability.

Yes, if you've  been saying that, I certainly did miss it.

Misread what you were saying? When I said that Bart's definition of
Pij is just a different wording of my definition of it, that both
definitions define the same probability, you said that they don't
necessarily define the same probability.

As I said, the bottom line is that, if Bart's actual wording is taken
literally, then you were mistaken in your claim that Bart's definition
and mine aren't merely different wordings of the same definition.
I repeat--you were mistaken. That mistaken claim was the issue that
was the initial subject of this discussion.

>
> >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.
>
>I'm unaware of any general controversy over conditional
>probability. It's used successfully in a lot of fields. And it's
>a natural tool for discussing strategy based on statistical
>information.

I didn't mean a general controversy about all uses of conditional
probability. I was referring to the controversy about the application
of Bayes' ideas. But I'm not saying this issue here has anything to
do with Bayes. It's just that a mis-statement was made, to the effect
that Bart's & my Pij definitions aren't just different wordings of
the same definition.

Mike Ossipoff



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