Mathematical utility expectation maximization in Approval

[MIKE OSSIPOFF]

I'd said:

> > Different wording, same thing. If i & j are the 2 highest votegetters,
> > and there's a tie for 1st place, then it's between them. If they
> > aren't the 2 highest votegeters, and there's a tie for 1st place, then
> > it isn't between them.
>
>They aren't the same.

(Ignoring ties with more than 2 candidates)

Would you post an example in which 2 candidates are the 2 biggest
votegetters in the election, and there's a tie for 1st place, and
those 2 candidates aren't the ones that are tied for 1st place?

Or would you post an example in which 2 candidates are not the 2
biggests votegetters in the election, and there's a tie for 1st
place, and those 2 candidates are the ones that are tied for 1st
place?


>It's easy to think they'd be proportional

...that what's proportional? I'm saying that iff 2 candidates are
the 2 biggest votegetters in the election, then, if there's a 2-
candidate tie, it's between those 2 candidates.

The fact that you thought I was saying something was proportional
suggests that you misunderstood what I said. My statement in the
paragraph before this one is what I'm saying.


>but keep
>in mind Bayes' Theorem for conditional probabilities.

Ok, so then you're saying that Bayes' Theorem means that
2 candidates can be the biggest votegetters in an election, and
not be the ones who are in a tie, when there's a tie? Or that 2
candidates can not be the biggest votegetters in an election, and
still be the two who are tied when there's a tie.

Instead of wading through the definitions and arguments that follow,
for the purpose of finding the part that expresses the misunderstanding,
I'll just repeat my request for the examples that I asked you for
above.

[definitions & arguments deleted]
>Since Pt is constant for all candidate pairs, and Pij|t is different for
>each
>pair of candidates, then the relationship between Mike's and Bart's
>definition isn't a proportional one.

I didn't say that the relationship between Bart's definition and my
definition was a proportional one. I said that both definitions
define the same probability. They're 2 wordings of the same
definition.

>
>While Mike has matched the correct definition to the notation he chose,
>I think Bart's conditional probability is better for determining strategy.

Both definitions, when used with the strategic value calculations
that I described, and that Weber and Merrill & others have described,
give identical results. Bart's definition and mine determine the same
strategy.

Both Pij definitions are wordings for the same probabilities, Richard.
Unless you can post the examples that I asked for above.

>The probability that A and B are front runners isn't the probability that
>your vote will decide between them.

Would you like to post a quote of where I said it was?

The probability that A & B are frontrunners in the election's count
is the probability that if there are any 2 that your vote can decide
between, it will be them.

>I suspect Mike's strategy as
>modified by Bart is mathematically equivalent to mine, which I defined
>in terms of differential probabilities. I didn't give a formal equation in 
>my earlier post but what I have in mind is something like

Bart didn't modify my strategy. My strategy isn't mine. Weber and
Merrill had described it before I posted here about it. Bart's
definition of Pij is the same as mine--a different wording of the
same definition.

You say that you didn't give a formal equation, and that what you
have in mind is something like...

Perhaps you should have a formal equation, a clearly-stated procedure
such as the one that I posted, and perhaps you should have a better
idea of what your procedure is, before finding fault with my
definitions. If you don't know what your procedure is, are you sure
that you couldn't be a little premature & presumptuous when finding
fault with my procedure and its definitions?

>Hopefully my differential method and Bart's method will prove
>equivalent.

Bart's method is the same as my method, which is the
same as Weber's method and Merrill's method.

Bart's method, if you mean Bart's definition of Pij, when used with
Weber's & Merrill's procedure, which I posted here, is also my
method, Weber's method, and Merrill's method. I fully admit that
Weber & Merrill wrote about it first.

Mike Ossipoff

_________________________________________________________________
Get your FREE download of MSN Explorer at http://explorer.msn.com