Posted on 10/01/2010 9:31:58 AM PDT by smoothsailing
PU or SU.
I’m still waiting to hear from you how much you clear in a year. I really get sick of bullies.
NOYDB.
Put up? Here you go. Your words:
“Maybe she can get someone for personal finances, too. I just hope that if she becomes a Senator, she’ll have someone to help with that budgetary stuff that she just can’t get right!”
Gee, Mister silk stocking here doesn’t like being treated the same way he’s treating O’Donnell.
Pleased to meet your acquaintance, your excellency. Shall it be the rolls or the bentley this evening?
I am not under investigation for using campaign funds for personal expenses. And...I’ll reply in FReepmail with more.
Expected Value is a measure of an ucertain event and its associated payout. In this case, the uncertain event is the tossing of a coin. The payout is $5 or $0. The expected value is the probability-weighted average of all the outcomes.
Another term that might make more sense to you is the Certain Equivalent. In other words, how much money would it be worth to you to NOT play the game? If you were given the choice of getting a certain $2.50 or to flip the coin and take the result, what would you choose? What if you were offered $2.00 or the coin toss? $3.00? For the coin toss, the certain equivalent would be $2.50, because over repeated tossings of the coin, the average would be $2.50.
Look at post #4. This is the application of expected value. If Casle would vote with the GOP on 5 bills and stab them in the back on 45, while O'Donnell is good for voting 100% for the GOP but only has a small chance of winning, what is the better bet?
Of course, the counter argument is that the first vote to caucus is the only vote that counts, because the rest is moot if the GOP doesn't control the committees, but then O'Donnell wasn't the only candidate to flip a strong win into a strong lose that week. Dino Rossi also fell dramatically against Patty Murray, putting us 2 seats down, so Delaware voters did not cost us a sure majority in the Senate.
-PJ
Thanks for the post, PJ. I've thought all along that Ross was making a fundamentally sound analysis.
I asked the question of what is the better bet from the perspective of the likelihood of the winner voting one way or the other. That is the payout, but there are several uncertainties at play that could be used as the basis for the certain equivalent.
1. If you think that Castle will vote 10% with the GOP and 90% with the liberals, at what probability of O'Donnell winning are you willing to vote for her?
2. If you think that the probability of O'Donnell winning is 15%, what percentage of voting with conservatives would Castle have to promise in order for you to vote for him?
In other words, what is the balance point between uncertainty and payout that would make you indifferent between two choices? Is that point acceptable to you? That's why you want to know the expected value of an uncertain outcome.
-PJ
Nope.
All that bafflegab about somebody playing Monty Hall just cements the point. First off, note that Ross didn't go to such trouble (and was wrong). You're trying to add to the problem in ways that somehow make him right, that have nothing to do with the simple coin toss he used to introduce his discussion.
Ross was, statistically speaking, wrong. And yet by creating a false problem you have, I think, pegged exactly what Ross was trying to do.
The math of the Delaware electorate is quite simply ugly for a Republican state-wide candidate, and Ross didn't really address that. His only serious "data" referred to an "intensity gap," and his implication was that this intensity gap would make up for the significant numerical superiority of Democrats in that state.
You will note that Ross never actually bothered to do the math on that situation -- much less did he discuss ways by which O'Donnell could overcome the Democrats' natural advantage. No, he merely spun a web of hopes and assumptions about a presumed "intensity gap." Partly that's because Ross evidently just wants her to win, but has no concrete reasons for why she should.
Back to his example: if it's a coin-toss, it will be with a coin that gets Donkeys far more than half the time. In that case, the "Expected Value" of the coin toss favors the Democrat. That, sir, is how the statistics really work. (For a fuller explanation, see Bernoulli trial.)
From your link:
E[X] = 1*p + 0*(1-p) = p
If we restate the formula with a different payout for p and 1-p ($5 for heads and $0 for tails), it would look like this:
E[X] = $5*p + $0*(1-p) = $5p
If p = the probability of a coin toss landing heads, and we substitute .5 for the probability of a fair coin toss, then the expected value E[X] of the coin toss is $5*.5, or $2.50.
-PJ
Nice try, but now you're making the same error Ross made. For a fair coin, on a single toss you'd have a 50% chance of winning $5.
I don't even know what that means. If you won't accept the definitions from your own citations, then there is no point in continuing this discussion.
-PJ
I not only accept the definitions, I even know how they're used.
It's you and Mr. Ross who apparently do not.
Why does a Dem stumping for a Dem defy explanation?
Oh come on, lighten up! Click the link, have a laugh, it won’t kill you! :o)
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