Is Marilyn Vos Savant wrong on this probability question?


by CantorSet
Tags: marilyn, probability, savant
Hurkyl
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#37
Sep12-11, 02:03 AM
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Quote Quote by SW VandeCarr View Post
We are talking about the probability of one unique sequence regardless of what it appears to be.
The point is that while we are talking about one unique sequence, many people don't think of one unique sequence and mentally replace the specific sequence with the notion of a 'random' jumble of numbers.
Studiot
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#38
Sep12-11, 02:29 AM
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I am with Hurkyl on this one.

Chiro the way to check this is to simplify.

The argument is the same if there are only two throws and thirty six possible outcomes.

I roll the dice, without seeing them, and a friend reads them 2 minutes later.
The result therefore remains hidden for two minutes.

What you are asserting is that

before the roll of the dice
P(4,3)= P(1,1)
After the hidden roll of the dice
P(4,3) > P(1,1)


I assert that
Before the roll of the dice
during the roll of the dice
one minute after the roll of the dice
10 years after the roll of the dice

that

P(4,3) = P(1,1) = 1/36


To suggest that P(4,3) > P(1,1) would admit the idea of considering comparison this for all 36 outcomes and summing to greater than unity.

If you really want to get somplicated you can consider the difference between results (1,1) and (1,1) or (4,3) and (3,4)

go well
DIABEETUS
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#39
Sep23-11, 01:27 PM
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No, she's right, depending upon the dice thrower's behavior (believe it or not)...

Assuming that the dice thrower only accounts throws that result in one of those two sequences, then yes, the likelyhoods of either having occurred are the same.

However, assuming that the dice thrower allows for ANY result, then ANY mixed sequence could pop up, and the dice thrower would then declare THAT particular mixed sequence as the one to compare with the sequence of twenty 1's. This would obviously happen WAYYYY more often than the rolling a series of all 1's.
Fredrik
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Sep23-11, 02:35 PM
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Quote Quote by DIABEETUS View Post
No, she's right, depending upon the dice thrower's behavior (believe it or not)...

Assuming that the dice thrower only accounts throws that result in one of those two sequences, then yes, the likelyhoods of either having occurred are the same.

However, assuming that the dice thrower allows for ANY result, then ANY mixed sequence could pop up, and the dice thrower would then declare THAT particular mixed sequence as the one to compare with the sequence of twenty 1's. This would obviously happen WAYYYY more often than the rolling a series of all 1's.
I agree that it depends on the dice thrower's behavior. The fact that she doesn't mention that, and the fact that she mentions something else as the reason ("because the roll has already occurred"), makes me inclined to describe what she's saying as wrong.

Her claim: But letís say you tossed a die out of my view and then said that the results were one of the above. Which series is more likely to be the one you threw? Because the roll has already occurred, the answer is (b). Itís far more likely that the roll produced a mixed bunch of numbers than a series of 1ís.

She's right if one of the numbers I give her is the actual sequence, and the other is a number I just made up. In that case, 66234441536125563152 is more likely to be the sequence I rolled, and 11111111111111111111 is more likely to be the number I made up. The reason is not that "the roll has already occurred". That's a garbage explanation. The reason is that the die is a better random number generator than I am.

If I had used a random number generator that's better than the die, then it would have been more likely that 11111111111111111111 is the sequence I rolled. The crappier the random generator, the more likely it is to produce a constant sequence.
DIABEETUS
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#41
Sep23-11, 02:52 PM
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Quote Quote by Fredrik View Post
I agree that it depends on the dice thrower's behavior. The fact that she doesn't mention that, and the fact that she mentions something else as the reason ("because the roll has already occurred"), makes me inclined to describe what she's saying as wrong.

........

She's right if one of the numbers I give her is the actual sequence, and the other is a number I just made up. In that case, 66234441536125563152 is more likely to be the sequence I rolled, and 11111111111111111111 is more likely to be the number I made up. The reason is not that "the roll has already occurred". That's a garbage explanation. The reason is that the die is a better random number generator than I am.

If I had used a random number generator that's better than the die, then it would have been more likely that 11111111111111111111 is the sequence I rolled. The crappier the random generator, the more likely it is to produce a constant sequence.

Because, as you said, she never mentioned ANYTHING about assumptions about how the dice are rolled and behavior and so forth, then technically she's wrong only on the account that the inquiry is INCONCLUSIVE.... there's no way of determining the probabilities without making one of those requirements (assumptions) first. However, on a more practical level, I think its obvious that she implied to exclude such ridiculous assumptions such as: the dice thrower only accounts for rolls that produce those two particular sequences, and that the dice roller could be lying, and stuff like that. But I also do agree that her explanation is VERY, VERY vague and over-simplistic.
Bacle
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#42
Sep24-11, 12:00 AM
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Just to state that Marylin Idiot-Savant has the bad habit of posting problems without clearly explaining the "boundary conditions". It seems too, that her IQ credentials are suspect; I myself have checked in record books, but I have found no official records of her claims. It is disingenous for Idiot-Savant to claim she gives no importance to the IQ matter, and yet repeatedly posts while claimimg to have " The world's highest IQ", and it is arguably this claim that explains why most would care to read her column.
Fredrik
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#43
Sep24-11, 12:25 AM
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Quote Quote by Bacle View Post
It seems too, that her IQ credentials are suspect; I myself have checked in record books, but I have found no official records of her claims.
Her Wikipedia page explains this. Link.

Guinness retired the category of "Highest IQ" in 1990, after concluding that IQ tests are not reliable enough to designate a single world record holder.
...
"Miss Savant was given an old version of the Stanford-Binet (Terman & Merrill 1937), which did, indeed, use the antiquated formula of MA/CA ◊ 100. But in the test manual's norms, the Binet does not permit IQs to rise above 170 at any age, child or adult. And the authors of the old Binet stated: 'Beyond fifteen the mental ages are entirely artificial and are to be thought of as simply numerical scores.' (Terman & Merrill 1937).... the psychologist who came up with an IQ of 228 committed an extrapolation of a misconception, thereby violating almost every rule imaginable concerning the meaning of IQs."
Bacle
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#44
Sep24-11, 12:36 AM
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Fredrik:
Thanks for the link. What I think is dishonest about Idiot-Savant is her claiming to attribute no importance to IQ, yet including the claim "world's highest IQ" on most of her columns on 'Parade' magazine (at least last time I checked). If she made no such claim, it is likely, I believe, that there would be fewer people asking her questions.
DaveC426913
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Sep24-11, 08:25 PM
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Quote Quote by Bacle View Post
Fredrik:
Thanks for the link. What I think is dishonest about Idiot-Savant is her claiming to attribute no importance to IQ, yet including the claim "world's highest IQ" on most of her columns on 'Parade' magazine (at least last time I checked). If she made no such claim, it is likely, I believe, that there would be fewer people asking her questions.
What makes you assume she is the one making that claim?
Bacle
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#46
Sep24-11, 11:45 PM
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DaveC (sorry, my quoting function is disabled for some reason):

I don't know if she's the one that makes the claim, but I assume she

knows the claim is being made, and she must know that readership

increases as a result of that claim; people want to know what (allegedly)

amazingly-brilliant has to say, not what just Marilynn Q Anonymous has to say. So, she

either uses that claim to have a larger readership (and likely be paid more), or

allows that claim to be used in her name, and yet she claims that she assigns little

importance to IQ (let alone the fact that she does not mention the controversy behind

the truth of the claim ) . But it is precisely the fact that she (allegedly) has the world's

highest IQ that attracts readers, and she must know this. I think she should either drop

the claim of having highest IQ-- if she wants to say that she attributes no major

importance --or accept that it is this claim that attracts a good portion of her readers.

And there is too the issue that she often gives strong opinions on ethical issues. I would

just like here to be consistent in her position.
DaveC426913
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#47
Sep24-11, 11:48 PM
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Quote Quote by Bacle View Post
I think she should either drop the claim of having highest IQ...

I would just like here to be consistent in her position.
I ask again. What makes you think she's making this claim at all?

How can she "drop" something that someone else is saying? She's have to make an effort to make a public announcement that 'those claims people are making about me are false'.
Bacle
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#48
Sep25-11, 12:02 AM
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DaveC: I am assuming she has some control of how she is depicted, i.e., I am assuming

she has the ability to tell the paper that she does not want to be depicted as having

the world's highest IQ (it would also be reasonable for her to try to explain away the

controversy surrounding her claim). And , if she does not have that ability, she has the

choice of not writing for Parade at all (she is married to a wealthy heart-doctor, so

I doubt she needs the money). She does ofter pass ethical judgement on

letters sent to

her, so I usually like those passing judgement , who declare others as being unethical, or

describe others' actions as being unethical, to act ethically herself.
chiro
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#49
Sep25-11, 01:33 AM
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Quote Quote by Studiot View Post
I am with Hurkyl on this one.

Chiro the way to check this is to simplify.

The argument is the same if there are only two throws and thirty six possible outcomes.

I roll the dice, without seeing them, and a friend reads them 2 minutes later.
The result therefore remains hidden for two minutes.

What you are asserting is that

before the roll of the dice
P(4,3)= P(1,1)
After the hidden roll of the dice
P(4,3) > P(1,1)


I assert that
Before the roll of the dice
during the roll of the dice
one minute after the roll of the dice
10 years after the roll of the dice

that

P(4,3) = P(1,1) = 1/36


To suggest that P(4,3) > P(1,1) would admit the idea of considering comparison this for all 36 outcomes and summing to greater than unity.

If you really want to get somplicated you can consider the difference between results (1,1) and (1,1) or (4,3) and (3,4)

go well
I already said in a prior post in this thread that I agreed with Hurkyl's statement that every chance has the same probability of occuring.

When I was talking about confidence, I was talking about the "believability" of getting something like 20 1's in a row. While it is true that this has the same probability as any other sequence, the "believability" of this sequence coming from a pure random process is not as believable as getting a more "random-looking" sequence.

It was this very idea of believability that I thought that Marilyn Vos Savant was talking about in the last quote, and that is why I defended her take on it.

Again, just to clarify I agreed with Hurkyl that the probability of every possibility is the same.
Bacle
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#50
Sep25-11, 03:01 AM
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Sorry for my detour.

Ii wonder if we can formalize the argument by using maximum likelihoods given

the fixed parameters of a multinomial with probability =1/6, using "backward probability"

. instead of the forward type, i.e., Bayes vs. "Standard" .
chiro
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#51
Sep25-11, 03:03 AM
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[Double post]
Studiot
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#52
Sep25-11, 03:23 AM
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I was talking about the "believability" of getting something like 20 1's in a row.
But that stems from common experience which can lead the unwary to inappropriate conclusions.

Continuing my example,

Although P(4,3) = P(1,1) it also = P(3,4)

So there are two ways of throwing a three and a four, but only one way of throwing two ones.
So if we don't differentiate between (4,3) and (3,4) then obviously you are twice a likely to throw a three and a four as two ones.

Taking this further there are 30 ways to throw two different numbers as against 6 for throwing two the same.

So throwing two different numbers in any order is five times as likely as throwing two the same.
Phrak
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#53
Sep25-11, 04:12 AM
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"In theory, the results are equally likely. Both specify the number that must appear each time the die is rolled. (For example, the 10th number in the first series must be a 1. The 10th number in the second series must be a 3.) Each numberó1 through 6óhas the same chance of landing faceup."

"But letís say you tossed a die out of my view and then said that the results were one of the above. Which series is more likely to be the one you threw? Because the roll has already occurred, the answer is (b). Itís far more likely that the roll produced a mixed bunch of numbers than a series of 1ís."

Bait and switch. Paraghaph 2 has nothing to do with paragraph 1.
Studiot
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#54
Sep25-11, 04:20 AM
P: 5,462
But letís say you tossed a die out of my view and then said that the results were one of the above.
Agreed, good point.


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