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Toby
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Registered: Jul 2000
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quote:
Originally posted by KRamsauer
Drown? You're getting your examples mixed up.

No, you just seem to be missing the forest for the trees.

quote:
Analyzing either problem (river or monty) correctly will always yield solutions at least as good as someone who looks at it with a gut feeling.

The catch is that the correct way to analyze the two problems in reality _is_ with a gut feeling and not with math. Or to quote another passage from the book where those quotes are derived, "You may think you have probability going for you when you follow the answer in her column, but there's the psychological factor to consider."

10-17-2002 09:47 PM

KRamsauer
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Registered: Apr 2002
Location: Houston, TX
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quote:
Originally posted by Toby
The only time that the odds are 2 out of 3 is if the host is required to offer the switch _all_the_time_ (which was not the case on LMAD) and has foreknowledge of the location of the prize. Again, you're letting raw statistics fool you into a conclusion not supported by reality. I don't need a stat prof. I used to watch the show. Again, the flaw is trying to impose statistics on reality. It just doesn't work that way.

Hm... The more I've thought about it, I've realized you can relax the "always offer the switch" assumption. So long as the host doesn't know where the prize is, it is still best to always switch when given the chance. In other words, if the choice of doors to reveal and the choice to reveal that door are made by seperate entities, it's still best to always switch. Only when the choice to allow a switch and then the choice of door to reveal covary does the strategy of switching not necessarily beat other strategies.
So even if Monty made the choice to allow a switch, so long as he didn't know what door contained the answer (he'd ask for an empty door to be revealed, not ask for a given door to be revealed), it still pays to switch every time given the chance. So in this light, my original formulation still holds if I don't know what door has the prize.
Conversely, if I know where the prize is, and I don't have a choice of whether or not to offer you a switch, again it always pays to switch. The solution is more powerful than I lead on, I guess.

Last edited by KRamsauer on 10-17-2002 at 09:58 PM

10-17-2002 09:52 PM

Toby
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quote:
Originally posted by KRamsauer
Hm.... So you're saying we can say nothing about advantageous strategies because they don't work always? Seems like you're demonstrating a great example of one well documented irrationality in human thought that values things lost much too highly, relative to things won. For instance, if a stock is overvalued at $70 a share, someone who bought at 50 is more likely to sell than someone who bought at $90 even though they both have the exact same value stock at the moment. Because it feels bad to admit you lost something, you take an irrational approach.

This assumes (incorrectly) that treating people like individuals and getting to know them instead of a statistic isn't the most advantageous strategy of all, and hence the most rational.

10-17-2002 09:54 PM

KRamsauer
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Registered: Apr 2002
Location: Houston, TX
Posts: 734

quote:
Originally posted by Toby
No, you just seem to be missing the forest for the trees.[B]The catch is that the correct way to analyze the two problems in reality _is_ with a gut feeling and not with math. Or to quote another passage from the book where those quotes are derived, "You may think you have probability going for you when you follow the answer in her column, but there's the psychological factor to consider."

Hm... I prefer to go with numbers and science. Afterall, science dictated the sun-centric solar system(and so much else). Guts told us we were the center. And there are many other examples. Science, done right, is the way to move forward. Science, done wrong, is worse than no science at all because it adds an air of authenticity to garbage. Someone who approaches the three-door problem witll be wrong more often than someone who uses his brain. I am comfortable with that knowing I am in the latter group. Won't you join me?

10-17-2002 09:55 PM

KRamsauer
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Registered: Apr 2002
Location: Houston, TX
Posts: 734

quote:
Originally posted by Toby
This assumes (incorrectly) that treating people like individuals and getting to know them instead of a statistic isn't the most advantageous strategy of all, and hence the most rational.

Depends on the situation. For politicians, knowing the aggregate needs of the people is the most important issue. Using specific cases (Horton, for example) is both bad policy and bad science.

10-17-2002 09:57 PM

Toby
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Registered: Jul 2000
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quote:
Originally posted by KRamsauer
Hm... The more I've thought about it, I've realized you can relax the "always offer the switch" assumption. So long as the host doesn't know where the prize is, it is still best to always switch when given the chance. In other words, if the choice of doors to reveal and the choice to reveal that door are made by seperate entities, it's still best to always switch. Only when the choice to allow a switch and then the choice of door to reveal covary does the strategy of not switching not necessarily beat other strategies.
So even if Monty made the choice to allow a switch, so long as he didn't know what door contained the answer (he'd ask for an empty door to be revealed, not ask for a given door to be revealed), it still pays to switch every time given the chance. So in this light, my original formulation still holds if I don't know what door has the prize.

No, it doesn't hold because it's not how the show worked, and _someone_ still knows which is correct.

quote:
Conversely, if I know where the prize is, and I don't have a choice of whether or not to offer you a switch, again it always pays to switch. The solution is more powerful than I lead on, I guess.

LOL...mental masturbation of that sort makes Baby Jesus cry.

10-17-2002 09:57 PM

KRamsauer
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Registered: Apr 2002
Location: Houston, TX
Posts: 734

quote:
Originally posted by Toby
No, it doesn't hold because it's not how the show worked, and _someone_ still knows which is correct.

Doesn't matter if someone knows. As long as that person isn't the person making the decision to offer the choice to switch, the solution holds. Think through it, you'll see.

Please note I changed the passage you quoted. I made a slight mistake but I think got the point.

quote:
LOL...mental masturbation of that sort makes Baby Jesus cry.

WHAT?!?

10-17-2002 09:59 PM

Toby
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Registered: Jul 2000
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Posts: 3034

quote:
Originally posted by KRamsauer
Hm... I prefer to go with numbers and science.

Are you married? What do you answer if your wife asks you if those jeans make her look fat, and they do?

quote:
Afterall, science dictated the sun-centric solar system(and so much else). Guts told us we were the center. And there are many other examples. Science, done right, is the way to move forward. Science, done wrong, is worse than no science at all because it adds an air of authenticity to garbage.

The point is that you're doing science wrong by assuming that you can predict an individual case from the general.

quote:
Someone who approaches the three-door problem witll be wrong more often than someone who uses his brain. I am comfortable with that knowing I am in the latter group. Won't you join me?

No, because in reality the three door problem is a psychological one. It's only in the fantasy world of certain stat books that it becomes a mathematical one. Personally, I find it the height of humor that were someone to only see this conversation they might assume that I'm some sort of bleeding heart.

10-17-2002 10:03 PM

KRamsauer
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Registered: Apr 2002
Location: Houston, TX
Posts: 734

quote:
Originally posted by Toby
Are you married? What do you answer if your wife asks you if those jeans make her look fat, and they do?[B]The point is that you're doing science wrong by assuming that you can predict an individual case from the general.[B]No, because in reality the three door problem is a psychological one. It's only in the fantasy world of certain stat books that it becomes a mathematical one. Personally, I find it the height of humor that were someone to only see this conversation they might assume that I'm some sort of bleeding heart.

Okay, now it seems you are arguing in a world with no rules. Using the rules of this, the solution holds. Using the rules of yours----well, it beats me. At least we finally have realized we are using different frameworks. I am using quantifiable numbers and observed phenomena. You are referring to feelings (like feeling bad when you kill 1 person after saving 99 when all 100 could have been dead had you done nothing) to which logic not necessarily applies. Oh well.

10-17-2002 10:04 PM

Toby
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quote:
Originally posted by KRamsauer
Depends on the situation. For politicians, knowing the aggregate needs of the people is the most important issue.

No, the design of our government was that the elected representative should always vote their conscience even when it disputed the will of the majority but protected the rights of everyone.

quote:
Using specific cases (Horton, for example) is both bad policy and bad science.

Don't confuse treating a specific case as a specific case with generalizing from a specific case.

10-17-2002 10:06 PM

KRamsauer
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Registered: Apr 2002
Location: Houston, TX
Posts: 734

quote:
Originally posted by Toby
No, the design of our government was that the elected representative should always vote their conscience even when it disputed the will of the majority but protected the rights of everyone.[B]Don't confuse treating a specific case as a specific case with generalizing from a specific case.

I said aggregate need, not majority want. Clearly they must do things against public opinion, but they should never stop trying to help as many people as possible. I was citing the reference to Horton as an example of bad science. The Republicans were implying Dukakis was going to make crime a problem everywhere because that one instance didn't work out. That is not valid science, as I'm sure you agree.

10-17-2002 10:08 PM

Toby
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quote:
Originally posted by KRamsauer
Doesn't matter if someone knows. As long as that person isn't the person making the decision to offer the choice to switch, the solution holds. Think through it, you'll see.

Please note I changed the passage you quoted. I made a slight mistake but I think got the point.

You've missed the point so badly at this juncture, that I don't care if you changed all of the passage. You need to go have a stab at Josh in Insane Ramblings.

quote:
WHAT?!?

*sigh*

10-17-2002 10:09 PM

KRamsauer
TreoCentral Staff

Registered: Apr 2002
Location: Houston, TX
Posts: 734

quote:
Originally posted by Toby
You've missed the point so badly at this juncture, that I don't care if you changed all of the passage. You need to go have a stab at Josh in Insane Ramblings.[B]*sigh*

What you're telling me is my analysis of the problem is not correct, but I've not yet seen any evidence to support your claim. If that counts as Inane (not Insane) Ramblings, I'm shocked.

10-17-2002 10:11 PM

Toby
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Registered: Jul 2000
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Posts: 3034

quote:
Originally posted by KRamsauer
Okay, now it seems you are arguing in a world with no rules.

No. Did you get the point of the 'foolish consistency' comment yet?

quote:
Using the rules of this, the solution holds.

And the point is that the rules bear no reflection upon reality.

quote:
Using the rules of yours----well, it beats me.

Exactly. I'm using human rules. Human's aren't always logical. Not exactly the way I'd like it, but I can either accept it or live in a cave.

quote:
At least we finally have realized we are using different frameworks.

I realized that from the beginning.

quote:
I am using quantifiable numbers and observed phenomena.

No, you're using what you'd like to believe are quantifiable numbers when you haven't actually seen them. IOW, you're placing faith in there not being an inherent bias or skew in them. Geez...I guess BobbyMike was right about some people treating science like a religion. *shrug*

quote:
You are referring to feelings (like feeling bad when you kill 1 person after saving 99 when all 100 could have been dead had you done nothing) to which logic not necessarily applies. Oh well.

No, I'm saying that killing that one person unneccessarily simply because the numbers worked that way in general is inhuman, and illogical. A foolish consistency is the hobgoblin of little minds.

10-17-2002 10:17 PM

Toby
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Registered: Jul 2000
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Posts: 3034

quote:
Originally posted by KRamsauer
What you're telling me is my analysis of the problem is not correct, but I've not yet seen any evidence to support your claim.

Watch Let's Make A Deal. Your 'problem' is a fabrication from a text book. It doesn't matter if you can concoct a solution which gives you 100% accuracy of predicting which door the prize is behind. We don't live in a textbook.

quote:
If that counts as Inane (not Insane) Ramblings, I'm shocked.

The output of Hoover Dam should be flowing through you about now.

10-17-2002 10:20 PM

KRamsauer
TreoCentral Staff

Registered: Apr 2002
Location: Houston, TX
Posts: 734

quote:
Originally posted by Toby
Watch Let's Make A Deal. Your 'problem' is a fabrication from a text book. It doesn't matter if you can concoct a solution which gives you 100% accuracy of predicting which door the prize is behind. We don't live in a textbook.

I was trusting you to read what I wrote, but if you didn't, instead relying on a game show, I'm sorry. And why doesn't it matter that you can use your brain to find the best solution? You are making no sense. You are telling me that thinking before you act is stupid and you should just "trust your gut."

10-17-2002 10:22 PM

KRamsauer
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Registered: Apr 2002
Location: Houston, TX
Posts: 734

quote:
Originally posted by Toby
A foolish consistency is the hobgoblin of little minds.

And I'd say dismissing logic is the hobgoblin of little minds thinking they are big--bigger than all the evidence in the world. Gut feelings caused the Challenger disaster. Looking at the data, using analytic techniques, not intuition, it is clear there was a disturbing chance of a catastrophe. Well, you know the rest.

10-17-2002 10:24 PM

Toby
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Registered: Jul 2000
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Posts: 3034

quote:
Originally posted by KRamsauer
I was trusting you to read what I wrote, but if you didn't, instead relying on a game show, I'm sorry.

I didn't read what you wrote because it doesn't reflect the reality of the game show, and hence is just as flawed as the original stuff that started this. I thought that using another silly example with medicine might point this out. You instead took it seriously and even worse elaborated it with a higher level of ridiculosity (I'm beginning to like that word).

quote:
And why doesn't it matter that you can use your brain to find the best solution?

Because such a situation does not nor is ever likely to exist. It's like debating how many angels can dance on the head of a pin. What does it matter if angels don't exist?

quote:
You are making no sense.

That's a distinct possibility, but there may be a point to it.

quote:
You are telling me that thinking before you act is stupid and you should just "trust your gut."

LOL...no. I'm telling you that thinking before you act involves more than simple statistics and probability when it comes to human relations. Does your wife look fat?

10-17-2002 10:38 PM

Toby
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Registered: Jul 2000
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Posts: 3034

quote:
Originally posted by KRamsauer
And I'd say dismissing logic is the hobgoblin of little minds thinking they are big--bigger than all the evidence in the world.

There is nothing logical in assuming you know a person's opinion on the middle east simply because of their ethnicity, especially when your bases for thinking you know the population is dubious.

10-17-2002 10:40 PM

KRamsauer
TreoCentral Staff

Registered: Apr 2002
Location: Houston, TX
Posts: 734

quote:
Originally posted by Toby
I didn't read what you wrote because it doesn't reflect the reality of the game show, and hence is just as flawed as the original stuff that started this. I thought that using another silly example with medicine might point this out. I'm telling you that thinking before you act involves more than simple statistics and probability when it comes to human relations. Does your wife look fat?

Are you calling my wife fat?

I'm not married and if I were, it would be completely irrelevent. Heck, it's still irrelevent. Gotta love two different spellings of a word in two sentences.

10-17-2002 10:44 PM

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