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Sam’s Monty Hall Problem is a problem…
Posted: 30 October 2010 05:30 PM   [ Ignore ]  
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The ‘Monty Hall Problem’ Sam (can I call you Sam?) on page 86 of The Moral Landscape is a problem for me. I had to sign up and post it here.
Sam claims this scenario shows how people can be logically confused and irrational even when they clearly intend to choose the most rational/logical choice.

He describes the “Let’s Make a Deal” game show and the idea that you’re given the choice of 3 doors to choose from. One has a car behind it and two have a goat. In other words…one is a ‘winner’ and two are ‘losers’.

He tells you you’ve chosen door #1 but instead it’s revealed that door #2 has a goat—is a ‘loser’. Since there are two loser doors, the show is eliminating one of them AND one choice.

You’re now allowed to ‘switch’ from door #1 to door #3. Most people, as Sam points out,  say that it’s a 50/50 bet now so there’s no reason to switch (or switching doesn’t make any difference), but he claims you ‘should’ switch for a better chance.

He says it violates ‘common intuition’ to switch, but claims if you stick with door #1 your chances are 1 out of 3 but if you switch to door #3 your chances are 2 out of 3. This is all on Wikipedia if you want to look it up.

It’s NOT true though that you’d switch to a 2 out of 3 chance. And it’s not based on the grounds of ‘common intuition’.

You start the game with a 1-in-3 chance of picking the winner. When you ‘pick’ door #1 (or ANY door), it doesn’t count because they don’t accept your pick. Because there are two losers, they can show you one of them without revealing if your attempted pick was the winner or not (door #2 in this case).
If door #2 had the car, by revealing it you’d simply lose the game—the end.
But because door #2 has a loser the game STARTS OVER.

You can ‘stay or switch’ from #1 to #3, but this is exactly the same as saying you can just choose #1 or #3. There is no more door #2 because it was revealed as a loser. So you now have, for a fact, a 50/50 chance now.

If you picked something and then the game again didn’t accept the pick but changed the game again then all new odds would be created as the game once again started over. But this is beyond the scope of the scenario Sam presents.

In starting over, you do not know which door has the winner and you only have two choices. Your ‘first pick’ of door 1 was an illusion. You never actually picked it. It never counted. It’s a flaw in semantics to call it a ‘first pick’ that then wrongly gets placed into an otherwise correct mathematical display of probability.

To have Harris use this flawed example to explain how other people use poor logic even when trying to think rationally becomes ironic and does damage to the points he tries to make.

I very much support the vast majority of what Sam says and wish I had the rhetorical skill he has so I could also be out there chopping down the irrational as surgically as he so often does.
But this book about the possibility of science based morality is a bit of a mess IMO and this Monty Hall Problem is just one little facet of it.
Note- I think his basic premise is probably true. That we should be looking to science to work on and develop the most appropriate paths based on facts to guide our moral lives. But so far his book isn’t doing it.

I also highly recommend Richard Carriers ‘Sense and Goodness Without God’ which has addressed this same subject of a rationally-based morality several years ago. It’s a bit collegiate and certainly dry, but actually lays out a path to rational morality whereas Sam seems to just keep saying that science should work on this issue. That’s good, but there are actually lots of answers available now and Sam I’m sure could easily and brilliantly present them.

Also Carrier’s book presents a hierarchical list of ‘ways of knowing’ with ‘faith’ being the one ‘invalid’ way (and specifically why that’s true). It’s been of great use to me and I wish he would write a more commercial/shorter/mainstream version of it. We need lots of ‘horesmen’ out there.

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Posted: 30 October 2010 10:19 PM   [ Ignore ]   [ # 1 ]  
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Azryan – thanks for posting your ideas about the Monty Hall Problem. 

Whenever I hear this stated to prove a lack of the ability of the human mind to correctly make rational decisions I want to yell out “wait – that’s a perfectly rational decision”.  I have read the mathematical proof that changing your selection is always the right choice but I think your explanation fits reality much better.

Here is another way to think about it.

Same scenario: three doors, a goat, a car, and one door with nothing behind it.  Monty calls the contestant to the stage who makes his choice.  Monty then opens one of the other doors and reviles – a goat.  Monty asks the contestant if he would like to change his door.  There is a bit of a hesitation and some dramatic music is played in the background.  Will he change?  Does he know that the probabilities recommend changing? So far exactly the same -right?  This is where I like to change the story a bit.

Just as the contestant is about to announce his choice the unthinkable happens.  Nuclear war beaks out, there is an explosion, the stage, CBS, Los Angles, and all of humanity disappear from the face of the earth. 

Now in the year 3535 a landing is made from the planet Zork and a team of Zorkian anthropologist alight and attempt to determine if life ever made a start on this lonely, radioactive rock.  They happen to stumble upon the original set of the Monty Hall show and find the three doors.  One open the other two still closed.  The remains of some sort of animal are still visible in the dust in front of one door.  They also find a script, miraculously saved from the centuries and because of their advance translation capabilities they understand the events that were about to take place on that faithful day.  They decide to finish the show – for old time sake.

Two doors still closed - one with nothing, the other with a car.
 
Please tell me how it’s not 50/50.

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Posted: 31 October 2010 02:34 PM   [ Ignore ]   [ # 2 ]  
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I hope you’re kidding? Your story is riddled with so many tangential details it seems designed purely for comedic intent. My guess is that you’re just really that bad at getting to the crux of a problem, but possibly just trying to intentionally confuse the issue for whatever reason.

note- I am 100% willing to be shown how I’m wrong in my reasoning, and was simply claiming that as Sam presented the case in his book, he did not prove his claim. He merely stated that it was true. Neither did his footnote changing the number of doors to 1,000 to ‘clarify his point’. For me, it didn’t do that at all.

If you honestly were trying to add something of value here you should not have made your story full on extraneous information that adds nothing -like planet Zork and the Zorkians in the year 3535. I’m sorry, but it makes you sound crazy.

For example, I tried to eliminate the idea of a ‘goat’ or a ‘car’ as a result and preferred the idea of one ‘winner’ and two ‘loser’ doors to help zero in on the actual issue of the logic of the problem.
Your story make the issue a massive fog-shrouded mess-intentionally or not I just don’t know.

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Posted: 31 October 2010 06:07 PM   [ Ignore ]   [ # 3 ]  
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grin Ever been accused of taking yourself to seriously?
Just wondering?

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Posted: 31 October 2010 06:35 PM   [ Ignore ]   [ # 4 ]  
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azryan - 31 October 2010 06:34 PM

I hope you’re kidding? Your story is riddled with so many tangential details it seems designed purely for comedic intent. My guess is that you’re just really that bad at getting to the crux of a problem, but possibly just trying to intentionally confuse the issue for whatever reason.

note- I am 100% willing to be shown how I’m wrong in my reasoning, and was simply claiming that as Sam presented the case in his book, he did not prove his claim. He merely stated that it was true. Neither did his footnote changing the number of doors to 1,000 to ‘clarify his point’. For me, it didn’t do that at all.

If you honestly were trying to add something of value here you should not have made your story full on extraneous information that adds nothing -like planet Zork and the Zorkians in the year 3535. I’m sorry, but it makes you sound crazy.

For example, I tried to eliminate the idea of a ‘goat’ or a ‘car’ as a result and preferred the idea of one ‘winner’ and two ‘loser’ doors to help zero in on the actual issue of the logic of the problem.
Your story make the issue a massive fog-shrouded mess-intentionally or not I just don’t know.


Dude, he agreed with you. He just went through an intentionally absurd scenario to make it all the more obvious.

At any rate, I’d say Harris’ error is even more obvious. Simply put, why does Harris think choosing to stay with door 2 isn’t a “new” choice under the “new” odds?

(Same as the “new game” scenario you mentioned.)

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Posted: 01 November 2010 11:59 AM   [ Ignore ]   [ # 5 ]  
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‘Dude’ (which comes across as condescending you ought to know), my point was I couldn’t even tell if he was agreeing with me. Which I made clear in the first sentence of my reply. That’s how weird what he wrote seemed to me.

So I tried to make a bit of a note about ‘how to make sense to get your point across’ in hopes it would help in the future. I honestly think he needs it. He didn’t make the point more obvious. (I’m assuming it’s a ‘he’ since the probability of a woman inventing Zorkians in the year 3535 is pretty much next to nil).

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Posted: 01 November 2010 12:25 PM   [ Ignore ]   [ # 6 ]  
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“-why does Harris think choosing to stay with door 2 isn’t a “new” choice under the “new” odds?-”

I think he might have just copied the scenario from Wikipedia and saw it as logical. But that’s what I wanted him to prove in his book, not just claim it’s right.

I find his logic nearly flawless in his previous books, but Moral Landscape is really giving me a lot of headaches (ironic since it’s mostly all about the brain?).
He doesn’t seem to come to any clear points through most of this book- or if he does they’re obscured by all the references to opposing views on the matter that he partially, somewhat, kinda disagrees with.
I’m not quite done and the last chapter I’m betting will make a clearer point probably in a summation of his whole idea that science should deal with morality. But it all seems so far like a random collection of ‘thoughts about thought’. Kinda interesting but not getting much of anywhere since mostly science hasn’t yet done what he wants it to do.
Maybe he should have focused more clearly on what science has already made strong cases for about morality?

I’m someone inclined to agree with him on science, morality, rationality and faith/religion…and he’s not really getting through to me here. My wife and I weren’t much moved by his recent TED ‘book-promo’ speech either. And we’ve both always loved watching him in interviews and debates before this.

I was a little surprised and ticked off too that he used Bill Clinton’s ‘stained-dress lie’ as an example of connecting the sudden knowledge of DNA proof ‘he did it’ that forced hims to connect to his ‘conscience’ that was otherwise in ‘another galaxy’.
Was the Prez lying? Yeah, but many (like me) feel that he should have never been subjected to such questions in the first place and it was between him and his wife, so lying to those whose business it was none of is not a failure of conscience in that respect.
Cheating on your wife of course IS a failure of conscience but that’s not the point Sam made.
I’d think a guy on the left like Sam would have tried to find a different example. He did seem to point out flaws in logic in both conservatives and liberals as if he was being even handed, but I think really wasn’t because the way that liberals were being biased actually is based on at least some moral logic whereas conservative bias seems not to be.

An example not in Sam’s book would be affirmative action. By definition it’s a bias. But the point is to COUNTER-balance the already massive and long-term bias that has already existed.
Conservatives of course would say “Yes it’s a bias. Get rid of it. Case closed. I mean we’ve got a black terro- uh.. afri… uh…guy in the white house and slavery was a long time ago and everybody liked the Cosby Show.”
And they’d be narrow-mindedly right, but ‘big picture-wise’ and morally wrong.

[ Edited: 01 November 2010 12:40 PM by azryan]
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Posted: 01 November 2010 03:17 PM   [ Ignore ]   [ # 7 ]  
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Azryan - So as not be confused – yes I agree with you - the reason that the Monty Hall paradox is so confusing is because the player never really made a first choice.  If every human interaction is considered a transaction then the initial selection of the door was an incomplete transaction and not really a selection at all.

Another error in reason that people get wrong is called ‘Hyperbolic discounting’, its one of a long list of cognitive biases.  This is the one where a person shows a preference for something that arrives sooner rather than later.  It’s usually given by:

    “Would you prefer a dollar today or three dollars tomorrow?”
    “Would you prefer a dollar in one year or three dollars in one year and one day?”

People who would choose three dollars tomorrow but not choose three dollars in a year and a day are accused of being “present-biased” but I would say that this is common sense at work.  We all should be present-biased to some extent.  If we always trusted in simple arithmetic to make our decisions we would have refinanced our home back in 2007 because it’s clear that the value can do nothing but go up.  You didn’t refinance did you?

Here comes another of those stories filled with tangential details that you seem to love.

You are offered a dollar today or three tomorrow.  You make a mental calculation and then choose ‘three tomorrow’.  Is this choice simple arithmetic or much more?  You make your decision base on a lot of variables.  The ones that come to mind are:

  1.  A dollar isn’t much and three dollars isn’t much either so its it’s a ‘so what’ decision
  2.  I know and love this person (it’s my mother) so I don’t think she will stiff me on the money
  3.  I have a wallet with a twenty in it so I don’t need the money right away anyway
  4.  I have a pretty good chance of living through the night (no Zorkian’s on the horizon)

All in all it’s a good bet.  I’ll take it.

I won’t go into the other ‘dollar in a year and day’ choice but It’s easy to see that *all* human decisions are made this way and to simply reduce it to math is a huge mistake.

Here comes another story.  A long time ago I met a young college student that was majoring in math.  I was studying engineering.  He proposed to me that I build a small computer that could fit in a back pack (this was in about 1970 so that would be difficult but not impossible) and fit it out with ‘toe switches’.  He would write some probability software for the machine. Then we would go to Vegas and watch a roulette wheel and encode the drop using the toe switches.  Then as the odds increased some small lamps in the frame of a pair of glasses would change from red to green meaning place your bet.

Since I could actually build a computer like that and being that he was a math major – we were going to be rich.

Then I made the mistake of observing that the wheel has no memory so that unless it were fixed (imagine confronting Bugsy Siegel with that assertion) there was no way to win with this idea.  We didn’t get rich but I did build a computer at about that time.

BTW – Another guy that I knew with the improbable name of ‘Carle Ohm’ actually did build a toe switch computer, took it to Vegas and made some money with it counting cards.  They finally caught up with him and pitched him out of town.

Moral – Tough to fit one off the shelf but I think that this will do:
    “Making moral decisions rationally will be *very* difficult but worth the effort”

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Posted: 02 November 2010 04:13 PM   [ Ignore ]   [ # 8 ]  
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Thanks for derailing this thread. Or at the least filling it with totally off-topic clutter.
Perhaps start your own thread about Sci-Fi aliens, Las Vegas trips, and your awesome computer building skills from the 1970’s ok?
But it was great to find out you know someone named Carle Ohm. That part really did add an important point to my thread topic.

BTW… reading what you wrote after the part where you make it clear that you agree with me…actually makes me think that you are not agreeing with me at all and forcing in some pointless emotional element onto a pure logic problem.
So now I’m inclined to think you’re really just that bad at making clear points.

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Posted: 02 November 2010 05:55 PM   [ Ignore ]   [ # 9 ]  
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Seems maybe you’re projecting there, Azryan.

Just a tad.

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Posted: 02 November 2010 07:53 PM   [ Ignore ]   [ # 10 ]  
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Azryan – Besides taking yourself *way* too seriously you also have a talent for rejecting a complement.  I said in both my replies that I agree with you.
 
I agree with you – You are correct.  The logic in the Monty Hall problem is flawed and I think that Sam should not have used it as an example of poor reasoning abilities.  My second post was about another example of poor reasoning abilities that is also flawed but for different reasons.

Enough said – I need to get on with my life.  You obviously need to buy one for a start.

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Posted: 03 November 2010 01:28 PM   [ Ignore ]   [ # 11 ]  
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As I said TWICE, your posts were so weird that I literally couldn’t tell you were agreeing with me. So I was suggecting if you were serious that you might wanna work on making yourself a little clearer.

And then you really added all kinds of stuff that had nothing to do with the clear post question -which remember is Harris saying both of us are wrong.

You keep saying I take myself too seriously. How seriously do I take myself? It’s a phrase that doesn’t even mean anything. It’s childish just like telling me to go buy a life. You do realize aside from my original post (and my confusion over what you’re even getting at) you posted way more than me in this thread. But I should ‘buy a life’?

And SkepitcX thinks I’m ‘projecting’ when I say that this JamesBrown is adding a pointless (and insulting) emotional element to a pure logic problem.

No… I’m not.

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Posted: 03 November 2010 04:29 PM   [ Ignore ]   [ # 12 ]  
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I have even a better idea. Piss Off

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Posted: 06 November 2010 07:55 AM   [ Ignore ]   [ # 13 ]  
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azryan - 30 October 2010 09:30 PM

The ‘Monty Hall Problem’ Sam (can I call you Sam?) on page 86 of The Moral Landscape is a problem for me. I had to sign up and post it here.
Sam claims this scenario shows how people can be logically confused and irrational even when they clearly intend to choose the most rational/logical choice.

He describes the “Let’s Make a Deal” game show and the idea that you’re given the choice of 3 doors to choose from. One has a car behind it and two have a goat. In other words…one is a ‘winner’ and two are ‘losers’.

He tells you you’ve chosen door #1 but instead it’s revealed that door #2 has a goat—is a ‘loser’. Since there are two loser doors, the show is eliminating one of them AND one choice.

You’re now allowed to ‘switch’ from door #1 to door #3. Most people, as Sam points out,  say that it’s a 50/50 bet now so there’s no reason to switch (or switching doesn’t make any difference), but he claims you ‘should’ switch for a better chance.

He says it violates ‘common intuition’ to switch, but claims if you stick with door #1 your chances are 1 out of 3 but if you switch to door #3 your chances are 2 out of 3. This is all on Wikipedia if you want to look it up.

It’s NOT true though that you’d switch to a 2 out of 3 chance. And it’s not based on the grounds of ‘common intuition’.

You start the game with a 1-in-3 chance of picking the winner. When you ‘pick’ door #1 (or ANY door), it doesn’t count because they don’t accept your pick. Because there are two losers, they can show you one of them without revealing if your attempted pick was the winner or not (door #2 in this case).
If door #2 had the car, by revealing it you’d simply lose the game—the end.
But because door #2 has a loser the game STARTS OVER.

You can ‘stay or switch’ from #1 to #3, but this is exactly the same as saying you can just choose #1 or #3. There is no more door #2 because it was revealed as a loser. So you now have, for a fact, a 50/50 chance now.

If you picked something and then the game again didn’t accept the pick but changed the game again then all new odds would be created as the game once again started over. But this is beyond the scope of the scenario Sam presents.

In starting over, you do not know which door has the winner and you only have two choices. Your ‘first pick’ of door 1 was an illusion. You never actually picked it. It never counted. It’s a flaw in semantics to call it a ‘first pick’ that then wrongly gets placed into an otherwise correct mathematical display of probability.

To have Harris use this flawed example to explain how other people use poor logic even when trying to think rationally becomes ironic and does damage to the points he tries to make.

I very much support the vast majority of what Sam says and wish I had the rhetorical skill he has so I could also be out there chopping down the irrational as surgically as he so often does.
But this book about the possibility of science based morality is a bit of a mess IMO and this Monty Hall Problem is just one little facet of it.
Note- I think his basic premise is probably true. That we should be looking to science to work on and develop the most appropriate paths based on facts to guide our moral lives. But so far his book isn’t doing it.

I also highly recommend Richard Carriers ‘Sense and Goodness Without God’ which has addressed this same subject of a rationally-based morality several years ago. It’s a bit collegiate and certainly dry, but actually lays out a path to rational morality whereas Sam seems to just keep saying that science should work on this issue. That’s good, but there are actually lots of answers available now and Sam I’m sure could easily and brilliantly present them.

Also Carrier’s book presents a hierarchical list of ‘ways of knowing’ with ‘faith’ being the one ‘invalid’ way (and specifically why that’s true). It’s been of great use to me and I wish he would write a more commercial/shorter/mainstream version of it. We need lots of ‘horesmen’ out there.

No.  This is a common fallacy.  Don’t look it up in Wikipedia.  Take a course in probability and statistics.  You have a 2/3 chance.

Your error is in assuming that Monty Hall doesn’t know what door has the goat and what door has the car.  He isn’t randomly choosing.  Change the game slightly by adding more doors.  If there were one hundred doors, you picked door number 37, and Monty then opened all doors but 37 and 65, would you still stick with your choice of 37?  Or would you realize that Monty, who knows all along which door it’s behind, has basically told you that the prize is behind 65?  You’re probability of picking the right one initially is 1/100.  But switching gives you a 99/100 chance of winning.  Mathematically there’s no difference between this scenario and the original Monty Hall Problem.

See ya!

SLD

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Posted: 06 November 2010 10:01 AM   [ Ignore ]   [ # 14 ]  
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sld - 06 November 2010 11:55 AM

Your error is in assuming that Monty Hall doesn’t know what door has the goat and what door has the car.  He isn’t randomly choosing.


Yeah, that makes a big difference ... I’m still trying to internalize it though—nail it down rather than relying on a vague intuitive sense. In any case, the fact that Monty knows makes a big difference.

Yup ... Monty knows.

The bastard!

That would make a great geek t-shirt ... maybe just the first part though.

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Posted: 07 November 2010 02:11 AM   [ Ignore ]   [ # 15 ]  
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SkepticX - 06 November 2010 02:01 PM
sld - 06 November 2010 11:55 AM

Your error is in assuming that Monty Hall doesn’t know what door has the goat and what door has the car.  He isn’t randomly choosing.


Yeah, that makes a big difference ... I’m still trying to internalize it though—nail it down rather than relying on a vague intuitive sense. In any case, the fact that Monty knows makes a big difference.

Yup ... Monty knows.

The bastard!

That would make a great geek t-shirt ... maybe just the first part though.

It would indeed!  He’s still alive by the way.  89 years old and married to the same woman for over 60 years!

I wonder if he gets royalties for the problem that bears his name?  It will make him more famous down the ages than his game show ever will.

More importantly, remember that Math isn’t always intuitive.  It is sometimes extremely counter-intuitive as this problem illustrates so wonderfully.  Another example from my college calculus days is this one: Take the graph 1/x and integrate it from one to infinity.  What’s the answer: infinity.  However rotate that curve around the x-axis and measure the volume of the space.  Answer: 2*pi.  So if some mathematician told you to paint the wall of the graph 1/x from 1 to infinity you would do it by creating the “trumpet” from one to infinity, fill it with 2*pi worth of paint and dip the wall in it. 

Doesn’t that just blow your mind?  I still can’t get my head around that one and it’s been 30 years since I took that course.

SLD

[ Edited: 07 November 2010 02:18 AM by sld]
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