Monty Hall Problem

[ELD]

 

I give up.  This must be a joke, or Asch part two.

(Correction, Asch not Milgram)

 

It's not a joke.  If you think you are rational, it's an important thing to be able to grasp.  Please verify yourself by checking wikipedia or something if you think everyone is somehow messing with you.

[AnarcoB]

Ok, I'm back from doing some reading.  It makes better sense as written on Wikipedia.

I was treating the second decision as a separate problem as opposed to a continuation of the initial problem.

I guess I've been studying too much about perception and emotion in the presence of social pressure (good stuff!).[:$]

 

 

[Lowe D]

It's hard not to feel pressured in a thread that is someone's extended game of Say Uncle.  What you're feeling might not be yours.

[ELD]

 

 

 

A similar problem: There are three boxes. In each box there are two balls. One box has two black balls, one box has two white balls, one box has a white and a black ball in it. If the first ball you get out of the box is white, what is the chance the other ball is also white?

 

 

Love it.  Never heard of that one.  Let's see if I understand.

So you pick a ball at random.  It's white.  You have a 2/3 chance of having pulled it out of the box with two white, and a 1/3 chance of having pulled it out of the 50/50 box.  The chances that the next ball is white would therefore be 2/3. 

Is that correct?

 

This is correct yes. Maybe this problem is harder because it involves conditional probability and most people dont even know what it is. The subtelity is in the part 'given that the first ball is white'. 

 

Yeah, I'm not familiar with conditional probability, but I have no doubt that this stuff can easily be handled via formulas as well   Just seemed like a very fun logic problem to me. 

 

It's hard not to feel pressured in a thread that is someone's extended game of Say Uncle.  What you're feeling might not be yours.

 

Why is this a game of Say Uncle?  I made this thread because I find the problem to be very fun, and I also wanted to see how people would react to being incorrect, and others being incorrect.  So far, there demeanor of the board is mostly civil, which is fantastic.

[Lowe D]

Uncle.

[Mister Mister]

  The interesting thing is that most people in the game show would not switch.

   I read a book where they compared this to a real life scenario:  Say you bought a ticket to a concert you really want to go to, but the night of the concert, there is a blizzard, and you know it will take 2 1/2 hours to get there, and another 2 1/2 back.  You cannot refund your ticket.  Will you still go?    What if you don't have tickets but your friend calls and says he is not going, and offers you a free ticket.  Will you brave the blizzard this time?  Most people will go in the first scenario, paying the added costs (5 hours of driving in a blizzard) of a product they have already invested in.  Most people will not bother in the second scenario, they feel they have no stake in it and will not invest the costs, even though the demand, or desire to see the concert may be equal. From a logical standpoint, however, they are the same.  Does that make sense?

[Nathan T_ Freeman]

 

  The interesting thing is that most people in the game show would not switch.

 
  I read a book where they compared this to a real life scenario:  Say you bought a ticket to a concert you really want to go to, but the night of the concert, there is a blizzard, and you know it will take 2 1/2 hours to get there, and another 2 1/2 back.  You cannot refund your ticket.  Will you still go? 
  What if you don't have tickets but your friend calls and says he is not going, and offers you a free ticket.  Will you brave the blizzard this time?
  Most people will go in the first scenario, paying the added costs (5 hours of driving in a blizzard) of a product they have already invested in.  Most people will not bother in the second scenario, they feel they have no stake in it and will not invest the costs, even though the demand, or desire to see the concert may be equal. From a logical standpoint, however, they are the same.  Does that make sense?

 

The Fallacy of Sunken Costs. This is another great example of counter-intuitive-but-true economic logic.

Honestly, I'd be amazed if this exact topic weren't already the subject of a long thread on this forum.

[ELD]

 

 

  The interesting thing is that most people in the game show would not switch.

 
  I read a book where they compared this to a real life scenario:  Say you bought a ticket to a concert you really want to go to, but the night of the concert, there is a blizzard, and you know it will take 2 1/2 hours to get there, and another 2 1/2 back.  You cannot refund your ticket.  Will you still go? 
  What if you don't have tickets but your friend calls and says he is not going, and offers you a free ticket.  Will you brave the blizzard this time?
  Most people will go in the first scenario, paying the added costs (5 hours of driving in a blizzard) of a product they have already invested in.  Most people will not bother in the second scenario, they feel they have no stake in it and will not invest the costs, even though the demand, or desire to see the concert may be equal. From a logical standpoint, however, they are the same.  Does that make sense?

 

The Fallacy of Sunken Costs. This is another great example of counter-intuitive-but-true economic logic.

Honestly, I'd be amazed if this exact topic weren't already the subject of a long thread on this forum.

 

As a poker player, I approve of other people believing in the Fallacy of Sunken Costs

[TheRobin]

is this really a fallacy though?If I bought a ticket (probably weeks in advance) there will be a lot of positive anticipation built up and not going would cause dissapointment. If I never had a ticket though, then there was no anticipation (and following dissapointment). So to me this sounds more of an example of evading negative (emotional) "costs" so to speak, then commiting an actual fallacy.hmm, I might miss a thing here though, how are both scnearios considered the same from a logical point considering in one there is a monetary investemnt made already and in the other one there isn't?

[Waster]

 

is this really a fallacy though?
If I bought a ticket (probably weeks in advance) there will be a lot of positive anticipation built up and not going would cause dissapointment. If I never had a ticket though, then there was no anticipation (and following dissapointment). So to me this sounds more of an example of evading negative (emotional) "costs" so to speak, then commiting an actual fallacy.

hmm, I might miss a thing here though, how are both scnearios considered the same from a logical point considering in one there is a monetary investemnt made already and in the other one there isn't?

 

I think it is more a bias. You are monetary and so emotionally invested in something, which results in an error of judgement: a bias. If we want to rationalize our bias we use fallacies to support them. People can accept fallacies if they have the same bias, cannot recognize fallacies or have no integretiy towards reason and evidence. 

So i think the cause is an judgement error because of emotions and the effect is a fallacy in the form of logic or reasoning errors.

So is it really a fallacy? If you focus only on the argument itself, yes. If you focus on the situation and the background, then no its a bias.

[ribuck]

The interesting thing is that most people in the game show would not switch.

Most people don't realise that the host knows the location of the prize and deliberately exposes a door that he knows to be empty. Most people "kind of assume" that the game is not rigged, and that the host is opening a door at random. In that case it wouldn't change the odds, so it's not surprising that most people don't switch.

[ELD]

 

The interesting thing is that most people in the game show would not switch.

Most people don't realise that the host knows the location of the prize and deliberately exposes a door that he knows to be empty. Most people "kind of assume" that the game is not rigged, and that the host is opening a door at random. In that case it wouldn't change the odds, so it's not surprising that most people don't switch.

 

That kind of assumption isn't based on the facts though.  In the example that I showed, there's no doubt he'll reveal a loser.  In the case of the show, you'ld just have to look at the past history to see if he's ever revealed the winner.