Two Plus Two Newer Archives  

Go Back   Two Plus Two Newer Archives > Other Topics > Science, Math, and Philosophy

Reply
 
Thread Tools Display Modes
  #51  
Old 11-20-2007, 12:46 PM
chezlaw chezlaw is offline
Senior Member
 
Join Date: Jan 2004
Location: corridor of uncertainty
Posts: 6,642
Default Re: Wait! Wait! - A Perfect Example?

[ QUOTE ]
But what about the Monty Hall problem? A logical approach will always ascertain the correct answer, while an illogical approach will not (can you give an example of how an illogical approach will yield a correct answer, and do so at least 50% of the time?). A coin flip will yield the correct answer 50% of the time.

Explain this, and you'll have me convinced.

[/ QUOTE ]
I once backed a horse called 'always switch' that came in at 100:1 so I switch.

or I watched this program a few times and the people who didn't swicth won each time so the law of averages says I should switch.

chez
Reply With Quote
  #52  
Old 11-20-2007, 12:54 PM
madnak madnak is offline
Senior Member
 
Join Date: Aug 2005
Location: Brooklyn (Red Hook)
Posts: 5,271
Default Re: Wait! Wait! - A Perfect Example?

[ QUOTE ]
But what about the Monty Hall problem? A logical approach will always ascertain the correct answer, while an illogical approach will not (can you give an example of how an illogical approach will yield a correct answer, and do so at least 50% of the time?). A coin flip will yield the correct answer 50% of the time.

Explain this, and you'll have me convinced.

[/ QUOTE ]

I really don't see the problem. In my experience, most illogical people don't think it matters which door you choose, about half choose to stick with their door and about half choose to change doors. I mean, the illogical approach of "I'm usually luckier with my second guess than with my first, so I'll change doors" is just as correct as the logical approach here. Or even the more psychological approaches, "I'm adventurous, I'll see what's in the other door," etc.

But even the "standard" illogical approach - "there are two doors and I don't know which is which, so it doesn't matter which I choose" is as good as a coin-flip.
Reply With Quote
  #53  
Old 11-20-2007, 02:04 PM
Lestat Lestat is offline
Senior Member
 
Join Date: Mar 2005
Posts: 4,304
Default Re: Wait! Wait! - A Perfect Example?

<font color="blue"> But even the "standard" illogical approach - "there are two doors and I don't know which is which, so it doesn't matter which I choose" is as good as a coin-flip. </font>

But this isn't the question... The question is a simple 50/50 proposition: Does it MATTER whether or not you switch? The answer is undoubtedly, yes. And you have just admitted that illogical thought will almost always produce the incorrect answer of, "No. It doesn't matter". So clearly, one has a better chance through flipping a coin to arrive at the correct answer of "yes, it matters", than using illogical thought.

There are probably countless better examples than the ones I'm giving. I just can't think of any right now. The last one that comes to mind is hand reading in poker...

Clearly, if you don't think logically (or if your opponent thinks more logically than you do), you are better off not thinking at all and resorting to game theory. Otherwise, illogical thinking when it comes to guessing your opponent's hand, assures you'll have the worst of it. Certainly, you'll be worse off than if you used game theory.

But I can see I'm not going to win this argument. Perhaps it's because I'm wrong. I just don't understand why I'm wrong.
Reply With Quote
  #54  
Old 11-20-2007, 03:31 PM
madnak madnak is offline
Senior Member
 
Join Date: Aug 2005
Location: Brooklyn (Red Hook)
Posts: 5,271
Default Re: Wait! Wait! - A Perfect Example?

[ QUOTE ]
But this isn't the question... The question is a simple 50/50 proposition: Does it MATTER whether or not you switch? The answer is undoubtedly, yes. And you have just admitted that illogical thought will almost always produce the incorrect answer of, "No. It doesn't matter". So clearly, one has a better chance through flipping a coin to arrive at the correct answer of "yes, it matters", than using illogical thought.

[/ QUOTE ]

Sure, people will typically arrive at the wrong answer here, but it's not because they're illogical. It's because one illogical reasoning process has more psychological appeal than the others. But you can easily use illogical reasoning to reach the incorrect conclusion on this question, too. "It matters because if you picked the right door you shouldn't switch."

The level of apparent absurdity increases as the question gets more abstract - that's because while all illogical processes are absurd, some concrete approaches "seem" to make sense. In reality, "it's going to come up black because I'm due" makes no more sense than "it's going to come up red because horseshoes are shaped like horse hooves." Remember, we're considering things logically - not psychologically.

[ QUOTE ]
Clearly, if you don't think logically (or if your opponent thinks more logically than you do), you are better off not thinking at all and resorting to game theory. Otherwise, illogical thinking when it comes to guessing your opponent's hand, assures you'll have the worst of it. Certainly, you'll be worse off than if you used game theory.

[/ QUOTE ]

When playing a game against someone who plays better than you, particularly in a game where psychology is relevant, it is more likely that your opponent will exploit your mistakes than it is you will exploit your opponent's mistakes. Therefore, cleaving to the game-theoretical approach is better than attempting gambles to take advantage of your opponent. Every time you deviate from game theory, you make a game-theoretical mistake that your opponent can exploit. So if you know the GT approach, then you should apply it against good opponents. Against poor opponents, you can extract extra value by making plays that are not GT-correct, but that are more profitable against irrational behavior on the part of your opponent. Basically the idea is that you don't want to walk into a trap - you want to be the one setting traps.

This has little bearing on considerations of boolean logical propositions.
Reply With Quote
  #55  
Old 11-20-2007, 07:51 PM
willie24 willie24 is offline
Senior Member
 
Join Date: Aug 2004
Posts: 726
Default Re: Wait! Wait! - A Perfect Example?

[ QUOTE ]
But what about the Monty Hall problem? A logical approach will always ascertain the correct answer, while an illogical approach will not (can you give an example of how an illogical approach will yield a correct answer, and do so at least 50% of the time?). A coin flip will yield the correct answer 50% of the time.

Explain this, and you'll have me convinced.

[/ QUOTE ]
[ QUOTE ]
but it doesn't prove the point you are trying to make - because there are many ways to arrive at "switch" illogically. for instance...well, i just thought of the number 13, so my pick must be unlucky

[/ QUOTE ]
Reply With Quote
  #56  
Old 11-20-2007, 08:11 PM
willie24 willie24 is offline
Senior Member
 
Join Date: Aug 2004
Posts: 726
Default Re: Wait! Wait! - A Perfect Example?

another way to think of it is this:

regarding a yes/no question that meets our criteria, "an illogical answer is usually wrong" must be false because:

if you knew you were incapable of logic - and were presented with one of these questions...then (if what you are saying were true) you would be better off using an illogical method of your choice to come to a conclusion, and then picking the opposite answer.

that can't work. i will assume its intuitively obvious enough why. (because i think it would be a pain to prove)
Reply With Quote
  #57  
Old 11-21-2007, 05:28 AM
MaxWeiss MaxWeiss is offline
Senior Member
 
Join Date: Dec 2003
Location: Henderson, NV
Posts: 1,087
Default Re: these debates remind me of...

The wording of your question and teh way you asked similar questions in this thread is very awkward to me. There are only two levels to your yes/no question.

The first is the gathering of all available and relevant information and utilizing it correctly through deduction and logically reasoning. There are no "levels of logic". An argument is either logical or not, assuming the same amount of knowledge. I think what you are getting into with your "levels of logic" is the second part of the question, which is simply knowing your opponent.

The problem is that these two things--gather evidence and knowing your opponents are completely independent of one another, although the final answer does incorporate both. Once all information is obtained and optimally used, there is some percent chance of yes versus no. With 100% information, you can tell 100% yes or no. There is no debate or "logic levels" about the event--it can be determined by evidence and logic. And one can make logical or illogical arguments, but logic is an absolute term, there are no varying degrees of it--there is only the addition of new evidence.

For the second part, you are trying to determine the likelihood of the yes/no answer based on another type of evidence--how well you know the other person. You are determining if he will do something. There only exist about 3 "levels of logic" in a two-sided situation such as your yes/no question. Once you pass level three, it just loops back to one. He knows that I know that he knows that---and so you just pick what you would have originally picked. With more variables or answers the levels might increase, but any further and you unnecessarily and erroneously complicate it.

But again, this is an entirely different situation. Either the yes/no is answered with evidence and logical argument or it is an estimation of another person based on what you know, or some combination thereof, but there is certainly a distinct probability of yes or no depending on what each factor says, and it certainly may not be 50/50.

I don't communicate well and I know this post might have been confusing but if you take anything away from it, let it be that an argument is logical or it is not. The rest is just knowing yourself and the other guy better than he knows himself and you.

Also, the probability of an event you described where each succeeding level of "he knows that I know" type of situation does in fact have a 50/50 chance if each smarter person continues to go opposite. That is simply the definition of limits in mathematics. However that would NOT happen in the situation you described where there is a 100% right answer. Person number two or three, or anybody capable of logical argument and proper use of deduction and inference, would immediately get the right answer (assuming they have all the evidence) as would each of the rest of the people.
Reply With Quote
  #58  
Old 11-21-2007, 06:45 AM
willie24 willie24 is offline
Senior Member
 
Join Date: Aug 2004
Posts: 726
Default Re: these debates remind me of...

[ QUOTE ]
And one can make logical or illogical arguments, but logic is an absolute term, there are no varying degrees of it...

[/ QUOTE ]

right. this is essentially what i'm trying to say. (edit: after writing this post, i realize that what i was trying to say is more like: knowledge of truth is knowledge of truth, there are no varying degrees of it - but yes, the statement applies to logic also.) i know i've confused the ideas of logic and evidence. in my scenario, good logic based on bad evidence = bad logic. that is probably technically incorrect. but isn't it true that it is roughly equivalent to bad logic, for practical purposes?

maybe it isn't. for instance, if my information is 5% complete, and i have perfect logic, i should be able to do somewhat better than 50% on a true/false question. if my information is complete, but wrong, then whether or not i'm right is completely dependant on how my wrong info relates to the truth. i don't think it is something that a probability can be put on. hmmm

then the differences of opinion between logical people regarding a yes/no question with a definite answer (that is unknown) must be due to different perceptions of the evidence, or actual inconsistencies in the evidence itself.

thus, rather than being at the mercy of limited logic, we are at the mercy of limited information!

the two ideas are similar, but not the same. with no logical ability, we do have a 50% chance on a yes/no question. with poor information, we cannot have a definite probability! our answer is completely correlated with our information. we obtain information through perception...

if i know that my perception is uninfluenced by reality, is it 50% to match reality on a yes/no question? i guess it would be, if there were a definite separation between perception and reality, but is there? what is reality beyond my perception of it? what now?
Reply With Quote
  #59  
Old 11-21-2007, 07:23 AM
willie24 willie24 is offline
Senior Member
 
Join Date: Aug 2004
Posts: 726
Default Re: these debates remind me of...

i just glimpsed the full significance of madnak's statement regarding 1/infinity as it applies to putting a probability on an event we have no information about.
Reply With Quote
Reply

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off

Forum Jump


All times are GMT -4. The time now is 08:20 AM.


Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2024, vBulletin Solutions Inc.