Re: Wait! Wait! - A Perfect Example?
 

The greatest indicator of intelligence is the ability to recognize one's own ignorance. With this acceptance of ignorance one displays a lack of conviction, and is destined to live a step below actualization. Therefore, the churning of the gears of humanity rely on the steady tread of the less enlightened.

Re: Wait! Wait! - A Perfect Example?
 

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The Monty Hall problem!

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Is quite simple really, after hearing the explanation anyone who disagrees with it is pretty dumb imo.

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You would think. But I know someone who just can't get his head around it. I've explained it over and over. He will even agree that if we used 99 doors he should switch!

Again, some people just cannot think logically about a given problem. I'm like this myself with some problems (although in my case, it's just that I don't understand how to work out the solution, and if I think about it, this is also the case for the person I just mentioned).

But my main point is that an irrational thought process is more likely to arrive at a wrong answer than if we were to choose an answer at random. Am I wrong about this?

Re: Wait! Wait! - A Perfect Example?
 

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The Monty Hall problem!

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Is quite simple really, after hearing the explanation anyone who disagrees with it is pretty dumb imo.

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You would think. But I know someone who just can't get his head around it. I've explained it over and over. He will even agree that if we used 99 doors he should switch!

Again, some people just cannot think logically about a given problem. I'm like this myself with some problems (although in my case, it's just that I don't understand how to work out the solution, and if I think about it, this is also the case for the person I just mentioned).

But my main point is that an irrational thought process is more likely to arrive at a wrong answer than if we were to choose an answer at random. Am I wrong about this?

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lol, you are supposed to switch. Assuming Monty knows where the car is, if he doesn't then it doesn't matter if you switch or not. But this problem is more commonly presented as Monty knowing where the car is, which means switching doors = 66.6% win rate. Your friend is right. lol.

Re: Wait! Wait! - A Perfect Example?
 

<font color="blue"> lol, you are supposed to switch. Assuming Monty knows where the car is, if he doesn't then it doesn't matter if you switch or not. But this problem is more commonly presented as Monty knowing where the car is, which means switching doors = 66.6% win rate. Your friend is right. lol. </font>

You misunderstood. I KNOW you're supposed to switch! My friend can only see the merit in switching if I use 100 doors as an example (it's much clearer that if you choose 1 door out of 100, and someone (who knows where the car is), eliminates the other 99, then you should switch). It's more difficult to illustrate this using just 3 doors.

But with just 3 doors my friend insists it's a 50/50 proposition and it doesn't matter if you switch or not.

But we're off the point. Does it make sense to you that if one thinks illogically about something, that he has a greater chance of being wrong, than if he uses a game theory type of approach?

Re: Wait! Wait! - A Perfect Example?
 

OK yeah, misunderstood. As for your question, though I have read very little of this thread as a whole, I would say it all depends on the question. But, if I were asked what would be the worst way to think about things in general, illogically would surely be up there.

It's probably quite rare to find yourself in a situation that benefits you to think illogically, while it would be more common to find yourself in a position that would benefit you to think in a way utilizing game theory.

Re: Wait! Wait! - A Perfect Example?
 

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The Monty Hall problem! Are you familiar with it? If so, I don't want to go into it. But this is a perfect example of where flipping a coin would give an illogical thinker a better shot of coming up with the right answer (which is to switch). If you do not think logically, you will invariably say it doesn't matter if you switch or not. This of course, is wrong!


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i just looked up the monte hall problem, and yeah, its pretty cool.

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.

OF COURSE it is true that if you use the most obvious illogical method that gives an answer opposite to the right method , you will be wrong...

Re: Wait! Wait! - A Perfect Example?
 

great thought/quote

Re: these debates remind me of...
 

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if we know someone has used an illogical method to arrive at an answer to a yes/no question, and that is ALL that we know, then, given the information we have, they are 50% to be correct. (assume we do not know the question, we do not know the answer, and we do not know who the person shares/doesn't share a viewpoint with etc)

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I don't think this is true. This seems similar to saying 1/infinity=0. It seems to make sense, in most cases it works, but it's not actually true. I don't think we can talk about probability in a vacuum. Take proposition n - a yes/no proposition. You know nothing, nothing at all. Is proposition n 50% likely to be true given your knowledge?

I think we can say that of all boolean propositions that have a value (we'll ignore the proposition "this statement is false"), there are as many true propositions as false propositions. I don't know that this necessarily implies that a random proposition has a 50% chance of being true. I think this is one of those tricky places where infinity destroys normal methods of assigning probability.

Is a random number 50% likely to be positive and 50% likely to be negative? In general we can assume so without running into problems, but I'm not convinced that the answer is "yes." Excluding 0 just to make things easier, there are just as many numbers on the negative side of the number line as on the positive side. This means a number is 50% likely to be negative and 50% likely to be positive, right? But wait - there are as many numbers below -(10^500) as above -(10^500). In fact, for any given number at all on the number line, there are as many numbers to the left of that number as to the right of that number. And we can say it doesn't matter, because even an arbitrarily large number is finite rather than infinite, and is overwhelmed by the infinity of the number line, but then we're basically saying that finite/infinite=0.

I do think I understand the point you're getting at, and trying to explain to Lestat. I've been thinking about how to describe this point since David's post about extrapolating intelligence trends. But I haven't figured it out. I said then that a stupid person have an edge over a smart person unless a random outcome would also have the same edge. That wasn't true, and was a bad way to express it. I think in this case I want to say something like "an illogical person will never be worse than random on average," but that's not quite what I want to say either. What do I want to say? I'll keep thinking about it.

For the specific purposes of this discussion, I do believe that a hypothetical illogical person is no worse than a coin-flip. In fact, an illogical person may be the same as a coin-flip. Unfortunately, I can't figure out how to demonstrate this principle (much less generalize it).

Re: Wait! Wait! - A Perfect Example?
 

You're wrong for two reasons, Lestat. First and most importantly, you're being selective. For any given yes/no question, there are as many illogical approaches that yield a "yes" answer as there are illogical approaches that yield a "no" answer. I believe the no free lunch theorem proves this. At least I hope it does, because otherwise the justification would have to be very esoteric. But I'm pretty sure it does given the appropriate constraints.

Because of this, a random illogical approach cannot be likelier to provide a yes response than to provide a no response, or vice versa, and therefore a random illogical approach cannot be worse than a coin-flip approach.

Second, it's important that we have no extraneous information. Your examples include extraneous information, and use psychological thinking based on assumptions about human action. It's possible to say in a specific situation that illogical people are more likely to choose the wrong answer than the right answer. This is because according to how people act they're likely to respond in certain ways to the details of the situation.

But we don't know any details! To use your ghost example, we know that there's a proposition ("a ghost is in my room"), but we don't know whether it's night-time, we don't know whether there's an eerie shadow, we don't know anything. All we have is the proposition itself. If you suggest that it's night-time and there's an eerie shadow, then you can say an illogical person is likely to answer "yes" to this question. But if I say that it's daytime and there are no shadows, then I can say an illogical person is likely to answer "no" to the question. For any situation or reasoning you can provide, I can provide a mirror situation or mirror reasoning. This isn't technically true due to self-reference complications etc, but it's true for all intents and purposes.

Just as each positive number has a negative counterpart, each situation making an illogical more likely to answer "yes" has a counterpart situation making them more likely to answer "no."

Re: Wait! Wait! - A Perfect Example?
 

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.

Re: Wait! Wait! - A Perfect Example?
 

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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.

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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

Re: Wait! Wait! - A Perfect Example?
 

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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.

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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.

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.

Re: Wait! Wait! - A Perfect Example?
 

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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.

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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.

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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.

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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.

Re: Wait! Wait! - A Perfect Example?
 

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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.

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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

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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)

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.

Re: these debates remind me of...
 

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

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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?

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.