these debates remind me of...

[swingbomb]

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.

[Lestat]

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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?

[theAMOG]

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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.

[Lestat]

<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?

[theAMOG]

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.

[willie24]

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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...

[willie24]

great thought/quote

[madnak]

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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).

[madnak]

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."

[Lestat]

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.