Random Thoughts Thread

**Hooahguy** · 10-03-2016, 04:03

Originally Posted by Montmorency

Bad idea if you cherish your gums and mouth.

Oh right I forgot about those. Nothing that a bit of mouthwash couldnt fix right?

**Viking** · 10-08-2016, 18:27

In a series of studies, Professor Stanovich and colleagues had large samples of subjects (usually several hundred) complete judgment tests like the Linda problem, as well as an I.Q. test. The major finding was that irrationality — or what Professor Stanovich called “dysrationalia” — correlates relatively weakly with I.Q. A person with a high I.Q. is about as likely to suffer from dysrationalia as a person with a low I.Q. In a 2008 study, Professor Stanovich and colleagues gave subjects the Linda problem and found that those with a high I.Q. were, if anything, more prone to the conjunction fallacy.

Based on this evidence, Professor Stanovich and colleagues have introduced the concept of the rationality quotient, or R.Q. If an I.Q. test measures something like raw intellectual horsepower (abstract reasoning and verbal ability), a test of R.Q. would measure the propensity for reflective thought — stepping back from your own thinking and correcting its faulty tendencies.

http://www.nytimes.com/2016/09/18/op...elligence.html

I anticipate that RQ and IQ are far from equivalent, but an almost nonexistent correlation would not be expected.

**Montmorency** · 10-08-2016, 19:31

I take issue with the equivocal use of set theory in the Linda problem.

It is given as a problem in which one answer should be treated as a subset of the other, but in fact it would make sense to treat them as intersections, meaning the probabilities are not per se limited.

For example:

A. Viking is a human.
B. Viking is a human and mortal.

Which is likelier?

If you leave aside the interpretation that human entails mortal, then we can go on to say that human need not be a subset of mortal, nor vice-versa.

So for all your notions of rationality you might as well deliver that there is no concrete answer to the Linda problem because probabilities of that sort are incalculable, if not outright invalid in their construction. Funny that Kahneman was behind this.

**Viking** · 10-08-2016, 22:06

I don't get your objection. Why shouldn't P(A) ≥ P(A ∧ B) for any choice of A and B?

**Montmorency** · 10-08-2016, 22:33

Because they are independent.

For example: If I have 6 marbles, which is more probable?

A. I have 3 black marbles.
B. I have 3 black marbles and 3 red marbles.

**Montmorency** · 10-08-2016, 22:40

Or:

I have at least one child. Which is likelier?

A. I have a son.
B. I have a son and a daughter.

The P(A) is not a component of P(B) or vice versa, at least not in just logical terms.

For example, in a real distribution perhaps P(A) is .25 while P(B) is .30, because people who have children are likelier to have 2 children than just one. A and B are separate events; B is not a subset of A.

**Viking** · 10-09-2016, 10:14

Originally Posted by Montmorency

For example, in a real distribution perhaps P(A) is .25 while P(B) is .30, because people who have children are likelier to have 2 children than just one. A and B are separate events; B is not a subset of A.

But now you have implicitly changed the definition of A to be "I have only a son". If you have a son and a daughter, you also have a son.

If you mean that A can be interpreted both ways, then I get your objection.

**Fragony** · 10-09-2016, 10:32

Viking is much much more likely as they still live in valhalla, viking comes from old Norsk meanin 'vikinger' old Norsk, anyways you are cheating on probabilty Montmorency, and no I am not going to say why