# Potential economic paradox (Tried it in General Fo

telerion
Posers and Puzzles 24 Sep '04 01:52
1. telerion
True X X Xian
24 Sep '04 01:521 edit

Please limit your answers to the options provided. No explainations from you needed at this point. Just a one-letter response is sufficient. Please do not post questions. Instead message them to me.

Ok here goes.

The following description applies to both questions.

There is an urn that contains 300 balls. 100 of the balls are red and 200 of the balls are either blue or green (Note: This does not imply that all 200 balls are the same color. It may be that some are blue and the others green. Maybe all are green. Maybe all are blue.)

Now there are two gambles, Gamble A and Gamble B.

Gamble A: You receive \$1,000 if the ball is red.
Gamble B: You receive \$1,000 if the ball is blue.

Which gamble do you prefer?

Ok. Got one?

Now choose from two different gambles.

Gamble C: You receive \$1,000 if the ball is not red.
Gamble D: You receive \$1,000 if the ball is not blue.

Which gamble do you prefer?

Thanks for you participation.

I'll keep a tally and fill every interested party in on this in a day or two.
2. 24 Sep '04 02:03

I calculated that A and B have a 1/3 probability, C and D have 2/3 probability. Hence would go for either C or D. ðŸ™‚
3. telerion
True X X Xian
24 Sep '04 02:08
Actually I need you to choose between A and B. Then choose between C and D. So valid responses are members of the set {AC, AD, BC, BD}There isn't necessarily a wrong answer here. ðŸ™‚
4. 24 Sep '04 03:14
B

C

oishi
5. 24 Sep '04 03:28
B, C

-Kev
6. royalchicken
CHAOS GHOST!!!
24 Sep '04 03:40
Choosing A over B and C over D is contradictory.

I don't think I can really make a choice.
7. bbarr
Chief Justice
24 Sep '04 03:51
Originally posted by royalchicken
Choosing A over B and C over D is contradictory.

I don't think I can really make a choice.
Don't you mean that choosing A over B or C over D is arbitrary?
8. royalchicken
CHAOS GHOST!!!
24 Sep '04 03:532 edits
Originally posted by bbarr
Don't you mean that choosing A over B [b]or C over D is arbitrary?[/b]
Simultaneously saying A&gt;B and C&gt;D entails a contradiction. Otherwise, classical probability is totally unable to deal with this question because the distributions are not given, or even hinted at.

I think alternative systems for making such a decision exist, I just don't know what they are.
9. royalchicken
CHAOS GHOST!!!
24 Sep '04 04:01
Saying A better than B is saying P(red) &gt; P(blue) while C over D is saying P(red,green) &lt; P(blue,green). Since P(any two colors simultaneously) = 0, this is equivalent to saying P(blue) &gt; P(red), a truly Feivelian construction.
10. telerion
True X X Xian
24 Sep '04 04:29
Originally posted by royalchicken
Saying A better than B is saying P(red) > P(blue) while C over D is saying P(red,green) < P(blue,green). Since P(any two colors simultaneously) = 0, this is equivalent to saying P(blue) > P(red), a truly Feivelian construction.
Royal don't spoil the fun . . . ðŸ™‚
11. royalchicken
CHAOS GHOST!!!
24 Sep '04 04:30
Originally posted by telerion
Royal don't spoil the fun . . . ðŸ™‚
Sorry to spoil your fun just to get my kicks at Feivel.

However, I didn't shed any light on the right procedure, so it's chill.

In Apologizingforbeingsuchageekship,

RC
12. Acolyte
24 Sep '04 16:35
Originally posted by telerion

Please limit your answers to the options provided. No explainations from you needed at this point. Just a one-letter response is sufficient. Please do not post questions. Instead message them to me.

Ok here goes.

The following description applies to both questions.

There is an urn that contains 300 balls. 100 ...[text shortened]... rticipation.

I'll keep a tally and fill every interested party in on this in a day or two.
Without doing the calculations and with a fairly obvious assumption, I'd guess that (B,D) is the worst choice as it maximises variance, and the others are equally good. However, if we're allowed to know the result of the first gamble before picking the second, then I'd go B, followed by D if I lost the first gamble and C if I won it.
13. Acolyte
24 Sep '04 16:36
Originally posted by royalchicken
Simultaneously saying A>B and C>D entails a contradiction. Otherwise, classical probability is totally unable to deal with this question because the distributions are not given, or even hinted at.

I think alternative systems for making such a decision exist, I just don't know what they are.
Go go gagdet Bayesian probability!
14. royalchicken
CHAOS GHOST!!!
24 Sep '04 16:57
Originally posted by Acolyte
Go go gagdet Bayesian probability!
My parents and I are about to pay large sums to have a guy in a cardigan explain that to me ðŸ˜‰.
15. telerion
True X X Xian
24 Sep '04 17:08
Originally posted by royalchicken
My parents and I are about to pay large sums to have a guy in a cardigan explain that to me ðŸ˜‰.
Yeah going through some of that right now.

Professor: You silly students thought that after a year you had econometrics down? All the hard stuff was behind you? Forget it! Now were going to change up the statistical assumptions and start fresh!

Me: Uh . . . I had classical econometrics down?