RESULTS OF PROBLEM #16

Well..the results are finally in on this intriguing giveaway opportunity! I have included the problem below for those who want to re-visit the challenge by BOLD Charles, who many thought was going to up to his neck in debt--after all, it was FREE money for the asking!! Or was it that simple?

It turns out that matters were not that simple, for a winner depended upon a considerable number of others who agreed in their choices, and many respondents calculated their chances of winning quite differently. As you will see from the entries listed below, several thought the winning choices were obvious--but many disagreed over what the 'obvious' rational choice was! Only one person--Jeff Glick--predicted correctly what the outcome would be...but Jeff, unfortunately, didn't win either. In fact, there WERE NO WINNERS, in spite of the FREE OFFER by Charles, for the choices cancelled out the proper numbers needed to win!!

For consider: There were 86 entries, so an A winner would require 26 A choices--24 responded A; a B winner (the big win) would require 65 B choices, but only 38 chose B; and of the 43 needed to win C, only 24 chose C. SO.....nobody won anything! Make what you want from this exercise in decision-making under uncertainty, but the results should be intiguing to many whose ideas on rational choice are being considered..After all, there was no risk, but only possible gain. Yet nothing was gained in the free choice options.

HHmm. Cheers--Ron Barnette, Zeno's Proprietor.

ORIGINAL PROBLEM

Ever-so-Bold Charles!

It seems that our man Charles has kept his eye on Zeno's players, and has done some calculating--at least to his own satisfaction. After the earlier challenge #13, Charles has now agreed to put his money where his mouth is! He has assured respondents that he will ACTUALLY PAY winners, if there are any, for any winnings in the latest Coffeehouse challenge...So let's get busy and see if we can outsmart Charles in this decision-scenario. Here's the challenge:

You are to choose either Box A, B, or C, and only one.

Choose Box A and you will win \$1 if 1/3 of those playing choose A also; otherwise, you win nothing;

Choose Box B and you win \$10 if 3/4 of those playing choose B also; otherwise, nothing;

Choose Box C and you win \$5 if 1/2 of those playing choose C also; otherwise, nothing.

So there it is--think about the best choice, and submit your entry. Charles is getting nervous!!!

Here are the submitted entries:

Below is the result of your feedback form. It was submitted by Karl Hillstrom () on Saturday, February 21, 1998 at 19:20:09

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state: WA

city: Seattle

country: USA

comments: I'll take B. Math and probabilities aside, the actual facts about money these days makes \$10 worth something to me, and not the others. That is, since I don't care if I win \$1 or \$5 or not, I'll take a chance on winning \$10.

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Below is the result of your feedback form. It was submitted by Metin Aktay () on Sunday, February 22, 1998 at 09:12:46

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city: Istanbul

country: Turkey

comments: Box B ofcourse, assuming a. all the rest of the players face the same set of win charracteristics as above and b. that all players are logical. Why would anyone choose anything other than B if all face the set above?

Below is the result of your feedback form. It was submitted by Eric v. d. Luft () on Sunday, February 22, 1998 at 10:50:30

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state: NY 13212

city: North Syracuse

url: http://www.hscsyr.edu/~lufte/index.html

country: USA

comments: B: If the entrants are greedy, and if the payout is dependent upon the private choice of each, it's very likely that 100% will choose B.

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>>Below is the result of your feedback form. It was submitted by Aly Kachra

>() on Sunday, February 22, 1998 at 18:53:44

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>>state: Ontario

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>>city: Toronto

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Below is the result of your feedback form. It was submitted by Lauri Kultti () on Monday, February 23, 1998 at 03:33:04

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city: Helsinki

country: FINLAND

B

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Below is the result of your feedback form. It was submitted by emma borg () on Monday, February 23, 1998 at 05:09:57

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city: london

country: UK

Below is the result of your feedback form. It was submitted by Brandon Cooke () on Monday, February 23, 1998 at 10:27:14

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state: Maryland

city: Bethesda

country: USA

comments: Box B is the box for me....

To: rbarnett@grits.valdosta.peachnet.edu

Date: Mon, 23 Feb 1998 11:17:02 PST

Content-Type: text/plain

Content-Length: 166

Status: O

X-Status:

I choose box A because of the lower % it takes to win.

Date: Mon, 23 Feb 1998 11:17:57 PST

Content-Type: text/plain

Content-Length: 147

Status: O

X-Status:

Box c is a winner! That's my choice

To: rbarnett@grits.valdosta.peachnet.edu

Date: Mon, 23 Feb 1998 11:15:57 PST

Content-Type: text/plain

Content-Length: 122

Status: O

X-Status:

I choose c

______________________________________________________

Get Your Private, Free Email at http://www.hotmail.com

Below is the result of your feedback form. It was submitted by Jamie Dreier () on Monday, February 23, 1998 at 15:33:17

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state: RI

city: Providence

country: USA

I'd go with B, but actually I'd feel bad if you guys had to

pay out \$10 to lots of people!

Below is the result of your feedback form. It was submitted by Drew Golden () on Tuesday, February 24, 1998 at 03:13:30

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state: CA

city: LA

country: USA

comments: Box c. Zeno was a logician not a mathemetition

Below is the result of your feedback form. It was submitted by Ken Duisenberg () on Thursday, February 26, 1998 at 12:30:38

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state: CA

city: Roseville

url: http://www.ecst.csuchico.edu/~kend/potw/

country: USA

comments: B - It's not my money. I'd rather win the most I could.

And if I don't, I'd rather save Charles his money.

Below is the result of your feedback form. It was submitted by Dan Duisenberg () on Thursday, February 26, 1998 at 15:24:45

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state: CA

city: Fremont

country: USA

comments: Sign me up for Box B.

Below is the result of your feedback form. It was submitted by Jim Harrington () on Thursday, February 26, 1998 at 23:43:41

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state: NH

city: Londonderry

country: USA

comments: Box "C" it is- I tend to doubt that 3/4 of the people responding trust the same amount of responders to choose Box "B"... it just doesn't seem likely to me... so I'll be perfectly content with my \$5... and if it turns out I was wrong, well- that's what I get, I guess...

Below is the result of your feedback form. It was submitted by Kenny Wright () on Friday, February 27, 1998 at 13:28:49

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state: CA

city: Rocklin

country: USA

Below is the result of your feedback form. It was submitted by Pete Duisenberg () on Friday, February 27, 1998 at 21:39:24

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state: CA

city: Auburn

country: USA

Below is the result of your feedback form. It was submitted by David Perone () on Monday, March 2, 1998 at 03:48:02

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state: IL

city: Chicago

country: USA

comments: Of course everyone will choose the highest paying box. I choose box B.

Below is the result of your feedback form. It was submitted by Clint Morgan () on Monday, March 2, 1998 at 20:44:56

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url: none

country: USA

Not simply because it yeilds the highest payout, but for the reason that it yeilds the highest payout. (HA, HA) :-)

Hoping and assuming that everyone playing is at least partially logical, it is obvious that they would choose B as I have and expect everyone else to choose B, as I have. This expectation does'nt come because of the clandestine desire for the highest payout, but the logical realization that, through an assumed teamwork, the 3/4 criteria could easily be met.

Below is the result of your feedback form. It was submitted by Shack Toms () on Tuesday, March 3, 1998 at 10:54:28

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state: VA

city: Charlottesville

country: USA

comments: I choose A. In the previous challenge the conditions for choice A were the closest of the three to being met, so it seems to me that it is the most likely to be met of any of the three. The lure of the \$10 may be great, but I think that the satisfaction of winning the contest with the more likely A may offset the more remote satisfaction of the \$10. By the way, will Charles decide when to end the challenge before or after tallying the results?

Subject: Submitted Form

>Below is the result of your feedback form. It was submitted by John () on

Tuesday, March 3, 1998 at 17:19:58

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>

>state: NH

>

>city: New London

>

>country: USA

>

>

Below is the result of your feedback form. It was submitted by Steve Maynard () on Wednesday, March 4, 1998 at 15:04:15

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state: PA

city: Erie

url: http://www.geocities.com/Athens/Parthenon/6598

country: USA

comments: I'm choosing box A... it maximizes my potential of winning anything... even though I think that too many people will jump at either B or C, despite their unlikely probablities, for me to win anything... cool interpretation of prisoner's dilemma though!

Below is the result of your feedback form. It was submitted by will downing () on Wednesday, March 4, 1998 at 18:33:14

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state: NV

city: las vegas

url: n/a

country: USA

Below is the result of your feedback form. It was submitted by andi richi () on Wednesday, March 4, 1998 at 21:11:41

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state: wv

city: shepherdstown

country: USA

comments: I choose box A. I consider the amount of money offered to be practically irrelevant; what's the big difference between one dollar and ten dollars? Obviously, the answer is nine dollars, BIG DEAL! Now consider the probability of the choices of those playing along, since this is what is relevant. The choice with the best probability of selection is box A.

Below is the result of your feedback form. It was submitted by James Worthy () on Thursday, March 5, 1998 at 06:47:10

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country: USA

comments: Go for C--b-s will never make it

Below is the result of your feedback form. It was submitted by Justin Nichols () on Thursday, March 5, 1998 at 14:14:46

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state: Georgia

city: Valdosta

url: http://www.valdosta.edu/~jdnichol

country: USA

comments: I choose Box B in hopes that everyone else who is playing would like 10 bucks from Dr. Barnette. If not...oh, well. Good puzzle Dr. Barnette!!

Below is the result of your feedback form. It was submitted by T-DOG () on Friday, March 6, 1998 at 08:40:37

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state: GEORGIA

city: VALDOSTA

country: USA

Below is the result of your feedback form. It was submitted by Kyle Calderhead () on Friday, March 6, 1998 at 10:48:05

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state: MN

city: Minneapolis

country: USA

No, this won't win. Probably nobody will -- especially if someone went to the trouble to figure out a "safe bet" (I notice that the payout ratios have been changed). It does raise an interesting question though -- if this experiment is repeated (even without the real money) several times, does any choice _eventually_ win once people have a better idea of what other people will do?

Below is the result of your feedback form. It was submitted by Deb Peaks () on Friday, March 6, 1998 at 13:56:13

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url: None

country: USA

comments: I pick A--takes fewer to win!

Below is the result of your feedback form. It was submitted by Lauren () on Friday, March 6, 1998 at 17:26:30

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state: N.S.W.

city: Sydney

country: Australia

comments: I guess I choose 'B' because I'm greedy and frankly, expect everyone else to be too.

Below is the result of your feedback form. It was submitted by Jim Stevens () on Sunday, March 8, 1998 at 15:43:48

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country: USA

Below is the result of your feedback form. It was submitted by Mary M () on Sunday, March 8, 1998 at 15:46:12

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country: USA

comments: I choose Box c, since a's will cancel out b's! I hope!!

Below is the result of your feedback form. It was submitted by Michelle Abellera () on Tuesday, March 10, 1998 at 07:53:37

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state: Kent

city: Canterbury

country: UK

comments: Box A because the chances that 3/4 of the people will pick box B are low- there are always idiots like me out there that will prevent the "B-choosers" from ever reaching 3/4. If what I said didn't make any sense, don't worry- I didn't understand it either. :P

Below is the result of your feedback form. It was submitted by Henri Peacock () on Wednesday, March 11, 1998 at 16:48:01

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country: USA

Below is the result of your feedback form. It was submitted by D.L.Rahe () on Wednesday, March 11, 1998 at 17:57:51

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state: CO

city: Westminster

country: USA

Below is the result of your feedback form. It was submitted by Emily Rahe () on Wednesday, March 11, 1998 at 17:59:20

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state: CO

city: Westminster

country: USA

Below is the result of your feedback form. It was submitted by Matthew Meyer () on Thursday, March 12, 1998 at 14:07:40

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state: OH

city: Massillon

url: http://gozips.uakron.edu/~meyerm

country: USA

Below is the result of your feedback form. It was submitted by Ross P Cameron () on Friday, March 13, 1998 at 08:32:16

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city: Glasgow

country: Scotland

comments: I choose box A purely because it requires the smallest number of people to choose it for a reward to be given. It therefore has the best possibility of success. I still don't think however that anyone will receive any money, because box A has the best chance for success but it still requires a third of the people to choose it. ie the votes must be shared equally between the three choices OR A must be in favour of A, I don't beleive this will happen as others will rely on everyone else to choose the higher award possibilities. So by doing this I'm probably spoiling others chances, but there you go. Life isn't fair!!

-----Original Message-----

From: Roy Abrams <Roy Abrams>

To: rbarnett@grits.valdosta.peachnet.edu

<rbarnett@grits.valdosta.peachnet.edu>

Date: Sunday, March 15, 1998 4:13 PM

Subject: Submitted Form

>Below is the result of your feedback form. It was submitted by Roy Abrams

() on Sunday, March 15, 1998 at 16:13:28

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>state: IL

>

>city: Univ. Chicago

>

>country: USA

>

>comments: I go for box c!

>

Below is the result of your feedback form. It was submitted by Yorick Liddleman () on Sunday, March 15, 1998 at 20:10:13

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country: USA

Below is the result of your feedback form. It was submitted by () on Monday, March 16, 1998 at 21:31:45

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country: USA

Below is the result of your feedback form. It was submitted by Josh Bombino () on Tuesday, March 17, 1998 at 19:21:40

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state: Pennsylvania

city: Bethlehem

country: USA

Below is the result of your feedback form. It was submitted by Garrett Lack () on Wednesday, March 18, 1998 at 21:38:43

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state: CA

city: santa cruz

country: USA

Below is the result of your feedback form. It was submitted by Everett Atkins () on Thursday, March 19, 1998 at 22:12:44

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state: PA

city: Pittsburgh

country: USA

comments: I select box a, since it takes the least number to win...

Below is the result of your feedback form. It was submitted by William A Alder () on Friday, March 20, 1998 at 11:59:05

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state: TN

city: Knoxville

country: USA

Below is the result of your feedback form. It was submitted by Carl () on Sunday, March 22, 1998 at 13:05:19

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state: Missouri

city: Monett

country: USA

comments: Having nothing to lose and everything to gain why would any rational individual choose anything but B?

Below is the result of your feedback form. It was submitted by Eric Sotnak () on Sunday, March 22, 1998 at 22:08:36

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state: OH

city: Akron

country: USA

comments: B. My goal is entirely mercenary: \$10 sounds like a good deal for very little effort (filling out this entry). The answer is the best choice if it pays, just as one has bought the right lottery ticket if it pays (irrespective of any probabilities involved). It is the wrong answer if it fails to yield \$10. Not having to purchase a lottery ticket here, I can live with that.

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Below is the result of your feedback form. It was submitted by Michael A. Schell () on Tuesday, March 24, 1998 at 08:59:04

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state: Ontario

city: Gravenhurst

url: http:\\www.geocities.com/Athens/Parthenon/6175

Nobody Else is going to choose A. They will think that everyone else will choose B. So Why am I picking A??? Cause nothing anyone ever does EVER makes sense.

Below is the result of your feedback form. It was submitted by Acerbus () on Wednesday, March 25, 1998 at 12:12:00

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state: Ontario

city: Gravenhurst

Below is the result of your feedback form. It was submitted by Bill Talbott () on Wednesday, March 25, 1998 at 18:33:07

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state: WA

city: Seattle

country: USA

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Below is the result of your feedback form. It was submitted by Cindy Zuschlag () on Wednesday, March 25, 1998 at 18:55:44

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state: PA

city: Greenville

country: USA

comments: Box A, because that way I maximize my chances at winning SOMETHING.

Below is the result of your feedback form. It was submitted by Laszlo J. Taba () on Tuesday, March 31, 1998 at 16:46:34

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state: Va

city: Fairfax

country: USA

comments: Box B, because I think that more people will go for more

money, and I'm poor.

Below is the result of your feedback form. It was submitted by Reena () on Tuesday, March 31, 1998 at 17:35:14

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state: GA

city: Valdosta

country: USA

Below is the result of your feedback form. It was submitted by Shayla () on Tuesday, March 31, 1998 at 17:40:50

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state: United States

city: Valdosta, GA

country: USA

comments: I choose Box C because no one wants to win only \$1 (Box A). Everybody wants to win \$10, but are afraid to pick that box because if 1/2 of the people don't agree, they won't win anything. So, logically, Box B is the way to go.

Below is the result of your feedback form. It was submitted by SEAN TENNEY () on Wednesday, April 1, 1998 at 15:55:27

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state: GA

city: VALDOSTA

country: USA

comments: It seems to me that most people, greedy urchins that they are, would pick box B because it has the highest monetary value. Thus, box B is my choice.

Below is the result of your feedback form. It was submitted by Milla Suomalainen () on Thursday, April 2, 1998 at 10:00:09

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city: Parikkala

country: Finland

Below is the result of your feedback form. It was submitted by John Pormann () on Friday, April 3, 1998 at 12:42:31

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state: NC

city: Durham

url: www.ee.duke.edu/people/jpormann.html

country: USA

Below is the result of your feedback form. It was submitted by Kenneth E. Roko () on Monday, April 6, 1998 at 23:58:22

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state: PA

city: State College

country: USA

Below is the result of your feedback form. It was submitted by Charles Albright () on Thursday, April 9, 1998 at 05:00:50

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state: ca

city: Sacramento

url: csus.edu

country: USA

comments: Any one who picks B or C is a fucking idiot. There will always be people like me to fuck it up for every one else

Below is the result of your feedback form. It was submitted by Jaakko Puolimatka () on Tuesday, April 14, 1998 at 06:38:53

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state: -

city: Oulu

country: Finland

comments: Box A: There are three choices, so every box gets 1/3 of the 'choises'. But if players are 'smart-smart' they know that everybody chooses box A. So everybody '2nd degree smart' chooses beetween boxes B and C, so 1/2 is the right answer (and box C) But if everyone is that smart, they all pick up the same box, so there is not really a right box. However, if there are enough players, who pick their box random, every box gets 1/3 of choises.

Below is the result of your feedback form. It was submitted by Rachel Greshes () on Tuesday, April 14, 1998 at 00:18:17

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state: FL

city: Palm Bay

country: USA

Hopefully enough people would want that outcome and would choose the same, resulting in 3/4 of the people picking the same.

Below is the result of your feedback form. It was submitted by Michael Walsh () on Tuesday, April 14, 1998 at 16:57:41

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state: Il.

city: Wheaton

country: USA

Below is the result of your feedback form. It was submitted by mike zeddies () on Friday, April 17, 1998 at 00:36:16

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state: mi

city: ann arbor

country: USA

comments: I choose B. This is in fact what I wish everyone _else_

to do--and for starters, if I am to win anything, there

needs to be _some_ sort of winner. In order for choice A

to win, I'd have to hope that those who select B or C

number no better than if the choices were random. However,

I feel there is a great incentive for others to choose

either B or C, and particularly B, thus making it unlikely

that A would garner the votes necessary to make it the

winning choice. Which leaves B and C--B's not bad, but I

think people are either going to be clever and smug, and

choose A, in order to "play it safe", or choose B, because

of the huge reward. C, being the "moderate" choice, I feel

will not garner more than it's share under a random

selection process, because it seems too "wimpy" or "tricky".

Which leaves C--and I think that if I want to do as well as

I can, I ought to at least perform in a manner which will

benefit the most people in the best way--that is, if 3/4

of the voters were to win \$10. I should behave in the

manner most likely to produce the best results, in the

manner which I believe others--or any agent in this

situation--ought to behave. I also want myself to win the

best award available, so I cast my vote for what is, in

fact, the best reward!

Below is the result of your feedback form. It was submitted by Brandon Bakken () on Friday, April 17, 1998 at 09:56:08

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state: Wi

city: Albany

url: P.O. 129

country: USA

Below is the result of your feedback form. It was submitted by Jason () on Friday, April 17, 1998 at 14:38:35

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state: MO

city: St. Louis

country: USA

Below is the result of your feedback form. It was submitted by David M. Lundeen () on Friday, April 17, 1998 at 17:21:47

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state: MI

city: Ann Arbor

country: USA

Below is the result of your feedback form. It was submitted by Amy Howard () on Friday, April 17, 1998 at 17:28:48

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state: Kentucky

city: Florence

country: USA

comments: Box A -- I'm sure you don't want to pay out any more money than you have to -- so I'm reasoning that Box A is the right answer. If the other respondents use the same logic as myself, they'll choose the same answer.

Below is the result of your feedback form. It was submitted by Ryan Earehart () on Saturday, April 18, 1998 at 16:20:50

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state: AZ

city: Lake Havasu City

country: USA

comments: \$1 or box A because 1/3 is less than one half or 3/4ths

Below is the result of your feedback form. It was submitted by James Cleere () on Saturday, April 18, 1998 at 21:46:05

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city: Toronto

Below is the result of your feedback form. It was submitted by Amy Musgrove () on Saturday, April 18, 1998 at 21:47:03

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state: CA

city: Berkeley

country: USA

Below is the result of your feedback form. It was submitted by Scott Sulsberger () on Sunday, April 19, 1998 at 16:18:31

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state: Ga

city: Valdosta

country: USA

comments: Box B.....There is more money to win than the other boxes. People will be

lured into the higher monetary purse and in so doing fulfill

the reqirment that 3/4 choose box b.

Below is the result of your feedback form. It was submitted by Alex Tracy () on Sunday, April 19, 1998 at 17:34:57

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state: GA

city: Atlanta

url: userwww.service.emory.edu/~rtracy/index.htm

country: USA

I like going out on a limb.

Below is the result of your feedback form. It was submitted by Charles Peters () on Sunday, April 19, 1998 at 20:36:30

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city: Vancouver

country: BC

comments: Box A--since nobody likes a loser!!

Below is the result of your feedback form. It was submitted by Janice Armstrong () on Sunday, April 19, 1998 at 20:37:55

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state: WA

city: Seattle

country: USA

Below is the result of your feedback form. It was submitted by Liz () on Monday, April 20, 1998 at 02:22:23

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state: MN

city: northfield

country: USA

comments: Choice...B. The odds are that no one will win anything in all three cases because everyone will vary so much that no real consensus could be drawn, so I will try for the most money. :)

Below is the result of your feedback form. It was submitted by Jeff Glick () on Monday, April 20, 1998 at 04:26:45

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state: ca

city: valencia

country: USA

comments: This is practically hopeless. Each choice requires, as a necessary part, that some particular fraction of the respondants pick the particular box in question. Yet logically, if there is a discrepency between the exact proportion of people who choose the letter and the proportion of people required to choose the letter, then nobody wins. Consider the following possibility: Suppose that precisely twenty-five people play. In that case, it will be logically impossible for there to be any winners whatsoever, as 25 is not evenly divisible by 2,3, or 4 (which is of course required to acheive an exact poriton of 1/2, 1/3, or 1/4 respectively).

Below is the result of your feedback form. It was submitted by Chase Knight () on Monday, April 20, 1998 at 10:54:57

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country: USA

comments: Box B ...If people over analyze this choice,and choose the

other two boxes then that will disturb me very much so.

Below is the result of your feedback form. It was submitted by Jeff Bourgeois () on Wednesday, April 22, 1998 at 21:45:25

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state: LA

city: Bossier City

country: USA

comments: Box B is obviously the Value Choice.

Below is the result of your feedback form. It was submitted by Adam Potthast () on Thursday, April 23, 1998 at 01:00:59

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state: MO

city: Kirksville

country: USA

comments: I choose Box B -- a simple choice because I have nothing

to lose, so I should maximize my gain. The only reason to

pick A or C is distrust in thinking that someone is actually

more likely to send out \$1 instead of ten. However,

if there is doubt about the motives of the sender at all

then one should not care which amount is given.

The smart choice is Choice B, since there is no investment.

Below is the result of your feedback form. It was submitted by Sarah Small () on Monday, April 27, 1998 at 16:26:05

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state: OH

city: Akron

country: USA

Below is the result of your feedback form. It was submitted by Helen Freeman () on Monday, April 27, 1998 at 16:26:45

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state: GA

city: Atlanta

country: USA

Below is the result of your feedback form. It was submitted by Alfie Johnson () on Monday, April 27, 1998 at 16:27:46

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state: CA

city: SF

country: USA

Below is the result of your feedback form. It was submitted by Liz McKinney () on Tuesday, April 28, 1998 at 22:44:12

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state: FL

city: Gainesville

country: USA

Below is the result of your feedback form. It was submitted by Carles Rudman () on Tuesday, April 28, 1998 at 22:45:36

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city: Oxford

country: UK

comments: I select box A, since its odds are favoured

Below is the result of your feedback form. It was submitted by Harry Nesomber () on Tuesday, April 28, 1998 at 22:46:34

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state: Utah

city: Salt Lake City

country: USA

comments: I go for box c

Below is the result of your feedback form. It was submitted by () on Wednesday, April 29, 1998 at 18:53:54

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country: USA

Below is the result of your feedback form. It was submitted by ernie claere () on Saturday, May 2, 1998 at 21:20:16

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url: Quebec city

country: USA

Below is the result of your feedback form. It was submitted by pierre natesne () on Saturday, May 2, 1998 at 21:21:31

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city: quebec city