ZENO'S COFFEEHOUSE Results #8
The Eighth Coffeehouse Challenge
THE LOUIS MARINOFF CHALLENGE
As a result of two previous challenges (#1 and #5), Professor Louis Marinoff (City College of New York) has requested that Zeno's patrons be given a chance to re-address the earlier attempts at decision-making under uncertainty, in light of a thoughtful analysis he constructed of the situation before you. Recall that the earlier two results yielded _no winners_ in the no-risk choice-situation under review. According to Marinoff, this 'Tragedy of the Coffeehouse' would be avoided, upon review of his analysis. As he states in his concluding remarks below,
"Nonetheless, I assert that if a third empirical trial
were held, and that if each player were rational and contemplated
this analysis before choosing, then the tragedy of the coffeehouse
would be averted. Sufficient numbers of formerly costly riders
would switch to box B, such that at least one-fourth of the players
(and possibly very many more) would select that option. So my
prediction about human behavior in our problem is recursive: I
predict that at least one-fourth of those who reason through my
prediction will corroborate it."
So we decided at Zeno's to repeat for a third time the initial challenge, and to take up Louis Marinoff's challenge to the challenge. What follows is the challenge, along with the latest results. Marinoff's orginal analysis is included here.
Our challenge involves a hypothetical decision-making problem, in repeat of the first and fifth, with no risk and only possible gain, if you choose correctly. The choice has you decide in favor of your reasoned self-interest, in light of what you think others will decide on theirs, and how they think others---including you---think they will decide, etc. Give this some thought, and then choose either Box A or Box B in your response. You may wish to review the results of the earlier Zeno's challenge in light of this new opportunity...it might make a difference, or it might not.
Rules:
1. If you choose Box A, you will receive $1000, as long as everyone else chooses Box A as well; otherwise, nobody who chooses Box A will receive anything.
2. If you choose Box B, you will receive $100, as long as at least one-fourth of others choose Box B as well; otherwise, nobody who chooses Box B will receive anything.
As you reflect on your perceived options and review the results of the earlier runs at this decision-scenario, make up your mind and make your choice, Box A or Box B.
THE RESULTS!
Thirty-Four entries (only) were submitted this time, and FOUR votes were cast for Box A, with the other THIRTY going for B! So we have thirty hypothetical winners! This is exactly what Marinoff predicted would happen. However, some found fault with the way he set it up, and some disagreed with Marinoff's analysis. I have included the responses below for you to read. This was indeed fun, and intellectually challenging---and I'm not convinced we've heard the last word! Cheers, and enjoy...
From: Michael Britton
Well, I'm all for option B, but that would have been true from the
outset. The chances of everyone choosing option A are pretty low, and
even if it were a clearly rational choice, I think there would still be
someone who'd do something else. (Professionals are predictable, but
the world is full of amateurs!)
The mathematical demonstration provided by Marinoff didn't really affect
this decision, except perhaps to convince me that it would be even more
likely that people would choose option B instead of A.
Marinoff's statement about players falsifying predictions is
interesting, though. A situation which is akin to this is the game
"rock, paper, scissors." The first game between two total strangers who
say nothing is purely random. If, however, one of them says, "I know
that you're going to choose a rock," the game has changed entirely, and
it becomes a matter of guessing how the psychology will work out. Such
a statement effectively destroys the symmetry of the game. Similarly,
if both players choose the same option in a first trial, the second has
lost its randomness, since the symmetry of the three options has been
eliminated.
To explore this, I propose a follow-up game, which I will call the
division game. Here's how it works.
Players have the option of joining team A or team B. They do this
secretly. They may also post information publicly when they choose
their team (but not before!). Before choosing their team, they should
read over that public information from previous players, since it might
influence their decision. Players are not constrained to be truthful in
providing this information, though, so beware!
At the end (and since this is time-dependent, the deadline must be known
at the outset!), the number of people on each team is made known, and
10,000 (imaginary) dollars is divided among the people on each team.
The objective of the players, of course, is thus to be on the SMALLER
team!
It would also be interesting to try this in a situation where people
could post information before deciding their team, or where private mail
between players could be exchanged... lots to explore here.
Just thoughts...
Mike &8-D
From: Maris Darbonis
I choose box B.
Hey, this is really a different experiment from those first two. The short formulation of it is: you can
choose between box A and B as you like, but do choose box B.
In addition to my considerations I get the authoritative analysis of
Louis Marinoff.
Maris
From: Gilles Gour
Bonjour,
in the light of all the convincing theoricizing (spelled
correctly?)that has been going on about this challenge, I think that the
probability of all participants choosing "A" is closer than ever to nil.
I will therefore obediently join the statistical herd and vote for box
"B". Or should I...
Gilles Gour
Montreal
From: Erik J Tielking
BOX B
From: "William R. Wagenseller"
Organization: HEALD COLLEGES
I choose BOX B - A real no brainer as Louis Marinoff has already stated HE is going to choose BOX
B & hence
not everyone is choosing BOX A.
However, if Mr. Marinoff is not playing the game, I would go with BOX A.
REASON: If anyone does not choose BOX A, then all who did would be made losers by the one who
did not choose
it. Via the golden rule - a classical rule for decision making - I choose BOX A because that is what
I would
wish everyone to do for me.
From: Karim Abdel-Hadi
Subject: Box B
And even though I didn't bother reading that big long explanation, I
just assumed that common sense would dictate that not everyone would
pick the same thing, therebye making box A a rather stupid choice.
If this one works out though (meaning everyone wins), what do you
suppose would happen if instead of $1000 (or whatever it was), everybody
who chose box A could win $1 000 000 providing that 4/5 of the people
picked it, and that everyone who chooses box B could win $100 (or
whatever) iff 2/5 of the people pick it?
From: Joe Tamburro
Box B all the way. I chose this before, btw, for similar reasons to
those espoused by the prof.
From: shack@esinet.net (Shack Toms)
OK, I agree with Louis Marinoff's analysis. I'll choose B.
Now where do I want to spend that virtual $100..... Hmmm......
This is a fascinating twist to the problem and if LM is correct
(as I believe he is) should result in a dramtic shift in
behavior. If so then this will show the power of education in
that without the analysis a repeat of the former tragedies would
have been likely.
Interestingly, even if his analysis were faulty it would still
have been self-fulfilling in that it would be almost beyond
comprehension that no one would fall for it.
Shack
From: Mark Young
Organization: Acadia University
Once again I vote for B!!!
But I'm not convinced that Marinoff really understands the Internet. If
he really wants to win this contest (that is, get 1/4 of the people to
vote for B), he shouldn't spend his time writing long, boring (sorry, but
it was pretty boring) articles about why people should vote for B. I
mean, *I* read it (and the original argument, which I used to inform my
second vote), but I'm a math geek from way back. What this campaign
needs a short, plausible argument and a memorable slogan. Here's my
version:
---
Look, there are always a few assholes around -- people who just want to
be contrary. If we vote A, they'll vote B, and everyone gets screwed (no
one gets any money). If we vote B, they'll vote A, and the only ones who
get screwed will be them (we all get $100, and they get nothing). That
means the best bet for the rest of us (non-assholes) is to vote B. Don't
let the anti-social people cheat you out of $100.
A is for Assholes. Vote B.
---
...mark young
From: scott haney
I choose box B! But I'm not rational! I have snakes in my head! wa wa wa
wa where is the hyena? wooooooooo!
--
Scott Haney rhaney@cacd.rockwell.com
From: Rob Meredith
Box B.
Rob Meredith.
From: rodrigo@uclink4.berkeley.edu
I choose option B.
Rodrigo Caceres
email: rodrigo@uclink4.berkeley.edu
From rdeloren@eclipse.net Fri Aug 30 16:54 EDT 1996
From: "Ralph G. DeLorenzo"
Reply-To: rdeloren@eclipse.net
I choose box A.
From: Your Name
Organization: Middlebury College
Box A,
because the best attinable outcome is best understood as a product of
rational self-interest, in which case everyone should choose "A" and
there is no constraint to its attinability.
But then again not everyone chooses rationally.
Better make that Box B.
From: Janine Johnson
b
From: Randy Black
B
I just voted B and wanted you to know that your analysis (below)of my motives on the
earlier vote was right on the mark. Both the maximum payoff and the desire to be a
good guy motivated my choice. Knowing that being a good guy is consistent with B
and that A is a highly improbably payoff have changed my vote. This time it's truly
*enlightened* self-interest.
(Thanks)
Randy Black
UCI
Some, perhaps, were motivated by the
gambler's fallacy: that the wager with the largest payoff is best
(regardless of respective odds). I hypothesize that most who chose
box A did so out of misguided cooperative predisposition. Prisoner's
dilemmas and free riding are lately much-discussed; free riders
attract moral censure; Pareto-optimal outcomes in such problems
are attained through cooperation; choosing box A is the analog of
cooperating; and thus a well-intentioned majority chose box A. Or so
I surmise.
From: Jeramie
I Pick Box A
From: jonathan roy hunsberger
Hey, i'm not changing my answer (of course i never voted before,
this is the first time i've seen this page). After reading the
first one i said 'B', and i still say 'B'. Something like what
Marinoff details was going through my mind, but i'm not the sort
to hash out the gritty details.
From: Bavagnoli
I choose box B
Gabriele
From: Karsten Bohlmann
I chose B the first time. I chose B the second time.
I choose A
now because I think the morons who ruined my gain twice
do not deserve a third chance. So another (O3) would
actually make me feel better (be a bigger gain) than a
virtual 100 bucks ...
From: Emma Osman
I choose box B.
Do I get a real $100??:->
--
Emma Osman
eosman@cybergraphic.com.au
From: "John C. Hollingsworth"
Organization: Graduate Student at UNC Charlotte
B
--
John C. Hollingsworth jchollin@uncc.edu
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41A Hickory Hall (704) 595-5693
UNC-Charlotte, NC, USA 28223
http://www.coe.uncc.edu/~jchollin/index.html
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From: Linda Sayle
Box B - YEAH, YEAH, you've convinced me in the terms of
this test, but in real life, with real money, would anyone
vote for anything but Box A? Aren't we back at the point
of Zeno's paradox which to some extent is the paradox
between the theoretical and the "real" world? (in that the
arrow etc never arrives in the paradox but definitely does
in the world)
Linda Sayle
From: "Judith A. Little"
Box A, eternal optimist that I am.
From: Tim Wright
I choose option B for the 3rd test
From pwoodruf@benfranklin.hnet.uci.edu Sat Oct 5 00:51 EDT 1996
From: "Peter W. Woodruff"
I choose Box B, but I doubt that the (no doubt) triumph of B means very
much, since the (excellent) analysis serves as an opinion leader
undermining the cooperative instinct which supports Box A (to put it
another way, it raises the probability of not choosing A so high that
even the most altruistic can't ignore it). Thanks again for your page;
Peter
From: Sirius
B
From: Suzanne Elizabeth McCalden
In light of the new information, Box B is my choice. Let's hope the
results of this one will bear fruit.
From: Elwood Robinson
box B
From: mfepsdp@afs.mcc.ac.uk
X-Personal_Name: David Potts
I choose box B
From: "Carolyn weiler"
I am choosing Box B, and I am only thirteen,
Thanks, Lauren
From: DCK Curry
Disagreeing with Marinoff's analysis, the only rational choice
on a third try is A. Unless, of course, as is the case,
we know that Marinoff himself will vote for B, guaranteeing that
A cannot be the outcome. His analysis, then, whether right or wrong,
changes the situation in a fundamental way. Hence I must vote for B.
From: Juliean Galak
Box B