"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.
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.
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: firstname.lastname@example.org (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 email@example.com From: Rob Meredith Box B. Rob Meredith. From: firstname.lastname@example.org I choose option B. Rodrigo Caceres email: email@example.com From firstname.lastname@example.org Fri Aug 30 16:54 EDT 1996 From: "Ralph G. DeLorenzo" Reply-To: email@example.com 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 firstname.lastname@example.org From: "John C. Hollingsworth" Organization: Graduate Student at UNC Charlotte B -- John C. Hollingsworth email@example.com ---------------------------------------------------------------- Senior in Geography 41A Hickory Hall (704) 595-5693 UNC-Charlotte, NC, USA 28223 http://www.coe.uncc.edu/~jchollin/index.html ---------------------------------------------------------------- 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 firstname.lastname@example.org 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: email@example.com 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