The name of the show is 'Unan1mous' so we can presume the vote for the winner needs to be unanimous. It will be interesting to see if contestants will be able to vote for themselves. Either way it will be interesting. I am going to refrain from predicting what will happen here until we get a better sense of the rules (tune back in March) but it should be clear to all that the basic set-up here is akin to the Prisoners' Dilemma: in order to generate the maximum prize, all but one individual will have to sacrifice winning anything at all. This is usually a recipe for social disaster and I am pretty sure that is what Fox is banking on. Even better, the bigger the disaster, the cheaper the program is to produce.
Experimental economists go to alot of trouble to conduct experiments that test the predictions of game theory. But reality television is offering a new dimension to all of this with much higher stakes. In an earlier era, Scientific American offered its own slice of reality. Formulated by Douglas Hofstadter, in June 1983, Scientific American made the following (seemingly extraordinary) offer:
Well, what happened? It turned out that the vast majority of people in the world sacrificed for the common good and did not subit a 'claim.' However, a few thousand others did including one person for a googol entries (that is, 10 to the power of 100 or what Google would have been called if their founders could spell). So there was no chance of Scientific American paying out.
This talk of holding back in the face of strong temptation brings me to the climax of this column: the announcement of a Luring Lottery open to all readers and nonreaders of Scientific American. The prize of this lottery is $ 1,000,000/N, where N is the number of entries submitted. Just think: if you are the only entrant (and if you submit only one entry), a cool million is yours! Perhaps, though, you doubt this will come about. It does seem a trifle iffy. If you'd like to increase your chances of winning, you are encouraged to send in multiple entries without limit. Just send in one postcard per entry. If you send in 100 entries, you'll have 100 times the chance of some poor slob who sends in just one. Come to think of it, why should you have to send in multiple entries separately? Just send one postcard with your name and address and a positive integer (telling how many entries you're making) to:
Luring Lottery c/o
You will be given the same chance of winning as if you had sent in that number of postcards with ‘1' written on them. Illegible, incoherent, ill-specified, or incomprehensible entries will be disqualified. Only entries received by 5:00 PM on June 30, 1983 will be considered. Good luck to you (but certainly not to any other reader of this column)!"
Given this, it is a wonder why Fox didn't make this more interesting: say $10m or $100m or even a googol million! But how much faith you one put in game theory translating into reality.
For any of my students out there, one thing you can be sure of: I am going to find a way for this to be on the exam.