jeff@heurikon.UUCP (02/09/84)
A few weeks ago I asked net.math if anybody knew of the results of the "Luring Lottery". Here is a summary of the lottery details and the responses I received concerning the results. Don't read this if you're in a hurry (it's pretty thick) - come back later. Summary of the Luring Lottery ######################################################################### Part I: Summary of the original article where the lottery was announced: (This is based on an article which appeared in the June 1983 issue of Scientific American. It was in the regular mathematical column and was written by D. Hofstadter. I'm recalling this from memory so the specifics (numbers, etc) are just approximations.) The author began by discussing a paradox which resulted from a "game" played by independent, rational, intelligent people. Such a group was chosen to participate an were asked to pick one of two alternatives. One alternative was called "C" (for "cooperate") and the other was "D" (for "defect"). Each person stood to "win" a certain amount of money depending on how they and the others replied. None of the players were aware of the other players responses. If all participants said "C" they would each win, say, $30. However, If one (and only one) of them defected and said "D", that person would win more (e.g., $50) and the others would win less ($10). If many of them said "D", all would win very little ($2). The result of this is that if all "cooperated" they would each win a modest amount, if one person "defected" the defector would take home more than those who "cooperated" and if many "defected", all would loose. How would you respond? Cooperate means you could win but if just one of the others defects you'd "loose". Why not be the only defector? Would you be? If each person thought they would be the only defector they should defect. But if each thought that, they might *all* defect, thus loosing. ARGH!!!! What to do, what to do? The author detailed the actual results of such a game he played using 20 of his colleagues. If all participants were totally rational and logical they should *all* choose to cooperate, because they would all realize that that was the only way for them to maximize their own return. The central theme was that since each person *should* think along the same lines (the logic would compel them to do so) each should cooperate, realizing that the others will do so too. The actual discussion of this took many pages, so I won't say more except to suggest you read the article if you're interested. Anyway, the players in the actual game made a few "emotionally" based responses and 20 or 30 percent "defected". Too bad. With that as background, the author announced the "Luring Lottery". Anybody who wished could enter. The prize was $1,000,000/N where "N" was the total number of "entries" received. The only cost of entering was the stamp for a postcard. Furthermore, you could increase your own chances of winning by entering more than once, but doing so would also reduce to value of the prize - for everyone. You could enter as many times as you liked using only one postcard just by indicating the number of entries you wanted to make on that single card. The prize would be: $1,000,000 ----------------------- total number of entries ####################################################################### Part II: The responses to my request for results: The first response, which I received very promptly, was: > Well, here is a situation very similar to what D.H. was talking about. > Do I send a reply, along with 200 other people, and help to flood > the net or do I flip a coin and let it decide? > > The Luring lottery was Hofstadter's swan song. He went into a harangue > about how someone could have made a fortune if we had all cooperated, > described the various attempts to represent numbers slightly less than > infinity, refused to say who had come closest, then wished a pox on us > all and resigned. > Griff Smith, AT&T Bell Laboratories Thereafter, my mail was very quiet. I was beginning to think Griff had a point (would he be the only respondent or was the flood yet to come?) Then I started getting requests for copies of whatever further info I received. Laura Pearlman (trw-unix!pearlman) had these comments on the results: > I don't remember which issue the results were published, but here's > what I remember about the entries: > > Number of people Size of entry > 1 Avogadro's number > some very, very big (> 1,000,000) > some more 1,000,000 > a few relatively small (1<n<100) > many 1 > > According to the comments on the postcards which people sent > their entries on, Hofstadter (or was it Martin Gardner?) concluded that > each person who sent in a large entry seemed to think that he or she > was the only person to do so. > He also said that many of the people who sent in one entry > seemed to think that that was the "rational" thing to do. (I'm not > sure of my terminology -- it's been awhile. What I mean is that they > seemed to think that sending in one entry was the best thing to do, > working under the assumption that everyone else will decide to do > whatever you decide to.) He received NO cards of the form he was > hoping for, which was "Well, I think that N people will probably enter, > so I used my handy-dandy random number generator to get a number > between 0 and 1, and I'm sending in (one entry/no entries) because > the number I got was (less than/greater than) N." And Tom Turano provided the details: > The approximately 2000 entries had the following distribution: > number of entries/card number of cards received > 1: 1,133 > 2: 31 > 3: 16 > 4: 8 > 5: 16 > 6: 0 > 7: 9 > 8: 1 > 9: 1 > 10: 49 > 100: 61 > 1000: 46 > 10**6: 33 > 10**9: 11 > 6.023x10**23: 1 > 10**100 (googol): 9 > 10**googol: 14 > > Obviously most of the people who read the article failed to get the idea. > Hofstadter laments this, not that he really expected otherwise. Well, I guess *somebody* got a little bit of nothing.... And the postage required just to send out the prize certainly would have been may times the value of the prize itself. What could be loosely termed "results" were were published in the September issue. What really bothers me is this: Why would *anybody* want to send in an entry with any number greater than, say 1000? If you send anything really big in, you destroy the prize. I think that the original instructions were unclear and people not only thought they stood a better chance of winning by submitting many entries but also thought the prize would be relatively high. It's simply sabotage to submit a lot of entries. Hao-Nhien Vu (pur-ee!vu) wants to "calculate a theoretical optimization of that lottery". Good luck, Hao-Nhien!! I think there are better odds being at the end of a chain letter a chain letter. :-) ######################################################################## Part III: An additional comment: If you've read this far, maybe you would like to ponder this: What if the rules of the Luring Lottery were modified slightly so as to make *everybody* a winner in direct proportion to the number of entries they submitted. Obviously, rather than the total award being zilch as with the original lottery, the total payoff now would be $1,000,000. Each "entry" would be awarded exactly $1,000,000/N, where "N" is the total number of entries received. Just think! If only a thousand people entered AND if each only entered once, each would win $1,000. However, if one of those thousand people wrote "one billion" on their entry (the others still entering only once) *that* person (a defector) would walk away with nearly all the prize: [1.0E9 * ($1.0E6/(1,000,000,999)]. Wow! Wouldn't you like to be the *only* person to feed in ten octodecillion entries? But, what if everybody tried to play that sneaky trick?. I guess you'd win roughly $1,000,000 divided by the number of people who submitted entries - as long as nobody came closer to infinity than you did! The only sure winner would be the post office. I'd just love to try such a lottery here on the net, but I don't want to be responsible for funding the prizes. What we ought to do is require an entry fee of some sort. Nah! we'd all find some way to cheat. And who could tell one infinity from another? ######################################################################### Please direct any further discussion of the Luring Lottery to the net. I've exhausted my thoughts on the subject. Cheers! -- /"""\ Jeffrey Mattox, Heurikon Corp, Madison, WI |O.O| {harpo, hao, philabs}!seismo!uwvax!heurikon!jeff (news & mail) \_=_/ ihnp4!heurikon!jeff (mail - fast)
jeff@rlgvax.UUCP (Jeffrey Kegler) (02/10/84)
Could someone tell me what happened to Hofstadter's Scientific American
column? It seemed to disappear rather suddenly, and without explanation.
--
Jeffrey Kegler, CCI Office Systems Division
...{allegra,seismo,mcnc,lime,brl-bmd}!rlgvax!jeffjeff@heurikon.UUCP (02/15/84)
> was there anything in the rules which would prohibit people from sending > in a card with a number less than zero to reduce the impact of folks who > sent in a card with very large amounts? > > chongo <-1*(10^(10^100))> /\--/\ Yes, the integer must have been positive. But, even if you *could* submit a negative number, in order for it to have any effect on the results it would have to be larger (in absaolute value) than any of the positive entries. If it wasn't, it would simply be swamped by the (probably) much larger positive entries, and have little effect. -- /"""\ Jeffrey Mattox, Heurikon Corp, Madison, WI |O.O| {harpo, hao, philabs}!seismo!uwvax!heurikon!jeff (news & mail) \_=_/ ihnp4!heurikon!jeff (mail - fast)