The "surprise exam" idea is cute enough for me to claim that I was thinking of it before I got to it in reading your post. But is there really any difference between throwing the die beforehand and revealing the winning number n later as opposed to waiting until later to actually make the random choice?

How about 2 identical prize packages: One for the 1000th facebook friend; and the Second for the facebook friend who signs up the most people between now and the time the 1000th person signs up.

The contest sounds . . OK. I just think you should use your radio listeners to winnow though some positions on a debate topic and come to some usable conclusions. things that might be useful to a political decision maker. Take the topic on Fresh Air today _Wired for War, a book by P.W. Singer. This topic should really be one of your philosophy talk topics . . . and then get feedback from your listeners in an organized way - maybe on team . . . and then come up with something useful to pass on to decision makers. You have a goldmine of radio listeners, but I think you need to be more creative in the mining process.
John

The possibility that people would hold off seems far less likely than the possibility that people would collude to hit the mark. With 998 members, for example, a pair of fans (or a fan with a friend) could sign up in quick succession, seizing the prize. The probability of collusion rises with each new member.
One interesting contest rule would be to hold a drawing at 1000, but give those who join earlier better odds.

In the meantime, I won't join the group because doing so might disqualify me from the prize :).

I love you guys...for your minds that is.
Philosophy talk is the only philosophy class since one on Plato 40 years ago at Flagstaff Arizona. I loved it. The teacher would get so excited you thought he was going to collapse before the end of class. If you were on the air back then and if I didn't need to make a living I would'a been a philosopher like you.
BUT......You're over thinking it! THINK OF YOUR ROOTS. What would Click & Clack do? Actually I would advise that you call them and ask them. I'll bet they would solve your paradox on air!
Richard

when you finally announce that you're having a contest, you start counting fans who sign up. you also announce the end date.
each person who signs up between those two dates gets a certain # of votes equal to the total # who signed up minus the position of that person. say you get 1,000,000 people to sign up. the first person would get 1,000,000 chances to win while the last person would get 1.
you reward those who sign up while you're deciding whether to have the contest by giving them the total # of chances too. makes you seem nice.
for those of us who are already fans, we ... um ... get the pleasure of watching this play out from the beginning?
surely someone can get some undergrad credit for writing a facebook plugin to make this happen.
too complicated? how long did it take for us all to learn that office gift exchange mechanism where you can take an opened gift from someone else but then a gift can?t pass to more than 3 people ? depending... but now, we all just mention that squirrely office gift exchange thingy and everyone eagerly shakes their head. you could start "that philosophy talk rewards system" the same way.
or combine these two methods and have three different gifts. you pick three winners in a certain order. the first one picks one of the gifts. the second winner can either take what the first person picked or...
thanks, that was fun!
and you guys are Great!!

Is it really fair to offer a prize only available to those who sign up after the contest is announced? Surely not. A fair contest will give both new and old fans alike a chance of winning. I humbly is that you hold a contest where the winner the person who suggests the contest idea you eventually use.
Of course, it wouldn't be fair if you announced this contest tomorrow and made the winnings only available to those who come up with ideas *after that*. Think of all the people who have already put in so much effort towards designing a contest! No, the only way to make *this* contest truly fair is to make it retroactive--anyone who has submitted a contest idea since 1/14/2009 should qualify.
And yes, the prize should be something really great.

Love the contest idea!
Logic is still a valid tool for discovering truth!
http://canweevolvenow.wordpress.com/the-eternal-cycle/