Markets in Everything!

At Bayes Camp, we aren’t just doing estimating exercises in class.  At the beginning of camp, the organizers told us that we could start prediction markets in anything we liked.  A staff member would estimate initial odds that a proposition was true or false, and we could add subsequent predictions.  You gained or lost points proportional to how much your prediction was more accurate than the one right before yours (full explanation at the bottom of the post).

The markets started pretty quotidian (Proposition: it will be raining here on Monday at noon), but eventually shenanigans started up.   People realized you could place bets that would change the behavior of the campers.  After someone posted a bet on how many people would be present at the beginning of breakfast, another camper posted a sign-up sheet to bribe him to attend or stay away.

Anyway, one afternoon, a group of campers and I tried to throw one of the instructors in the pool.  We were unsuccessful, but vowed to try again, so someone opened a prediction market on whether we would manage to throw him in by midnight that night.  That’s when I started recruiting a posse.  I figured, if we got enough people, we could go over in a group and increment the odds up to 99% that he’d thrown in, dividing the interval up so we’d all make the same amount if we managed to throw him in.  And once we’d written down the  new estimates, we’d all stand to gain by throwing him in, and we’d be committing to work together.

“What if someone writes a higher estimate than it’s their turn to?”

“Then we all defect and they’re on the hook for their high guess.”

“Will that be enough of an incentive?”

“Ok, we’ll also all commit to throwing defectors in the pool.”

(I should note at this point that instigator and ringleader are very strong words.  If everyone around me has agreed it would be fun to throw a teacher in the pool, but hasn’t taken any steps toward that goal, and I’ve got some ideas, I see my role as that of a facilitator).

So we lurked outside when we heard the instructor coming back, and then surrounded him.  As the posse closed the circle around him, he asked, “What are you, a bunch of wolves?”  Then we lunged.  We wrestled him to the ground, but he turned out to be really agile and wriggled out of our grasp.  We were still between him and the house, so we managed to grab him a few more times, but, even with six of us to one, he kept managing to squirm away.  Finally, he managed to feint pass us and run up a tree.  While we stood around the base, he rested briefly and then suddenly leapt to the ground, rolled, and took off down the street, leaving us dumbfounded.

After we gave up and trooped back into the house, I pulled people together to read “Wolves” from Hyperbole and a Half.  (You should all open a new tab and read that now).  I find the story hilarious, but a lot of my fellow campers started looking ashamed.  They were identifying with the six-year-olds in the story, and they were suffering major moral pangs for running an instructor out of the retreat.

“Maybe we shouldn’t have kept chasing him,” one person said.

“Did we take it too far?”

I looked at my fellow conspirators conscience-stricken faces and came to a realization of my own.  I got up and snuck over to the prediction market board and shorted the market to .01 = True (thrown in the pool), .99 False.  If they were feeling that bad, there was no way they’d help me try to throw the teacher in when he came back to go to bed.  Luckily, they were too absorbed in their guilt to beat me to the board.

Pow! Instant utils for me.

(Assuming you think my increased chits outweigh the other campers surprise at my ruthlessness.  But I think the fact that one of them has nicknamed me “Wolf Pack” more than compensates).

Scoring metric: X = your estimate that the proposition is true.  Y = the person before you’s estimate that the proposition is true.  These range from 1-99 and are all integers.  (Zero and one are not probabilities)

If it actually turns out to be true, your score is: 100*log2(x/y)

If the proposition is false, your score is: 100*log2[(100-X)/(100-Y)]