Getting Paid to Lose Weight

The results are in.? I’m happy to report that my eBay auction ended with a winning bid of $282.85.? Twenty-three bidders put in a total of 45 bids.? The bidders were a mixture of seasoned eBay users (some with more than 150 eBay purchases) and newbie eBay users.
The winning bidder is a co-author of mine and auction guru, Peter Cramton.? Peter has lots of friends in New Haven who will tell him if it looks like I’m not in compliance.? Friendship, he tells me, was not his motive.? In fact, he engaged in bid snipping – entering the fray with one minute to go (5 a.m.!) so as not to induce unwanted competition: “I definitely did not intend to push the price up,” Peter emailed me. “I was looking for profits. Profit maximization was my objective.”? So I am especially indebted to eBay bidder “gody22” who bid $277.85 at 4:19 in the morning. It was gody22 (who is unknown to me) who pushed Peter up so high.
The auction itself is a kind of prediction market.? Very crudely, if bidders thought that I might forfeit at most once during the year, a winning bid of $282 would indicate a market belief that I have a 57 percent chance of forfeiting once ($282 = .57*$500).? At the other extreme, if bidders thought I have an equal and independent probability of forfeiting each and every week, the $282 bid would indicate (using a binomial distribution) that I have about a 1.09 percent chance of forfeiting in any given week.? That probability would give Peter a 32 percent chance of one forfeiture, a 9 percent chance of two forfeitures and a 1.6 percent chance of three forfeitures.? This 1 percent weekly probability is probably a lower bound.? The probabilities of forfeiture from week to week are neither independent nor identical – particularly in light of the upcoming holiday season.
Speaking of predictions . . .
The end of the auction also means that we have a winner of my Freakonomics prediction contest.? A signed copy of Carrots and Sticks will soon be making its way to David V who just about nailed it with a prediction of $282.? Sheridan, however, also deserves honorable mention for predicting:

i guess the final bid will be the average of all the bids guessed on this blog… ala the jellybean guessing game.

The 39 commenter predictions ranged from $0.01 to $1,250.? The average of this right-skewed distribution was a bit high at $393, but the median bid hit it almost exactly.? The median prediction was none other than David V’s $282.? Talk about your wisdom of crowds.? Pretty cool that the median commenter accurately predicted the results of the eBay prediction market.? (Of course, this is not as interesting a result if David V turns out to be gody22).
Is it better to give or receive?
Finally, I’d like to thank Rafael for suggesting:

I think you should be donating the money to a charity instead.

It’s probable that the winning bid would have been higher if I had committed to give the money to charity.? That was the approach taken by the originator of this idea, the great James Hurman, who promised to give the proceeds of his smoking commitment auction to the Cancer Society of New Zealand.? But I decided to keep the money in part because I want to increase the chance that the winning bidder will hold me to my commitment.? I want the winning bid to reflect a cold-hearted calculation.? Not giving the money to charity decreases the chance that the winner will let me off the hook if my weight comes in a bit over some week and I have some sob story to tell.? And like Peter, I also have a bit of a profit motive.? I’ve put a lot of money at risk in the past to lose weight without ever being compensated.? This fairly simple auction shows that it is possible to get paid by non-altruistic strangers for doing what is good for you.