# 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.

1. Drill-Baby-Drill Drill Team says:

Stop this dieting nonsense, having an eBay auction, trying to second guess market psychology and getting the world mobilized about your waistline………..Just have the surgery!

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2. Ville P. says:

This means everyone else thinks Peter Cramton paid too much.

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3. Eric H says:

You said, “a winning bid of \$282 would indicate a market belief that I have a 57 percent chance of forfeiting once (\$282 = .57*\$500).”

Wouldn’t the market belief be significantly lower than that? The winner of the auction is at the most extreme right tail of the distribution of expected values. If each bidder in the auction bowed out at the point in which he/she believed it would no longer be profitable, then the average or median of those points would be your market prediction – not the highest bid. The highest bid is only determined by two players – the winner and the next to highest bidder – not the whole market.

The market believes poor Peter bid more than the expected value!

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4. Justin James says:

I still want to see you offer something for long-term weight loss, say, 2+ years.

Or better yet… I want to see you guys do something similar to prove that incentives work (I don’t think they do, incidentally). I want to see you wager your own personal money on a drug addict staying clean, or an overweight person losing weight, long term. Say, \$1,000 of your money against \$1,000 of my money, with the person to receive half if they accomplish the goal.

In my experience, incentives rarely work long term except for folks who are ready to make a serious commitment to change anyways. All of these things you want to incentivise are things which people should be doing for themselves anyways (sometimes to literally save their lives). If someone won’t drop 50 lbs. to save their life, what makes you think that a financial reward would do it? Also, most people can’t think long term enough for a long term incentive to work.

J.Ja

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5. Andy says:

Eric H (#3) makes a very good point.

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6. Nate C. says:

I’d like to see Peter offer derivatives on the contract. I’d be more willing to spend \$28 for the opportunity to win \$50 on default, as I’m sort of poor. What do you say, Peter?

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7. Sheridan says:

a very interesting result.

i do think incentives work at a variety of levels, but they need to be tailored to the individual (i.e. utility is unique) and i agree that many people do not think about their behaviour over the long term.

and here’s ancedotal evidence:

my former employer offered our workplace individual incentives as a reward for results and hard work. i chose education (hence my burgeoning interest in economics) and a colleague chose additional days off work.

perhaps some people would prefer the lure of a holiday rather than the potential loss of \$26,000 as their incentive…

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8. Rob says:

I also question the market prediction mentality. Actually, it’s probably more complicated than the median bidder considering the number of people who saw the auction, decided the price was too high, and didn’t bid probably would lower the median price. But it’s difficult to really have an answer because there’s no concept of scarcity. This is the market prediction for a supply of one future contract, and if you had offered more, the market clearing price would be lower. So the real question is: would you be willing to put up another identical future contract? While e-bay may have given us a picture of the demand curve, we have to know the supply curve to get a real picture of equilibrium.

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