Professor Orzel's coin estimation contest is now over, and the graph above shows his plot of the estimates submitted by people who entered the contest. The red vertical line shows the true correct value of $165.26. The median and mean of the guesses were $77.12 and $83.30, roughly half of the true value.
My own guess was based on a simple strategy: choose the middle of a large open interval that was on the high side of the 50 or so guesses already submitted by the time I entered. Why?
1) Stakes were low*, and it was rational for me not to spend a lot of time computing a complex estimate.
2) By the time I entered, a lot of people had already submitted guesses, most of which seemed grounded in plausible reasoning, so it was rational for me to "free ride" off their computational efforts.
3) I knew from the MBA study that, on average, people typically tend to underestimate the value of a bunch of coins, and Geeky Mom's recent post also reminded me of this tendency. On the other hand, the Bazerman-Samuelson experimental data also told me that there is usually at least one person who guesses too high.
4) So I wanted to guess high, but I didn't want to outflank the highest guesser.
5) And I wanted a large open interval so I could take the midpoint of that interval and hopefully "control" a large amount of numeric real estate. At the time I submitted my guess, I saw a large open interval on the highish side, running from $120.94 to $150.92, so I submitted a guess which was midway between those two points, which was $135.93. So, if nobody else had come along afterwards, I would have "controlled" the entire span between $128.43 and $143.43. (Of course, people did come along and poach on my real estate, but what can you do? It's a free country, as they say! Actually, if I'd been obsessive, I'd have waited until the last possible moment, in order to take all possible data from other people's guesses into account, but I'm not THAT obsessed!)
How did I do? Well, I didn't win. That honor went to Michael Day, who submitted a guess of $166.10. (At least he wasn't one of those folks poaching on my "turf.")
But at least I did better than the median or mean, and I also came closer than Professor Orzel himself, who said he would have guessed $130. And, of course, he had some informational advantages (what the SEC would call "insider information," if this were a marketable security.)
Professor Orzel asks:
Now, why were the rest of the guesses so far off? Isn't the "wisdom of crowds" effect supposed to make an average of a large number of estimates better than any individual guess?
As I mentioned in my last post, winner's curse is not a factor in this contest, because it's not an auction situation. In an auction, you would expect sophisticated bidders to bid somewhat on the low side, because they are worried about the winner's curse phenomenon.
However, as I pointed out before, Professor Orzel's contest isn't an auction, so there's no winner's curse involved. (If there HAD been an auction of the coin jar, it would most likely have been won by that person on the far right of the histogram, who thought the coins were worth $327. If everyone were rational, and took winner's curse into account, they would likely have bid less than their estimates. The question is whether they would have adjusted their bids ENOUGH.)
But the question remains: why is the average of the estimates in this case so far below the true value? (Even worse than the estimates of those Bazerman/Samuelson MBA students, whose estimates averaged about 65% of the true value.) At least they were better than Geeky Mom's estimate. (It would be interesting to see the data from her bank, which runs an estimation contest.)
A few possibilities include the phenomena known as information cascades or herd instinct.
Basically, what it comes down to is this: when people were submitting their guesses, they were using the information they had about other people's guesses in formulating their own guesses. That means that our guesses were not independent of one another. You see this sort of thing all the time in financial bubbles and panics. Of course, the stakes here were much lower* than in the global financial markets.
Now, it was entirely rational for us to use all the information we had available in formulating our own guesses, including the guesses submitted by other people, especially those of us who were sophisticated in how we used the data. (I like to think that I was reasonably sophisticated in my use of the information, even if I didn't win the contest!) But other people might have used the early information in more naive ways, because they didn't take into account the fact that people have a tendency to underestimate values of coin containers, which led to an unfortunately inaccurate information cascade.
*No offense intended with the "low stakes" remark, Prof. Orzel, but all of us losers will just have to wait a little while until your book hits the bookstore shelves. Having to wait a little to read your book is a lot less painful than what the information cascades have done to the world economy in past year.