When crowds aren’t so wise

Alex Tabarrok recently related a familiar story about the ‘wisdom of the crowds’:

I ask the audience to guess my weight. They all wrote their guesses on a piece of paper. All the guesses was collected and an average guess – the “consensus forecast” – was calculated, while I continued my presentation.

I started my presentation and I naturally started telling why all of my forecasts would be useless – or at least that they should not expect that I would be able to beat the market. I of course wanted to demonstrate exactly that with my little stunt. It was a matter of demonstrating the wisdom of the crowds – or a simple party-version of the Efficient Market Hypothesis.

…I usually think of my own weight as being just below 80 kg…As always I was completely confident that the “survey” result would come in close to the “right” number. So I was bit surprised when the  ”consensus forecast” for my weight came in at 84.6 kg…So once I came back home I immediately jumped on the scale – for once I hoped to show that the Efficient Market Hypothesis was wrong. But the verdict was even more cruel. 84 kg!

And so, Tabarrok concludes, the market does not lie! Or at least, does not spread deliberate falsehoods. Except that’s a bit of a non sequitor, because there are two independent issues here: are crowds wise? And do markets reflect this wisdom?

One reason that crowds might be wise is that they are noise canceling. You and I may be able to guess something like someone’s weight from visual information fairly well but we can never be perfect – even a machine-like ‘optimal decoder’ will give a range of possible values due to little visual and personal quirks. But if we are all noisy in the same way, guessing independently from each other then the noise should disappear. Think of it like a drawing from a gaussian probability distribution – the more guess you make, the closer you get to the correct number.

Crowds can also be wise because they can generate more possible ideas. Just like the old saying goes, everyone is a bit different and will offer slightly different perspectives. Though you don’t even need that difference! A group of foraging animals aren’t all going to be checking the same areas for food, so when one finds a great food source others can join in.

There are a few clear problems that arise from trusting a crowd. A vast literature in ecology is dedicated to the question of when you should use social information instead of just your own personal information. Somewhat unintuitively, when the quality of personal information is lower it is less useful to pool with the crowd! And the size of the crowd matters; individuals in large crowds have an easier time of maintaining high group information even when personal information is of low quality.

Unfortunately, this assumes that there’s no talking in the group; nothing is being coordinated. Because when you start coordinating, when one person starts having influence, then suddenly opinions are correlated and can get dragged around in unfortunate ways. Now things are less diverse and you’re in a functionally smaller group (funnily enough, it also makes people more confident in the quality of their personal information).

Of course, this assumes you can trust others. Why should they provide you with their information? In the real world, my ability to get a good deal or an animal’s ability to find food may mean that if you find out, then I can’t get that deal! And the animal can’t get that food! Generally, it is better to trust the information from those whose goals don’t totally overlap with your own. In the wild, animals often do better when they don’t trust non-related animals of their own species (conspecifics) and trust other species (heterospecifics). And they prefer information from animals that have small home ranges, leading to information parasitization from animals that have larger home ranges! (I think that’s a pretty cool concept.)

And that brings us back to markets. Are crowds wise? Sometimes; but more importantly, should we trust the wisdom of the crowds? In a properly designed market, sure. I can’t think of why a one-time, everybody wins market wouldn’t be great. But when there are is low personal information (aka noise traders), group information goes down. When markets are small – and they are often quite finite! – group information goes down. When I can temporarily mislead an opponent about a reward, group information goes down. Markets can always lie.

References

Seppänen JT, Forsman JT, Mönkkönen M, & Thomson RL (2007). Social information use is a process across time, space, and ecology, reaching heterospecifics. Ecology, 88 (7), 1622-33 PMID: 17645008

King AJ, & Cowlishaw G (2007). When to use social information: the advantage of large group size in individual decision making. Biology letters, 3 (2), 137-9 PMID: 17284400

Lorenz J, Rauhut H, Schweitzer F, & Helbing D (2011). How social influence can undermine the wisdom of crowd effect. Proceedings of the National Academy of Sciences of the United States of America, 108 (22), 9020-5 PMID: 21576485