I'm not very convinced of the “wisdom of crowds”. There are numerous examples of how “the wisdom of crowds” is in fact the “idiocy of the mob”. Look at some political movements or some of the more extreme religions for instance, a good few of these make no sense, but they have a lot of people who believe them. In Vanatu, an island in the Pacific, there is a cargo cult called the “John Frum” cult who think that building replicas of USA air force bases from World War II will bring the USA and all their goods back to the island. A lot of people believe this.
There is a lot of research from social psychology showing that groups polarize decisions in contrast to individuals. A group will make a more extreme decision (cautious or risky) than an individual. There is also the fact that estimations of physical sizes and weights will tend to show a normal distribution, with the most common estimate, the mode, being the correct once. Here there is wisdom in crowds, or more like the wisdom of the normal distribution, the central limit theorem and statistics in general. Distributions are wonderful things.
One of the aspects of a lot of people being asked a question is that you are able to take advantage of a lot of peoples experience and knowledge. Recently a company called “Netflix” in the USA used the web and the crowds that access it to solve an interesting problem. While it is not the usual meaning of the term the “wisdom of crowds”, it is an example of the crowd can solve the problem. Netflix (www.netflix.com) rent DVD's of movies and TV programs to people. They send them via the mail and you maintain a list of which DVD's you want. They also try to predict which DVD's people who like to watch based on the DVD's they have already watched. Amazon does a similar thing with recommendations of products for people to buy. Netflix wanted to improve their predictive algorithm by 10% , which is quite a large improvement. They could have tried to hire all sorts of geniuses, but they chose a very unique way to solve the problem. They set up a web site (www.netflixprize.com) , posted a huge data set of movie DVD's, data about the movies and subscriber choices. They then offered $1,000,000 to anyone who could improve their algorithm by 10%. There were a few conditions, there was a deadline (September of 2009) and anyone who submitted a solution had to agree to document what the solution was publicly. Many companies allowed their employees to set up teams and compete, some individuals competed, and teams merged and re-formed over time. In the end there was a winning team, “Bellkors Pragmatic Chaos” .
In this case the wisdom was not “crowd think”, whatever that is. It was that Netflix leveraged the web and all the people who constantly look at it to get hold of people who wanted to solve this problem. For them the $1,000,000 was cheap. They could never have afforded to hire all the people who took place in the contest. They got access to world class computing facilities and minds and got some great publicity as well.
The winning algorithm was a technique called a “Restricted Boltzmann Machine”. It proved that numbers and math matter. It wasn't the crowd that solved the problem, but the crowd was the mechanism that made the solution possible. I'm inclined to think that this is the real wisdom of the crowd. People can come up with all sorts of strange beliefs, the ability to get people to address your problem is the wise part of the crowd. It's another of those examples of how the web changed the world in a radical way. Twenty years ago it simply would not have been possible. I gather there is going to be another Netflix prize. It's nice that it was the math that was wise in the end....
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