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July 25th, 2016

The result of the recent UK referendum on whether to stay in or to leave Europe has come as a shock to many of us. More than one correspondent has asked me “I thought there was this thing called group intelligence which said that, the larger the group, the surer they are to get the right answer?”

• Group intelligence only works if there is a known correct answer.
• It’s not intelligence; it’s statistics.

Here are some (modified) extracts from the book to show how group intelligence works, and under what circumstances.

With problems that involve figuring out the value of something (like a compass bearing or the number of jellybeans in a jar; scientists call these state estimation problems) the best way is to take an average of all the answers. With problems that involve choosing the right answer among a small number of possible alternatives, majority opinion serves us best. To take best advantage of either, we need just three conditions:

• The people in the group must be willing and able to think for themselves and reach independent conclusions, which are then pooled by taking an average or accepting the majority opinion, depending on the type of question being asked.
• The question must have a definite answer that can ultimately be checked against reality.
• Everyone in the group must be answering the same question (this may seem obvious, but it has hidden subtleties, because people may be interpreting the same question in very different ways).

When these three conditions are fulfilled, the mathematics of complexity leads us to three astounding conclusions:

• With state estimation questions, the group as a whole will always out-perform most of its individual members. Not sometimes. Always.

• If most of the group members are moderately well-informed about a question to which there are several possible answers (but only one right one), the majority opinion in the group is almost always bound to be right. If each member of a group of 100 people has a 60% chance of getting the right answer, for example, then the majority opinion in the group has a better than 99% chance of being the right one.

• Even when only a few people in a group are well-informed, this is usually sufficient for the majority opinion to be the right one.

In the recent referendum, almost none of these criteria were met. The role of the media and the demagoguery of the proponents ensured that most individuals were not reaching independent conclusions, but were influenced by the rhetoric and the opinions of those around them. People were not answering the same question, but giving different weights to the importance of different questions within a set. Many lies (shown up as such immediately after the result was known) were told and believed. And there was no unambiguously “right” answer.

As a result (in my humble opinion) the crowd made what must surely be one of the most fat-headed decisions in referendum history. Wisdom of crowds? If you believe that, you’ll believe anything.