Don't ask them tough questions.

Photographer: Rob Stothard

Brexit Casts Doubt on the Wisdom of Crowds

Mark Buchanan, a physicist and science writer, is the author of the book "Forecast: What Physics, Meteorology and the Natural Sciences Can Teach Us About Economics."
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During the next couple months, the various candidates to replace U.K. Prime Minister David Cameron will debate what to do now that voters have decided to leave the European Union. They should keep in mind that doing exactly what the voters said might not be the wisest -- or even the most democratic -- approach.

Direct democracy, in which voters decide specific issues en masse, is actually rather unusual. Typically, they leave such decisions to elected officials, such as a president or legislature, whom they provide with the time and resources needed to make well-informed choices.

As it happens, there may be a very good reason that government has historically developed this way: Smaller groups can actually make better decisions, particularly on complex issues. As researchers from Berlin's Max Planck Institute for Human Development note in a recent paper, the wisdom of crowds works well only on questions that individuals can answer relatively easily.

Suppose you're asking whether California's population is larger than Britain's (it's not). If you get nine people to vote, they'll probably get the right answer. If you get a million people to vote, they'll almost certainly get it right. The power of the crowd washes away the possibility of error.

But now try a harder question: If you fold a piece of paper on itself 25 times, will the result be taller than the Empire State Building? Most people would say no, even though the actual thickness would be about 10 miles. Asking a larger group to vote would only increase the certainty of getting it wrong.

The Max Planck researchers show that smaller groups perform particularly well when questions come in an unpredictable mix of easy and difficult. Under general conditions, they suggest, the optimal group size for making good decisions is fairly small -- often around 10 to 15, and typically less than 40.

No wonder decision-making bodies around the world work with small numbers. Think of juries, parish councils, central bank boards or parliamentary committees, which tend to have between five and 40 members.

QuickTake Brexit

Granted, this research might not apply directly to the U.K. referendum, which arguably didn't have a right answer. Yet it certainly suggests that a referendum was an awfully crude instrument for deciding such an important and difficult issue -- especially given that the British public holds wildly distorted views on, say,  the number of immigrants in the country (estimated by the public at more than twice the actual level).

Voters clearly expressed their discontent on a number of issues, including immigration and globalization.  U.K. leaders can't ignore this, but they should also question the naïve view that respecting democracy demands invoking Article 50 of the Lisbon Treaty, triggering the formal process of taking the U.K. out of the EU. There's a good reason that voters gave them the power and resources to examine such choices carefully. In deciding how to respect the voters' will, and whether this requires Britain to leave or stay, that is precisely what they should do.

This column does not necessarily reflect the opinion of the editorial board or Bloomberg LP and its owners.

To contact the author of this story:
Mark Buchanan at buchanan.mark@gmail.com

To contact the editor responsible for this story:
Mark Whitehouse at mwhitehouse1@bloomberg.net