Years ago, Dentyne chewing gum ran an advertising campaign with the line “four out of five dentists surveyed recommend sugarless gum for their patients who chew gum.” Of course there’s no mention of sample size. Maybe “four out of five” meant 80% of a large survey, or maybe they literally surveyed five dentists.

Even if they only talked to five dentists, you’d think that if four dentists out of five came to the same conclusion, it is quite likely that they have good advice. Individuals have their biases, but if a large majority comes to the same conclusion independently, maybe some underlying truth is responsible for the consensus rather than a coincidence of prejudices.

However, there is a fallacy in the preceding argument. It implicitly assumes that professionals make up their minds independently and that their prejudices are independent. That may be true on some small objective problem. Several scientists may conduct independent experiments and have independent errors. In that case, if most agree on a measurement, that measurement is likely to be accurate. But ask a group of scientists working in the same area if their area deserves more funding. Of course they’ll agree. Their financial interests are highly correlated.

James Surowiecki’s book The Wisdom of Crowds argues that crowds can be amazingly intelligent. Crowds can also be incredibly foolish. One of the necessary conditions for crowd wisdom is independence. The book gives examples of experiments in which the average independent estimates, such as the weight of a cow or the number of jelly beans in a jar, surprisingly accurate. But if there were an open debate rather than an anonymous poll, the estimates would no longer be independent.  If one influential persons offers a guess, other estimates will be anchored by that guess and tend to confirm it.

William Briggs has an excellent article this morning on scientific consensus. The context of his article is climate change, though I don’t want to open a debate here on climate change. For that matter, I don’t want to open a debate on the merits of sugarless chewing gum. I’m more interested in what the article says about how a consensus becomes self-reinforcing.