In the Times, Danny Finkelstein expresses disquiet about Operation Yewtree:

"My word against some bloke after more than 20 years is good enough for you?" [Liz Kershaw] asked. The police wouldn't need other evidence to charge?
"Well" replied the officer. "If it was just one girl obviously the Crown Prosecution Serivce would probably throw it out. But if more than one girl came forward, well..."
The clearest statement I have ever seen of the dubious policy of using legally weak individual allegations to support each other.

He's touching upon a widespread cognitive error here - correlation neglect.

If lots of women were to independently make allegations against someone, those allegations might be credible - though whether credible enough to overcome the reasonable doubt hurdle is another matter. The problem comes when the allegations might be correlated. If one allegation against a public figure encourages others to make allegations, the subsequent allegations might not have as much weight as they would if they were independent. The latter allegations might be cases of misremembering or mistaken identity. If so, there's a danger of an information cascade; several allegations might be due not to independent pieces of information which support each other but to a common mistake.

Now, I've used the word "might" a lot in that paragraph. But we do have a much clearer example of the danger of correlation neglect in criminal law. In 1999 Sally Clark was convicted of murdering her two babies on the evidence of a pathologist who claimed that the chances of two babies dying of cot death as Ms Clark claimed were vanishingly small. His statement was an example of correlation neglect; it might have been true if the chance of one baby suffering cot death were independent of the chance of his brother dying. But if there are common environmental risks of cot death, then the chances are correlated, so the chances of two deaths are much higher than the pathologist claimed. Ms Clark was eventually released on appeal.

It's not just prosecutors who are prone to correlation neglect. It also happens in investing. Benjamin Enke and Florian Zimmerman show that people fail to discount correlated signals about future returns, and so over-invest in assets which look good. And Erik Eyster and Georg Weizsacker show that investors treat (pdf) correlated assets as uncorrelated and so fail to diversify risk properly.

And, of course, it also happens in politics. We fail to discount the political opinions of our friends because they are correlated: our friends tend to have similar backgrounds and outlooks on life. We are, say (pdf) Glaeser and Sunstein, "credulous Bayesians", who over-react to weak information.

Such correlation neglect contributes to the bubblethink I discussed yesterday. It also generates political polarization (pdf) and overconfidence; Enke and Zimmerman show that it can be a source of stock market bubbles because investors become overconfident about future returns. In the legal context, such overconfidence can lead to false convictions.

These, of course, can have terrible effects: after she was released, Ms Clark drank herself to death. In this sense, correlation neglect can be deadly. Whether this has any relevance to the UK's decision to go to war in Iraq is a question I shall leave to others.