David Leonhardt writes a rather painful article in the New York Times "When the Crowd Isn't Wise" (July 7th, 2012). He notes that Intrade thought Obamacare was more likely to be ruled unconstitutional than constitutional:

[Intrade markets] continued to show about a 75 percent chance that the law's so-called mandate would be ruled unconstitutional, right up until the morning it was ruled constitutional.

The market-the wisdom of crowds-turned out to be wrong.

Corrections sees risk premia and self-insurance everywhere, but let's take the common view of Intrade markets, that the price/10 is equivalent to the probability the market puts on an event.

Are political writers like Leonhardt so ignorant of statistics to know what "wrong" means? 75% represents a

*distribution* of outcomes! If you looked at all Intrade markets that were at and around 75%, and then looked at the outcomes, if they were "right" (by Leonhardt's incorrect statistic) 100% of the time we should conclude these are poorly functioning markets.

No. If you predict something should happen with 75%, then it should not happen 25% of the time, and happen 75% of the time.

**Not happening 25% of the time means you are ***correct *in your guess about the __distribution__. 75% represents a distribution of outcomes. A 90% guess would be

*more wrong* than 75% in general, when the outcome actually happens 75% of the time. The relative entropy of the distributions is what helps us differentiate them statistically.

New York Times quality article.