CNN The AP is reporting that God has told the execrable Pat Robertson that a terrorist attack with a significant body count will occur in (late) 2007. In other news, God spake also unto me, saying that the weather on the Arabian Peninsula will be hot and dry, that a prominent American politician will be jailed for corruption next year, and that there’s good money in prophesying situations with a prior probability near or above 50%. Hallelujah!
Foundational information theorist Claude Shannon was the first to understand clearly that the quantity of information in a signal can be measured in terms of the unlikeliness (that is, the inverse prior probability) of the situation that the signal conveys. A good intuitive way to visualize this is in terms of gambling. Suppose that we are betting on the outcome of a coin flip: You put a dollar in the pot, I put a dollar in the pot, we flip a coin, and you call it, winner taking the pot. If there were a perfectly reliable oracle that could tell you how the coin would fall, you’d be rationally willing to pay up to 99¢ to the oracle for the tip, which would ensure that you’d come out ahead on every single flip. Consider, now, a different case: instead of flipping a coin, I’ll roll a six-sided die, which you’ll attempt to predict the outcome of. To make the payoffs fair again, I’ll be putting $5 into the pot each time, and you’ll be putting $1 in. The value of the oracle’s tip is now as much as $4.99, and the reason is that any given outcome of the die roll is much less likely than any given outcome of the coin flip — that is, it is less likely that I’ll roll a ‘3′ than that I’ll flip up ‘heads.’ (In fact, Shannon’s argument would be that the value of the fair wager that I have to make follows from the precise same logic; I pay more to “get a more reliable signal” and become more certain of the outcome.) Robertson is making a prediction on an event that is nearly 100% likely to occur somewhere in the world — his value as an oracle in this matter is much less than that of the hypothetical oracle’s prediction of a 50%-likely event like whether a coin flip will come up ‘tails.’ We shouldn’t reward him. He, in fact, should be paying extra for the kind of insurance that such a no-brainer prediction provides!
On a separate note: The CNN AP article also makes the mistake, memorably skewered by arch-skeptic Richard Dawkins in his book Unweaving the Rainbow under the rubric of PETWHAC (Population of Events that Would Have Appeared Coincidental), of giving Robertson partial credit for a vague fulfillment of a prediction:
In May, Robertson said God told him that storms and possibly a tsunami were to crash into America’s coastline in 2006.
Even though the U.S. was not hit with a tsunami, Robertson on Tuesday cited last spring’s heavy rains and flooding in New England as partly fulfilling the prediction.
No, just no. By that same logic, if I predicted that Pat Robertson would have a fatal heart attack, and some other person who attends his church had one (and the odds are good, since church congregations are full of older men and other bad heart disease risks), I’d get partial credit as a prophet. And if, further, one of his high-school classmates had a bad bout of pneumonia, but recovered, I’d get the same credit as he’s getting here for the “heavy rains and flooding” bit.
I suspect CNN.com the AP is publishing a lightly-edited press release. Bad CNN! No biscuit!
Update: CNN.com appears to have simply picked up a lazily-written AP story. So, actually, bad AP! No biscuit!
