Thursday, May 2, 2013

Monty Hall or Not.

The Monty Hall is a statistical puzzle that I try to use to explain how decision making can be skewed toward simpler logic or off into a tizzy.

Monty Hall's game show had three doors.  One with a prize and two with trash or goats.  With three doors you have a one in three chance of picking the right door.  After picking a door, Monte would give clues or offer bribes to get you to change.  Without anymore information, each door still had a one in three chance of holding the prize.  If Monte open one of the doors that did not hold the prize, then the odds changed.  Your door was still one in three, but since the other two had a 2 in three chance, with one opened that remaing door still had a 2 in three chance of holding the prize.  You would always be better off switching doors in that case.

The confusion is that the initial odds can't be forgotten.  Even though there are two doors and one prize, you only had a one in three chance to start, you will do better switching because Monte wouldn't open the prize door until the end of the show.  That biases the odds.

I mention this again because the discussion invariably turns to the economics of climate mitigation.  The original odds were 4C proposed by James Hansen  and 2 C proposed by S. Manabe.  Because of a disagreement between those two scientists, Jules Charney proposed a compromise and used the average of the two estimates.  The estimate for sensitivity became 3C +/- 1.5C.

Now if you are an economist trying to figure the cost and benefits of CO2 policy, you have choices.  Since the 3C is not a true estimate, you can ignore that value and use 2 C or 4C.  With 2C considered "safe" or at least managable, you have an act/don't act decision.  That makes wait a while and see a valid option for policy action and no regrets policy action with cost effective options with incremental steps as new information and technology becomes available the best option.

Using 3C, the odds are stacked toward imprudent policy action choices with less flexibility.  The game is biased not by science, but by a political compromise.  A goat door was added that was not part of the initial odds.  With three options and two deemed "bad", the activists win.  You lose the game.

You can't even point out this sleight of hand, whether it was intentional or not, because it is supposedly based on science and doubting science makes you some kind of Neanderthal idiot.  This is the legacy of the Merchants of Doubt.  Flawed but scientific sounding statistics are used to separate you from your wallet.

Just a thought for a rainy day.