The 50/50 Fallacy

Since a bunch of people are going ape shit (committing a common statistical fallacy) over Paul Krugman saying that there is a 50% chance of going into a global recession, I figured I would clear it up. The fallacy is as follows: There are two options, either we do go into a recession or, we do not go into a recession. Ok, now without knowing any details at all you could bet 50/50. But, this is not the case. We do know details, and many of them.

The 50% chance comment by Krugman was not a blind shot, he has evaluated the evidence for it and thus, made a calculated prediction. In order to better explain this, I will give the following example: lets say we are predicting the chance that an organism exists, say, a 16ft tall ant that is invisible and can withstand fire for up to 30 hours. Now, if you commit the fallacy I talk about above, you would say there is a 50/50 chance of this organism existing. But, obviously, there is not a 50/50 chance. The chance would be somewhere on the lines of 0.00000000001/99.99999999 (I know, the chance is less than this but you get the idea.) This is also important for people who claim that there is a 50/50 chance of God existing. This is again not the case and the chance is more on the lines of the giant ant I described above as we have no evidence for the existence of a God and a great amount of evidence against.

A quick update: I just thought of this example: Let’s say you go and buy a lottery ticket. What are the possible outcomes? They are either, A: You win or B: You lose. Now even though there are only these two outcomes, no one would think your odds are 50/50. If you do think that, maybe you should examine why you’ve bought 10 tickets in a row and none of those one the jackpot. Assuming the fallacy and thus, the 50/50 odds, then after buying 10 tickets your chances of getting the loss 10 times in a row would be 1/2(^10) or 1 in 1024. Now, it is easy to see that those are not the odds even though there are only two choices as everyone would win the lottery. The odds are given (by the lottery) but would be more in the lines of 1 in 14 million (if you see these odds as favorable, there are lotteries with much worse odds that you can choose from) rather than 50/50. Now, the absurdity of this fallacy should be clear.

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