I was thinking today, that I am guilty of in the past using statistics wrong. More specifically, I accepted "weirder stuff has happened" as a valid reason why I could at least give the time of day to something. The fact is, that it's not at all a reason to do anything. Here's an example
Let's say, Politician X has a .0001% chance of doing something so incredibly stupid that only one in a million people in the same position given freedom to do that action would do it(logical necessity). Suppose then, that Politician Y has a .001% chance of doing something that only one in one hundred thousand people, given freedom to do that action, would do it(again, logical necessity). My reasoning would go as follows;
X did action(X,t,P)
P < P2
:. action(Y,t+k,P2) is reasonable
However, as you can see when it's put in syllogistic form, there is a lot of missing conditions necessary.
Let's make a simpler example. Let's say you are flipping coins, and you flip a properly weighted coin 20 times in a row and it turns up heads. At this point, I could come up to you and bet you 20$ that sometime during the next 100 flips, there will be 10 flips in a row that are all heads. The problem is, there probably won't. The chances of 10 heads in a row in any 10 flips is 2^-10, so in 100 flips, well, you don't have to do the math to know full well that it's not that likely; it's a stacked game. So why is it that when dealing with world events, that it's different?
One possible reason is that sometimes the actor is the same. Just like, when you are not sure whether or not the dice is loaded, and you get 10 6's in a row, you can start to imagine that the dice is loaded, In other words, expressing this statement (stranger things have happened) does not express anything about the odds of the event, it expresses an opinion about the characters in question, but doing so in an obfuscated way that avoids criticism. Is it true that Politician X is an idiot of epic proportions? Does he have a hidden agenda? Perhaps; but does it follow that because X has a hidden agenda that Y does? What if Politicians X1 through X50 all do stupid things(such as claiming to be for family values and then getting caught with his hands in the underage male prostitute cookie jar). Can we start to infer something about the group in general? At what point? Obviously there's no perfect answers, but it's worth pointing out, lest any of you fall into this pattern of reasoning. I'll try to avoid it from now on.
This post has been inspired by Overcoming Bias, and I wouldn't be surprised if they have an article on it already.
