Odds 'R

The second in the series of posts that stem from comments that weren't there the last time I looked comes courtesy of Dan, who pointed me towards Odds'R, which is a book of trivia presented in probabilistic form. e.g.:

If you had been arrested for witchcraft during the infamous Salem witch hunt and trials of 1692, what would have been your odds of being executed?
a) 1 in 4
b) 1 in 8
c) Zero--they all got away on their brooms.

Also there's a board game, and I'm sure any moment now, you're going to be able to buy the Official Odds'R Bow Tie and Mustache Set™ in a store near you (dude, that tie totally rocks).

Dan asks:

Is asking the odds on such specific questions as above still a problem within your argument that the "odds" are statistically meaningless because the question was asked within a framework where "meaning" does not correspond to numbers, thus the "odds don’t have the meaning that they appear to have?"

I, being a crass opportunist, will use this question to launch a larger discussion of what probability actually "means."

What can we actually infer from the above question about witchcraft (b is the answer they give as being correct--I know, I can't believe it wasn't c, that pinacle of well-timed comedy, either. Oh my god...witches, brooms...stop. I'm gonna pee)? Only that there were some number of people arrested for practicing witchcraft in Salem in 1692, say 24, and that 3 of them were executed. To infer what the question actually states as being true ("if YOU, the person now reading this sentence, were a person living in Salem in 1692 and you were arrested for practicing witchcraft, 12.5% of the time you would be executed") would be completely fallacious, meaningless, and frankly kind of a weird thing to infer. I can say with certainty that this did not happen to you. The odds of it are zero.

The phenomenon of Odds-Are-Oneness tries to make some sort of statement about what we tend to think of as fate--weird things happen to us, things that seem like they were spectacularly unlikely to happen, but did. But we also notice the "weird" things, and ignore the incidents of similar phenomenon that aren't "weird" to us. To review my very first example, nobody took note of the thousands of times that the New York City Pick Three Lottery came up, e.g., 1-6-5 on May 13th, 1995. Except, of course, to the people who won the lottery that day, at which point it suddenly seemed a lot like fate to them, and they, if they're like the majority of people in the world, probably went back and created some narrative about what those numbers "meant" and "why" they won.

But I also think the answer to Dan's question is unequivocally yes. These odds don't have anything to do with probability. They can't possibly apply to you imagining yourself into the shoes of an accused witch in Salem in 1692. Or in the case of another question found in Odds'R on a favorite topic of mine, "What are the odds that a US state has a law on the books challenging the validity of evolution?" (given answer, 17 in 50)--I'm not saying there's no meaning in that statement, but it sure isn't about probability. It's for sure not telling us that when the next territory or protectorate votes for statehood that there's a 34% chance someone will toss in an amendment saying, "We vote for statehood, and P.S., Puerto Rico also declares that Darwin did crack."

So the open question is, is there actually any such thing as logical discrete statistical inference? Can we logically infer from the fact that one out of every million plane flights ends up crashing whether or not we should get on the next plane? Does knowing that one out of every fifty persons who takes Vioxx experiences heart failure within two years tell us anything about whether we should take it? Don't get me wrong, probability and statistics are not meaningless. Casinos make money. Carbon 14 decays. A relatively predictable number of people will buy things from Amazon in the next year. Over a large sample size, statistics and probability are inexorable. The longer you flip a fair coin, the closer it runs to 50% heads, 50% tails. And you still don't know a goddamn thing about what the next flip is going to be.