See Nate Silver, here:

"The Cleveland Cavaliers led for much of Game 1 of the finals against the Golden State Warriors and had a better than 70 percent shot at winning it when LeBron James put the Cavs up by four with 5:08 left to play."

Having just finished reviewing a book on Shackle, who largely holds the same view as Mises on case probability*, I find it interesting to ask just what Silver means here. Clearly, Silver is drawing upon a database of results that contains information on how often teams up four in a game with 5:08 to play won that game. Perhaps he has 200 records that match that criterion, and the team up four won 140 of those games.

"But so what?" ask Mises and Shackle. The Cavaliers aren't going to play the Warriors 200 times, starting from this identical situation, so they can win 70% of the time. This game won't result in a SchrÃ¶dinger's cat situation, with the Cavaliers 70% victorious and 30% defeated; no, one team or the other will have 100% won, and the other team will have been 100% defeated.

One plausible interpretation of what Silver is claiming is that it is about what kind of bets we should make in the situation cited. Say we are told "NBA team A is up four with 5:08 left on NBA team B. What odds will persuade you to bet on A or on B?" Then a reasonable answer might be, "If you give me better than 2.333 to 1 payoff on B, I will take B, or better than a .43 to 1 payoff on A, I will take A." (I think I got these calculation right!) Another reasonable answer might be, "Knowing so little, I'm not betting!"

Furthermore, in

Or imagine that, right after Lebron hit the shot to put the Cavs up four, he punched a Warrior player in the face, and was ejected. Now, we might reasonably think, "The Cavs are done for!"

In short, I think Silver's statement only has the superficial appearance of being an objective statement about the particular game he was discussing, and is actually an example of "probabalism," to coin a term: reflexively applying probability analysis to a situation without really considering what it means in that situation.

* I cite this article because it gives a succinct statement of Mises's views on probability, and not to endorse the author's analysis of the two-envelope problem.

"The Cleveland Cavaliers led for much of Game 1 of the finals against the Golden State Warriors and had a better than 70 percent shot at winning it when LeBron James put the Cavs up by four with 5:08 left to play."

Having just finished reviewing a book on Shackle, who largely holds the same view as Mises on case probability*, I find it interesting to ask just what Silver means here. Clearly, Silver is drawing upon a database of results that contains information on how often teams up four in a game with 5:08 to play won that game. Perhaps he has 200 records that match that criterion, and the team up four won 140 of those games.

"But so what?" ask Mises and Shackle. The Cavaliers aren't going to play the Warriors 200 times, starting from this identical situation, so they can win 70% of the time. This game won't result in a SchrÃ¶dinger's cat situation, with the Cavaliers 70% victorious and 30% defeated; no, one team or the other will have 100% won, and the other team will have been 100% defeated.

One plausible interpretation of what Silver is claiming is that it is about what kind of bets we should make in the situation cited. Say we are told "NBA team A is up four with 5:08 left on NBA team B. What odds will persuade you to bet on A or on B?" Then a reasonable answer might be, "If you give me better than 2.333 to 1 payoff on B, I will take B, or better than a .43 to 1 payoff on A, I will take A." (I think I got these calculation right!) Another reasonable answer might be, "Knowing so little, I'm not betting!"

Furthermore, in

*this*game we have a brand new situation: never before, in those 200 games, did*this*Cavaliers team face*this*Warriors team. Perhaps we know Steph Curry is great in the clutch. Perhaps we see that Kyrie Irving is hurting, and think his play will fall off. Perhaps we think Steve Kerr is a great end-of-game strategist. And so on. Any of those things might significantly change what bets we will be willing to take on the outcome, and with good reason.Or imagine that, right after Lebron hit the shot to put the Cavs up four, he punched a Warrior player in the face, and was ejected. Now, we might reasonably think, "The Cavs are done for!"

In short, I think Silver's statement only has the superficial appearance of being an objective statement about the particular game he was discussing, and is actually an example of "probabalism," to coin a term: reflexively applying probability analysis to a situation without really considering what it means in that situation.

* I cite this article because it gives a succinct statement of Mises's views on probability, and not to endorse the author's analysis of the two-envelope problem.

Gene, suppose that out of all the times that Nate Silver predicted there was a 70% chance of something happening, in about 70% of those cases it actually happened. And similarly for 30%, 40%, and so on. Then wouldn't that indicate that Nate Silver is able to determine some objective property of the situation? Otherwise how would he be able to achieve results like that?

ReplyDeleteKeshav, there is no argument about class probability. Shackle, Mises, and me are all fine with that idea: for some large CLASS of events, 70% of them turn out one way, and 30% another. But the fact that we can say this about the class just does not translate to single events: no SINGLE event (setting aside quantum mechanical type stuff) can turn out 70% went left and 30% went right, or 70% won the election and 30% lost it.

DeleteI think you're missing the difficulty in turning a statement about class probability into a statement about a single event.

Gene, I don't see why the mere fact that a single event either occurs or it does not occur means that there is no objective fact of the matter as to what the probability of the event occurring was before it occurred.

DeleteIsn't the fact that Nate Silver is able to reliably place events in the "70% chance of occurence" category an indication that there is some objective property of the situation that indicates to Silver that it belongs in that category? Otherwise, he wouldn't be able to do so reliably.

But he is only able to place a CLASS of events in the "70% chance of occurrence." You are simply begging the question by claiming that a SINGLE event can be given such a probability.

DeleteMe, you, Mises, Shackle, Keynes, and every other probability theorist AGREES that for some CLASS of events, assigning a probability of X% makes sense. Again, I think you are completely missing the difficulty about assigning probabilities to single events, something all of the significant probability theorists seem to have agreed upon (even though they may have come up with different solutions to the difficulty).

Look at it this way: suppose we have a class of events where we know sure that events 1, 3, 4, 6, 7, 9 and 10 will result in X. And we know for sure that 2, 5, and 8 will result in Y. The probability of X in this class is 70%. But it is certainly not 70% for event 2!

Or think about your own field: consider a radioactive element X with a half-life of 1 year. How was this arrived at? By studying the whole CLASS of atoms of this type, and determining that half of them decayed in one year. But what is known about what any particular atom will do? NOTHING: it might go on being an X atom for a million years, or it might decay in 1 second.

DeleteThe knowledge is all about the class of atoms. There is NO knowledge about what the individual atom will do at all.

This is an excellent illustrative example. Based on this logic, what, if anything, can we say about the probability of any individual event?

DeleteKeynes took it to be a subjective estimate. Perhaps that is right: I'm not sure.

DeleteI am reading a book on the history and underpinnings of probability I think you would like. Willful Ignorance.

ReplyDeleteThanks.

Delete