What is the probability of something that either happens or doesn't?
Give me the odds you'd take on a bet. That's (sorta) the probability.
Before diving into today’s post, I wanted to thank the eagle-eyed reader that noticed I had failed to link to anything here on Tuesday’s newsletter:
Here is a thread of leaks that have happened in the past.
The link is here:
It’s updated now on the web, but if you missed it when reading it by email last week, have at it.
Earlier this week, I said that we would discuss this guy’s objection to the discussion:
When reading the post, I had a feeling that some of you might be thinking (or shouting into the computer) “but what does it mean to say the lab leak has a 10% chance of being true? It either happened or it didn’t!”. Well, yes, it either did happen or it didn’t happen, it didn’t 10% happen, or 20% happen, or any other number except 0% or 100%, and we’ll probably never know.
As it turns out, there is a simple way to reframe this question in such a way that turns these one-off events, for which it seems quite difficult to put degree-of-confidence in, into one-of-many events. You may already do it in your day to day life. And that is to put a price on it. What odds would you accept if placing a wager with a friend? Implicit in those odds is a probability.
Prices behave just like probabilities; the act of removing arbitrage from a market of bets makes wager prices do everything, mathematically, that probabilities are supposed to do (an exhaustive set of probabilities must sum to 1, the probability of two things happening together must be less than either happening independently, &c). In fact, they work so well, we may go so far as to say that prices are probabilities.
Presumably the wager-maker not only places bets on the origin of covid, but also on the Nets winning the NBA championship, the color of the next car to show up on their block, and all other manner of things that either will or won’t happen, but that in no sense can happen 23% of the time. So there really is no contradiction, no paradox; any one-of-one event can be converted into a one-of-many event by thinking about it as one bet among many.
De Finetti, an Italian statistician/philosopher, came up with this way of thinking. He actually went way further, stating that probability does not exist. Or, at least, there is no concept of an “objective” probability — each event, from the perspective of each individual, has its own probability, represented by the odds they would accept on that event. Things that seem like objective probabilities are more like market clearing prices. I happen to like this way of thinking, and it’s my personal conception of probability.