Thoughts on Probability and Uncertainty
By Arnold Kling
Eric Falkenstein watched the Youtube of the Caplan-Boettke debate on Austrian economics. Falkenstein concludes,
What is needed is something constructive, something the Austrians, Post-Keynesians, or Taleb, have failed to do.
Let me place this in the context of my introduction to the philosophy of probability. I say that probability can be axiomatic, empirical, or subjective. When I say, “There is a probability of 0.5 that the flipped coin will come up heads,” I could be saying:
1. That is the definition of a fair coin.
2. I have observed lots of coin flips, and the empirical frequency of heads is 0.5
3. My personal opinion is that there is a probability of heads of 0.5
I think these are three different uses of the term “probability,” and we make philosophical errors by confusing them. The statement about the coin fits best with an axiomatic approach. A statement about the probability of selecting an American male at random and having him be 7 feet tall or higher rests on an empirical notion of probability. And the probability that inflation will average more than 6 percent over the next five years is largely subjective.
Subjective probability is particularly important with regard to non-repeatable events. If you believe that macroeconomic history generates sufficient repetition, then you would move the inflation forecast over into the empirical category. I would not do so.
One way to make the term “radical uncertainty” operational is to say that we are talking about a forecast for a non-repeatable event, where in order to forecast you cannot simply look at empirical data (such as the proportion of men over 7 feet tall in a large sample) but must do extensive interpretation of the meaning of historical data. That is, whenever the most applicable definition of “probability” is subjective probability, we are talking about radical uncertainty. That may or may not conform to what the Austrians think of as radical uncertainty.
For axiomatic probability and for empirical probability, there is reason to hope that different people will come to agreement. We can all agree that the probability of rolling two dice with a sum of 8 ought to be 5/36. We can all agree that if, say, 0.004 percent of men are over 7 feet tall (I have no idea what the true number is), then choosing a man at random gives us a 0.004 percent chance of choosing a man over 7 feet tall.
But we need not come to agreement over the probability that inflation will exceed 6 percent on average over the next five years. If Robin Hanson sets up a betting market, then those of us who put our money where our mouths are can produce a market-based estimate of the odds. But that market-based estimate is just, in the end, another version of subjective probability. A rational person may disagree with the market forecast, and yet be unwilling or unable to place a large enough bet to move that forecast.
For me, radical uncertainty refers to non-repeatable events. (By the way, the line between a repeatable event and a non-repeatable event is not necessarily simple to draw. Is A-Rod’s next at-bat in postseason a repeatable event? Or not? In this case, I would treat it as a repeatable event.) It means that the applicable definition of probability is subjective probability. And it means that reasonable people do not necessarily have to come to agreement on the probabilities before the uncertainty is resolved. This latter point nay cause smoke to pour out of Robin Hanson’s ears.
Returning to Falkenstein’s complaint, I think that there is a basic conundrum. Perhaps his idea of “something constructive” is something that works more like axiomatic probability or empirical probability. However, those definitions do not apply for non-repeatable events.