Thoughts on Probability and Uncertainty

I have taken "radical uncertainty" to apply, not as Bryan uses in the debate, the case of knowing literally nothing (which is, as he asserts, difficult to imagine), but instead describing a case where what one does know informs the situation so little that it cannot be used to make decisions.

Or, I suppose in Bryan-speak, a case where the probability is incalculable, p = ?

I don't think a 'p=?' case is impossible, particularly when one is relying on myriads of other actors with private knowledge and private motives. I may be able to guess that they know something I don't, and I can guess at their motives insofar as I have general knowledge of possible motives, but overall only with a small degree of probability of being correct in any individual case. When multiplied by thousands or millions of participants, I might arrive at a uselessly small 'p' in short order, even in a universe where it were somehow possible to prove that my initial probability values were accurate.

To clarify, as I wrote that rather badly. It isn't, of course, the 'p' that would get small, since that would imply I knew something to be unlikely. I meant that the _range_ would become so broad as to be practically infinite, leaving me with a fat "?" as an answer. This is in contrast to the Bryan-esque (at least in the debate) view that I will somehow always have sufficient knowledge to be be able to put it to use churning out probabilities that I can apply to any given situation.

I agree. This is what David Henderson and I said in our book, Making Great Decisions in Business and Life:

If I pull a foreign-looking coin out of my pocket, what probability would you assign to my flipping a head? The answer is fifty percent if the coin is fair. What if the coin isn’t exactly clean, balanced, unblemished, and symmetrical? You have to believe that the coin is fair to assert 50 percent, and beliefs are based on information. If we flipped this particular coin 10,000 times and counted the number of heads and tails, then you might have more reason to assert a 50-percent probability, but you also, at that point, would have much better information. Probabilities move from subjectivity towards objectivity as our information improves. But it is only the trivial cases that have perfect information and can be called objective. Not only the majority of cases, but also the most interesting cases must be called subjective because they’re based on our personal assessments of future events.

Ask a 5 year old if inflation is going to average more than 6% over the next 5 years. That illustrates radical uncertainty to me. I have no difficulty in imagining that I'm that 5 year old in many situations.

Bryan says that we always know something reasonable. But in his book he argues that often times the median voter is like the 5 year old of the previous example. Pressed to assign a probability the median voter will give a completely subjective answer based on factors that are not related to the given problem.

Complaining about Taleb not being constructive seems to suggest that Falkenstein hasn't understood one of Taleb's main points: that simply being able to honestly admit ignorance is itself valuable. Complicated non-linear systems need not necessarily yield their underlying probability distributions to either empirical or axiomatic understanding, and in those cases, is it not better to admit you just don't know what's going on and act accordingly, than to come up with an apparently plausible (but in fact not meaningfully testable) subjective narrative about the system?

Popper's propensity interpretation of probability is the most useful. You should include that.

Zane Selvans - but what does it mean to "admit you just don't know what's going on and act accordingly" if the decision you're facing is a long-term one like building a power station?

Re: non-repeatable events.

It has always fascinated me that certain markets produce prices which, after the fact, prove to be (on average) the best guess. Of course, the efficient market hypothesis asserts this (by and large correctly I think) for the stock market. But betting markets also produce this. Try beating the spread consistently on NFL games if one doubts this.

Does this have any thing to do with "probability"? I think so. Even in a world of radical uncertainty, sports betting markets pick the spread which has a "50-50" chance of being out guessed by any individual bettor. Economies are more complex than betting markets.

But, if the above is true, can we infer that certain political economy policies are less likely to be successful than others---even in a world of radical uncertainty?

Just like value is always subjective and not intrinsic, aren't all human-made probabilities always subjective? Isn't probabilizing the same process as valuing?

It seems to me that you are saying that probability is subjective in only 1/3 cases, but otherwise it is an objective & intrinsic quality of something.

Not knowing the best course of action to take under uncertainty doesn't change the uncertainty. Sometimes, we just have to admit we don't know.

But I think in a lot of circumstances, even when things are radically uncertain, you can make rational decisions. Are the consequences of being wrong severe and negative? If so, can they be limited, and if not, maybe the prudent thing to do is walk away altogether. Or are the consequences of being wrong, or exploring naively, potentially enormous and positive?

You say that the probability of the coin coming up heads is 50%.

What are the betting odds?

I would require much better odds than even money before I would make a wager.

It's worth noting that probability predictions for non-repeatable events can be analyzed like those for repeatable events, assuming you have some meaningful way to collect a bunch of them.

The simplest way is to take a bunch of p_i's for a series of upcoming events and sum them to x. If more than x of those events occur then in general you are under-estimating their likeliness, and if less then you are in general over-estimating.

You can then partition in various ways and see where estimations are furthest off, etc. Good confidence windows for the distance between x and the number of outcomes are a little tricky, but "good enough" solutions aren't so bad.

And of course, as with repeatable events, it's important to keep an eye out for implied assumptions of independence.

For example this is a good way to rate weather predictions where the probabilities of the predictions vary. But you can look at predictions of interest rates and stock prices as well.

Building a bit on Steven H Noble: if you flip a coin to test whether it's a fair coin, how many times do you have to flip it before you think 50% is no longer a "subjective" probability? If you make a series of predictions of various events, assigning 60% odds to each event, and, after that many predictions, I find that about 20% of the events take place, can I assert that your subjective odds are "wrong"?

Subjective Economics differs for everyone. When someone is involved in the economic decision they will have some sort of subjective opinion. Ideally, someone outside the decision or prediction should be putting in his opinion also to bring in a subjective point of view. But this also brings in another view in normative economics. There is no such thing as completely objective opinions. To say opinion is to say subjective. Therefore, subjective probability always occurs when predicting an outcome.