The other part was a simple reminder that “peak oil” cannot be directly measured. All we have as measurable data are price and current production data. The next step is always an extrapolation based upon an assumption. One starts, for instance, with the assumption that Hubbert’s method will hold for world production, and that a calculation done today will yield an accurate “high production” and “high production date.”

How do you put error bars on that assumption, that Hubbert’s method, a heuristic, will hold?

(And I might also comment that in the year since this post, the “Hubbert’s date” for Peak oil has moved and argued again and again.)

If we look at, say, the global warming predictions, we get a range in possible rises in average temperatures – I have heard from 3 to 6 deg C. But how much faith should we put in this distribution? Clearly it is of worse quality than if the same distribution was provided for the temperatures in New York tomorrow. How could we “measure” or otherwise agree on this quality factor? Could the measure include whether the model that produced the distribution can be tuned by real feedback or not.

Sometimes there are technical problems with assigning equal odds to all outcomes. If I know that a cube factory produces cubes with edges that vary between 1 and 2 units of length, then I also know that the factory produces cubes whose volumes vary between 1 and 8 units cubed. Suppose that’s all I know about the factory. If my probability distribution for lengths is uniform, then my probability distribution for volumes is not uniform, and vice versa. For example, if I think that there’s a 0.5 chance that a randomly selected cube will have edge length > 1.5 units, then I must think that there’s a <0.5 chance that a randomly selected cube will have volume > 4 units cubed. I cannot consistently assign equal odds to all possible lengths, and assign equal odds to all possible volumes.

We might think this sort of a case is a good candidate for an “I don’t know” response. If somebody else has the same information that I do, and he says his estimate that a randomly selected cube has an edge of length >1.5 is 0.5, I might say I think he’s doing something wrong. Namely, he’s decided to be uniform over length rather than volume for no reason. I would have the same objection if he had a degree of belief 0.5 that the volume of a random cube would be >4. You might think that in this situation, it would be inappropriate to have precise degrees of belief about the expected length, or the expected volume, of a random cube in the factory.

If I were asked what my expected length for a random cube in the factory was, I think I’d just say that I expect that the length of a cube is between 1 and 2. I don’t think it would be reasonable to offer any particular expected length between 1 and 2.

ChrisA: The intent of having a “no one can know” option is interesting. Its just going to be very difficult to practically implement or realistically price. Nice theoretical concept though.

My simplistic view is that “I don’t know” is equivalent to assigning equal odds to all outcomes. Solves Robin’s scoring rule and sign challenge.

Any prediction market which is trying to estimate a “no-one can know” factor should be recognisable by having a very flat distribution, but not necessarily. So perhaps prediction markets should routinely include a “no one can know” option. This would pay off if the prediction market result was false (say outside a sigma or two). If this option is attracting a lot of money – it perhaps would say that the prediction made by the market is not very useful.

“You’re wrong” automatically implies that some expected value of some random variable is different. In the absence of explanation, there are generally obvious default ones such as expected utility.

“We just don’t know” has several possible rational interpretations as used in rhetorical discourse as mentioned above, any one of which may be meant.

It is of course preferable to fully explain what you mean in the course of subsequent argument, but I do not think that the summarized statement is “worse than useless.”

It is also possible that the person making the argument means it in an irrational form; however, it seems to me that you stated that we’re already assuming that the participants are both rational and can agree on what random variables to measure. If you insist on translating the rhetorical into that particular irrational meaning, then I must agree with you that it is an impermissible statement. If that’s what your entire argument is, then I totally agree with you.

But as a statement about actual argumentation and rhetoric, I disagree, as outlined above.

In that case, I think that your original phrasing of the post was essentially useless and misleading. If someone says “you are wrong,” then it’s an entirely natural consequence to assume that they’re saying that expected utility (or whatever) is lower by taking the other person’s advice. According to the trivial interpretation of your argument, that’s a “sign of the bias” right there. It thus seems to me useless to insist that someone who says “you’re wrong” in *any* way provide a “sign of the bias of some random variable given a probability distribution.” Merely by saying “you’re wrong,” we can assume that they’re claiming that expected utility would be maximized by taking some other option.

I agree that the person claiming “you’re wrong” has an obligation to offer an alternate course of action, but if one is not mentioned I believe that it is reasonable to assume that the alternative is the status quo to the position offered by the other party. Thus it seemed to me that your objection is essentially contentless and redundant, at least in this trivial fashion.

Since it’s obvious to me that any claim that someone is wrong involves a claim that their expected utility claims are wrong and do not actually maximize utility, to me the natural interpretation of your original point “tell me the sign of the bias” was a claim that someone had to offer a point of dispute with the original new piece of information offerred by the other party– i.e., dispute the price of oil itself or its distribution. I see that that’s not what you meant.

“That’s a signed bias on the probability mass for that set of points – too much, rather than too little. In plain-language strategic thinking, this would come out as “You’re focusing too much on what you think is the most likely outcome, and not thinking about possible exceptions.”"

Yes absolutely, but my point, as above, is that it’s “worse than useless” pedantry to attempt to claim that “you are wrong,” especially as used in casual rhetoric, does not automatically assume a claim that *some* sort of expected value (esp. expected utility) is different. Again, in casual rhetoric, I believe that a reply of “show me where my bias is” is generally going to be taken as a request to focus on the particular measurements of the random variables brought up originally, especially on focusing on the original expected value offered, such as a price of oil.

I think fundamentally we agree that “you’re wrong” must rationally contain a disagreement about some expected value of some random variable. Where we disagree is in what the natural interpretations of rhetorical discourse are. To me, “you’re wrong, because we just don’t know” should automatically indicate that I disagree about some expected value of a random variable and prefer some alternate course to the one you’re suggesting– if not explicitly stated, then the status quo. It may be that the point you’re attempting to make is so trivially obvious to me that to demand that people state it in rhetorical discourse seemed useless and redundant, so I incorrectly searched for an alternate meaning. To me, “you’re wrong, because we just don’t know” is not “worse than useless,” because I automatically interpret “you’re wrong” as implying the necessary claim that *some* expected value is different and then interpret “because we just don’t know” as an imprecise statement of one of several possibilities.

One possibility is a statement that the other person’s variance is wrong, or that the first person is not considering other alternatives or that the random variable brought up by the first person had a random variable with poorly understand states that cause it, making it difficult to hedge against, unlike other alternatives. To me it is also reasonable to assume that the first person may have made one of several very common mathematical errors, especially that of deriving variables which are non-linear measurable functions of estimated random variables by using only the expected value of the estimates rather the entire distribution. In particular, if the function is complicated enough, then it can be too computationally difficult or intensive to properly derive the variable of interest (such as utility) using the entire distributions of the estimated variables. In which case, “we just don’t know” also has, to me, a natural interpretation of “in order to perform this calculation given our resources, we must make many simplifying assumptions (often including using expected or maximum likelihood values for estimated parameters). However, the equation of interest is highly non-linearly dependent on the estimated parameters and if the calculation were performed correctly without such mathematical simplifications, the results would be different.”

Considering how poorly understood this mathematical point is, I think it’s a reasonable interpretation. (For example, much statistical literature recommends that people use an estimate for a standard deviation of a population based on a sample by using an estimate which is not unbiased, but rather the square root of an unbiased estimator for the variance, which is not the same, not that many people realize it. The entire concept of the unbiased estimator has problems in certain probability distributions and so too do maximum likelihood estimators in certain situations.)