How does one decide which uncertainty is Knightian? My hunch is that we tend to label something Knightian uncertainty iff it’s something the bookie might already know; if this is the case, it’s a sign Knightian uncertainty is really about suspicion.
(On a side note, I propose we label the rule of being suspicious of bets the Cider-Ear Principle or perhaps Masterson’s Law)
How does one decide which uncertainty is Knightian?
Knightian uncertainty is the one which you have no idea what it looks like. Speaking a bit more technically, you don’t know anything about the distribution—neither its class, nor the shape, nor the parameters.
Is it knightian if you have some idea what it looks like, but not exactly? If you know the mean but not the shape, or that it’s skewed normal shape, but not the direction of skew, is that Knightian and therefore not usable for utility calculation?
Maybe we need a new term then, because the examples above (weighted coin between .4 and .6, unknown number of black balls) don’t seem to meet your definition of Knightian.
Now I’m really confused. It seems like my knowledge (confidence in my probability assessment) of the shape of a distribution is continuous in the same way as my knowledge (the probability assessment itself) about a discrete future experience. I never know absolutely nothing about it (alien spies: I at least know that I can’t assign 0 to it). I also never know absolutely everything (there are very few actually perfect fair coins).
Are you saying that your belief in probability distributions is binary (or at least quantized to a small number of states)? You know it perfectly or you know nothing about it?
I don’t get it well enough to be certain that I don’t buy it, but that’s where I’m currently leaning. Especially if you bite the bullet that uncertainty is about knowledge rather than about reality (probability is a limitation of a decision agent, not present in the base reality), this just makes no sense.
It seems like my knowledge (confidence in my probability assessment) of the shape of a distribution is continuous
You are right. Knightian uncertainty isn’t a separate discrete category, it’s an endpoint of a particular interval on the other end of which sits uncertainty that you know everything about, e.g. the probability of drawing a red ball from an urn into which you have just placed 10 red and 10 black balls.
Knight himself called known uncertainty “risk” and unknown uncertainty “uncertainty”. He wrote: Uncertainty must be taken in a sense radically distinct from the familiar notion of Risk, from which it has never been properly separated.… The essential fact is that ‘risk’ means in some cases a quantity susceptible of measurement, while at other times it is something distinctly not of this character; and there are far-reaching and crucial differences in the bearings of the phenomena depending on which of the two is really present and operating.… It will appear that a measurable uncertainty, or ‘risk’ proper, as we shall use the term, is so far different from an unmeasurable one that it is not in effect an uncertainty at all.”
How does one decide which uncertainty is Knightian? My hunch is that we tend to label something Knightian uncertainty iff it’s something the bookie might already know; if this is the case, it’s a sign Knightian uncertainty is really about suspicion.
(On a side note, I propose we label the rule of being suspicious of bets the Cider-Ear Principle or perhaps Masterson’s Law)
Knightian uncertainty is the one which you have no idea what it looks like. Speaking a bit more technically, you don’t know anything about the distribution—neither its class, nor the shape, nor the parameters.
Is it knightian if you have some idea what it looks like, but not exactly? If you know the mean but not the shape, or that it’s skewed normal shape, but not the direction of skew, is that Knightian and therefore not usable for utility calculation?
Generally speaking, it’s Knightian if you have no idea.
Example: what is the probability that an alien civilization has been surreptitiously observing Earth for a while?
If you, say, know that the distribution is skewed normal but don’t know the skew sign, that’s not Knightian at all.
Maybe we need a new term then, because the examples above (weighted coin between .4 and .6, unknown number of black balls) don’t seem to meet your definition of Knightian.
Now I’m really confused. It seems like my knowledge (confidence in my probability assessment) of the shape of a distribution is continuous in the same way as my knowledge (the probability assessment itself) about a discrete future experience. I never know absolutely nothing about it (alien spies: I at least know that I can’t assign 0 to it). I also never know absolutely everything (there are very few actually perfect fair coins).
Are you saying that your belief in probability distributions is binary (or at least quantized to a small number of states)? You know it perfectly or you know nothing about it?
I don’t get it well enough to be certain that I don’t buy it, but that’s where I’m currently leaning. Especially if you bite the bullet that uncertainty is about knowledge rather than about reality (probability is a limitation of a decision agent, not present in the base reality), this just makes no sense.
You are right. Knightian uncertainty isn’t a separate discrete category, it’s an endpoint of a particular interval on the other end of which sits uncertainty that you know everything about, e.g. the probability of drawing a red ball from an urn into which you have just placed 10 red and 10 black balls.
Knight himself called known uncertainty “risk” and unknown uncertainty “uncertainty”. He wrote: Uncertainty must be taken in a sense radically distinct from the familiar notion of Risk, from which it has never been properly separated.… The essential fact is that ‘risk’ means in some cases a quantity susceptible of measurement, while at other times it is something distinctly not of this character; and there are far-reaching and crucial differences in the bearings of the phenomena depending on which of the two is really present and operating.… It will appear that a measurable uncertainty, or ‘risk’ proper, as we shall use the term, is so far different from an unmeasurable one that it is not in effect an uncertainty at all.”