A more typical example: I can look at a chain of options on a stock, and use the prices of those options to back out market-implied probabilities for each possible stock price at expiry.
Gotcha, this is a great example. And the fundamental reasons why this works are 1) the immediate incentive that you can earn higher returns by pricing the option more correctly; combined with 2) the fact that the agents who are assigning these prices have (on a dollar-weighted-average basis) gone through multiple rounds of selection for higher returns.
(I wonder to what extent any selection mechanism ultimately yields agents with general reasoning capabilities, given tight enough competition between individuals in the selected population? Even if the environment doesn’t start out especially complicated, if the individuals are embedded in it and are interacting with one another, after a few rounds of selection most of the complexity an individual perceives is going to be due to its competitors. Not everything is like this — e.g., training a neural net is a form of selection without competition — but it certainly seems to describe many of the more interesting bits of the world.)
Thanks for the clarifications here btw — this has really piqued my interest in selection theorems as a research angle.
Gotcha, this is a great example. And the fundamental reasons why this works are 1) the immediate incentive that you can earn higher returns by pricing the option more correctly; combined with 2) the fact that the agents who are assigning these prices have (on a dollar-weighted-average basis) gone through multiple rounds of selection for higher returns.
(I wonder to what extent any selection mechanism ultimately yields agents with general reasoning capabilities, given tight enough competition between individuals in the selected population? Even if the environment doesn’t start out especially complicated, if the individuals are embedded in it and are interacting with one another, after a few rounds of selection most of the complexity an individual perceives is going to be due to its competitors. Not everything is like this — e.g., training a neural net is a form of selection without competition — but it certainly seems to describe many of the more interesting bits of the world.)
Thanks for the clarifications here btw — this has really piqued my interest in selection theorems as a research angle.