I expect that the main problem with Goodhart’s law is that if you strive for an indicator to accurately reflect the state of the world, once the indicator becomes decoupled from the state of the world, it stops reflecting the changes in the world. This is how I interpret the term ‘good,’ which I dislike. People want a thermometer to accurately reflect the patterns they called temperature to better predict the future — if the thermometer doesn’t reflect the temperature, future predictions suffer.
A problem I have with this reinterpretation is that “state of the world” is too broad. In looking at a thermometer, I am not trying to understand the entire world-state (and the thermometer also couldn’t be decoupled from the entire world-state, since it is a part of the world).
A more accurate way to remove “good” would be as follows:
In everyday life, if a human is asked to make a (common, everyday) judgement based on appearances, then the judgement is probably accurate. But if we start optimizing really hard based on their judgement, Goodhart’s Law kicks in.
The point of Goodhart’s Law is that you can only select for what you can measure. The burger is a good analogy because Instagram can’t measure taste or nutrition, so when Instagram is what optimizes burgers, you get burgers with a very appealing appearance but non-optimized taste and nutrition. If you have the ability to measure taste, then you can create good taste, but you run into subtler examples of Goodhart (EG, Starbucks coffee is optimized to taste good to their professional tasters, which is slightly different from tasting good to a general audience).
Just specifying the variable you’re interested in doesn’t solve this problem; you also have to figure out how to measure it. The problem is that measurements are usually at least slightly statistically distinct from the actual target variable, so that the statistical connection can fall apart under optimization.
I also take issue with describing optimizing the appearance of the burger as “narrower” than optimizing the burger quality. In general it is a different task, which may be narrower or broader.