So what is your argument, that it doesn't apply everywhere therefore it applies nowhere?
You're misunderstanding the root cause. Your example works as the the metric is well aligned. I'm sure you can also think of many examples where the metric is not well aligned and maximizing it becomes harmful. How do you think we ended up with clickbait titles? Why was everyone so focused on clicks? Let's think about engagement metrics. Is that what we really want to measure? Do we have no preference over users being happy vs users being angry or sad? Or are those things much harder to measure, if not impossible to, and thus we focus on our proxies instead? So what happens when someone doesn't realize it is a proxy and becomes hyper fixated on it? What happens if someone does realize it is a proxy but is rewarded via the metric so they don't really care?
Your example works in the simple case, but a lot of things look trivial when you only approach them from a first order approximation. You left out all the hard stuff. It's kinda like...
Edit: Looks like some people are bringing up metric limits that I couldn't come up with. Thanks!
> So what is your argument, that it doesn't apply everywhere therefore it applies nowhere?
I never said that. Someone said the law collapses, someone asked for a link, I gave an example to prove it does break down in some cases at least, but many cases once you think more about it. I never said all cases.
If it works sometimes and not others, it's not a law. It's just an observation of something that can happen or not.
You're right. My bad. I inferred that through the context of the conversation.
> If it works sometimes and not others, it's not a law.
I think you are misreading and that is likely what lead to the aforementioned misunderstanding. You're right that it isn't a scientific law, but the term "law" gets thrown around a lot in a more colloquial manner. Unfortunately words are overloaded and have multiple meanings. We do the same thing to "hypothesis", "paradox", and lots of other things. I hope this clarifies the context. (even many of the physics laws aren't as strong as you might think)
But there are many "laws" used in the same form. They're eponymous laws[0], not scientific ones. Read "adage". You'll also find that word used in the opening sentence on the Wiki article I linked as well as most (if not all) of them in [0]
I disagree with all of those examples, they are misunderstanding what it means for the metric to break down in the context of the law, but alas. "If you run a different race" lol.
That's the key part. The metric has context, right?
And that's where Goodhart's "Law" comes in. A metric has no meaning without context. This is why metrics need to be interpreted. They need to be evaluated in context. Sometimes this context is explicit but other times it is implicit. Often people will hack the metric as the implicit rule is not explicit and well that's usually a quick way to make those rules explicit.
Here's another way to think about it: no rule can be so perfectly written that it has no exceptions.
could you explain what you think the difference is?
a metric is chosen, people start to game the system by doing things that make the metric improve but the original intent is lost. increasingly specific rules/laws have to be made up to make the metric appear to work, but it becomes a lost cause as more and more creative ways are found to work around the rules.
Exactly, that's the definition. It doesn't apply to timing a 100m race. There's many such situations that are simple enough and with perfect information available where this doesn’t break down and a metric is just a metric and it works great.
Which is not to the detriment of the observation being true in other contexts, all I did was provide a counter example. But the example requires the metric AND the context.
Do you know certain shoes are banned in running competitions?
There's a really fine line here. We make shoes to help us run faster and keep our feet safe, right? Those two are directly related, as we can't run very fast if our feet are injured. But how far can this be taken? You can make shoes that dramatically reduce the impact when the foot strikes the ground, which reduces stress on the foot and legs. But that might take away running energy, which adds stresses and strains to the muscles and ligaments. So you modify your material to put energy back into the person's motion. This all makes running safer. But it also makes the runner faster.
Does that example hack the metric? You might say yes but I'm certain someone will disagree with you. There's always things like this where they get hairy when you get down to the details. Context isn't perfectly defined and things aren't trivial to understand. Hell, that's why we use pedantic programming languages in the first place, because we're dealing with machines that have to operate void of context[0]. Even dealing with humans is hard because there's multiple ways to interpret anything. Natural language isn't pedantic enough for perfect interpretation.
You're misunderstanding the root cause. Your example works as the the metric is well aligned. I'm sure you can also think of many examples where the metric is not well aligned and maximizing it becomes harmful. How do you think we ended up with clickbait titles? Why was everyone so focused on clicks? Let's think about engagement metrics. Is that what we really want to measure? Do we have no preference over users being happy vs users being angry or sad? Or are those things much harder to measure, if not impossible to, and thus we focus on our proxies instead? So what happens when someone doesn't realize it is a proxy and becomes hyper fixated on it? What happens if someone does realize it is a proxy but is rewarded via the metric so they don't really care?
Your example works in the simple case, but a lot of things look trivial when you only approach them from a first order approximation. You left out all the hard stuff. It's kinda like...
Edit: Looks like some people are bringing up metric limits that I couldn't come up with. Thanks!