There are two parts to what people generally refer to as the "Housing Crisis". One is the simple fact that homes are too expensive. The other part is that building new, expensive houses pushes existing, poorer, renting residents out of communities and scatters them across the outskirts of cities where they have to spend eight hours a day commuting.

Many people think the solution to the first part is building more houses. Many people also think that building more houses conflicts with solving the second part. To me the question is this: given that people like communities and presumably would be happy to pay money for them, why isn't this currently a factor in the housing market?

Regular Goodhart

Normal Goodhart's law goes like this:

• A system $S$optimizes for $X$
• $X$is correlated with $U$, which we want
• So we like system $S$and give it more power
• With too much power, $S$ makes lots of $X$at the cost of $U$
• Now we have no $U$

One case of this is distributional shift, where for very big $X$, it's no longer correlated with $U$. For example height and basketball ability.

An example in a typical market would be like this:

• Company in market optimizes for making profit
• Good products are correlated with profit
• With too much power the strategies like "make good product" are dominated by other strategies like "form a total monopoly" or with enough power, extreme cases like "take over France for slave labour"

This is a case of standard Goodhart.

One-Track Goodhart

Now consider the following case:

• Housing developers optimize for making profit 
• Various factors are correlated with house price: sufficient supply of places to live, nice communities, being pleasant to live in
• With such an undersupply, the factor of supply/demand dominates everything else
• Now housing developers are incentivised to remove existing housing in favour of servicing the parts of the market where undersupply is greatest

Note how we've gone out of the distribution where profits correlate with a bunch of human profits. Now they only correlate with producing as much housing as possible for the most underserviced part of the market (as a function of wealth to spend), which in this case is lots of expensive apartments. We've not done this by letting the market optimize harder for profit, we've done it due to making one factor dominate the optimization process by pushing the situation out of distribution.

Instead of doing $X$ at the cost of $U$, $S$ does element $u_{32}$ exclusively at the cost of elements $u_1$ through $u_{31}$. It's fervently pursuing it at the cost of everything else. The biggest difference between this and "standard" Goodhart is that the direction of optimization is towards the region where the Goodharting is less strong, and something external is pushing it away. Of course just giving the system loads more optimizing power might not be always good from the perspective of regular Goodhart, or generally, so this isn't the necessarily the answer.

(If someone can come up with a better name I'll take it)

Satisficers

The reason this can occur is that markets have some satisficer-like behaviour. Around the situation where "everyone has somewhere to live", adding more houses decreases the price a lot less than removing houses increases the price. And the more demand exceeds supply for "places to live", the harder the market incentivises supply of that. This is why markets can even work in the first place.

But with forces like those affecting housing markets pushing them out of a situation where all demands are close to being supplied, the demand for "enough houses" completely dominates.

I suspect other cases are common in satisficer-like systems, particularly humans. Examples include basically all human biological needs and impulses sometimes.

Takeaways

Just because a system is currently not optimizing for something, doesn't mean it's incapable of optimizing for it. This might be due to too much optimizing power, or it might be due to being pushed backwards by other factors into a different part of the optimization landscape where one factor dominates, it might even be trying to optimize out of that part of the distribution but being prevented from doing so by external forces.