system
A chat on subreddit /r/NoStupidQuestions
human
How would you determine what the cap is, if not via the free market?

If you really want to keep housing prices reasonable you should ban investment firms and the like from snatching up homes with the intent of turning them all into rentals, or using some sort of market manipulation to sell at a huge profit. I'd give that a shot first.
gpt
Especially considering houses are not the same. Do you also limit size and amenities to keep houses affordable? Force people to sell at a loss because they upgraded too much?