My guess is that rather than policing any of various muggle institutions, they investigate, as we do in our own world, whenever anyone appears to suddenly come into possession of large amounts of money for no clear reason, and if they find out they did something illegal, they throw them in jail.
This would require a wizarding equivalent of the IRS, which I've never heard of. I've never seen mention of taxes, but they obviously have to pay the ministry employees something. One of the consequences of their primitive monetary system is that it is very easy to obtain money without the government knowing it. Perhaps they could use muggle taxes to buy gold to be minted into galleons, and pay employees that way. In cannon, the prime minister knows about the wizarding world, and it's possible that information of it is just highly classified.
I suppose money could be magically tracked, but there would still need to be a ministry department. And if that is possible, it easily defeats most money-making strategies.
If any money tracking is going on, I suspect it's done by the goblins, who I believe canonically have means of magically tracking things.
You don't need to magically track money though, to keep record of how much money is in people's bank accounts, and take notice if someone who's not supposed to have lots of money suddenly starts making a lot of very expensive purchases.
This is a new thread to discuss Eliezer Yudkowsky’s Harry Potter and the Methods of Rationality and anything related to it. This thread is intended for discussing chapter 81, which should be published later today. The previous thread passed 400 comments as of the time of this writing, so it will pass 500 comments soon after the next chapter is posted, if not before. I suggest refraining from commenting here until chapter 81 is posted; comment in the 12th thread until you read chapter 81. After chapter 81 is posted, I suggest all discussion of previous guesses be kept here, with links to comments in the previous thread.
There is now a site dedicated to the story at hpmor.com, which is now the place to go to find the authors notes and all sorts of other goodies. AdeleneDawner has kept an archive of Author’s Notes. (This goes up to the notes for chapter 76, and is now not updating. The authors notes from chapter 77 onwards are on hpmor.com.) When posted, chapter 81 should appear here.
The first 5 discussion threads are on the main page under the harry_potter tag. Threads 6 and on (including this one) are in the discussion section using its separate tag system. Also: one, two, three, four, five, six, seven, eight,nine, ten, eleven, twelve.
As a reminder, it’s often useful to start your comment by indicating which chapter you are commenting on.
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically: