Thank you very much for this question, because I think it exposed a weakness in my own explanation.
In the social science literature, they use the term “audit”, but they don't use it in the financial sense. The audit simply describes the process I outlined where two testers, say one black and one white or one woman and one man, ask a landlord for a room or an employer for a job. They call that an audit, but it's quite confusing, because obviously the tax authorities also have an audit and it means something else.
I think the reason audits are exciting to me is that you can have an audit without transparency. Remember that I said you don't get to see the inside of the landlord's brain. That's why the audit is exciting. We can audit platforms like Facebook and Google without transparency by simply protecting third parties like researchers, investigative journalists and civil society organizations like NGOs, who wish to see if there are harms produced by these systems. To do that, they would act like the testers in my example. They would act as users of the systems and then aggregate these data to see if there were patterns that were worrying.
Now, this has some shortcomings. For example, you might have to lie. Auditors lie. The people who go in to ask a landlord for a room don't actually want a room; they're testers working for an NGO or a government agency. So you might have to lie; you might have to waste the landlord's time, but not very much.
Usually on systems like large Internet platforms, it's hard to imagine that an audit would be detectable. However, it's possible that you would provide false information that makes it into the system somehow, because you aren't actually looking for a job; you're just testing. There are definitely downsides.
As I mentioned, you also need some sort of system to continue...after your audit finds that there is a problem. For example, if you found that there was something worrying, you would then need some other mechanism like a judicial proceeding, say, involving some disclosure. You could say that transparency comes later through another process, if you needed to really understand how the system works. However, you might never need to understand that. You might just need to detect that there is a harm and tell the company they have to fix it, and they're the ones that have to worry about how.
This is why I'm excited about auditing, because it gets around the problems of transparency.