Isn't that a payjoin?
Discussion
*payjoin csse
A payjoin is just a special kind of coinjoin done with the merchant. The merchant obviously knows how to unmix it, so it does not protect you from him specifically.
I'm sorry but I don't see the "obviously" part. can you help me to understand that?
Sure thing. If you participate in a 2 person coinjoin, you can "obviously" unmix it since you know what inputs and outputs are yours (the remaining ones are form the other participant).
So if you use payjoin with a merchant, you gain privacy from 3rd parties (chain analysis, criminals, IRS, etc) but you gain no privacy from that merchant itself, since he also is participating in the coinjoin.