Title 14 of the Code of Federal Regulations is the law governing Aeronautics and Space. It is under this that all federal regulations governing air travel reside. Here's a link to the portion that governs the Office of the Secretary of Transportation....

There's more stuff in there too...governing FAA, FAR 121 which is the Federal Aviation Regulation governing AA's (and the other airlines' operations). Here's the link to the high level .... you can then drill down to the parts you are interested in reading.

I should point out here, that in my opinion, it would've been perfectly fine if the OP had agreed that being rebooked on the nonstop as opposed to the connection was "compensation" enough. I do not think that AA is "required" to give the OP a voucher in this case. However, it sounds as if the OP "volunteered" to give up his seat...and in their understanding...it was in exchange for the voucher. If the agent had another understanding, they should've made that clear to customer whom could've then decided they would either not take the "bump" and stick with the original flight or just take the nonstop without a voucher and be thankful for the better schedule. That's up to the OP. In this case, I think the supervisor made the correct decision. And I also think that this is a good lesson to all of us... make sure to the extent possible that you and the agent have agreed on what the final outcome is going to be before you volunteer.