For any reputable conference, authors with a conflict of interest will recuse themselves from discussions about their paper. They won't have a vote on the paper, and if things are very well administered, other committee members won't even know that the paper is from that particular author, only that the author has a conflict of interest. Indeed, there are many reasons for a conflict of interest:
- Current or prior colleague at the same university.
- Current or prior collaboration or co-author on a paper or papers.
- Current advisor / student relationship.
These guidelines are generally spelled out in the paper submission guidelines, too (if you are an author and have a conflict, you should list them). Also, in many program committee meetings, committee members go in and out of paper discussions based on whether they have a conflict for a particular paper or not.
is there any regulation, either ethical or by law, that prohibits this type of thing?
Ethical: sure (see above).
Legal: no. I'm not sure why people think there are a lot of legal rules that dictate how independent, non-government conferences and journals are administered. I've seen this in a number of questions recently, and the bottom line is that a conference has its own rules to abide by, and that's about it. Conference organizers have a vested interest in making things fair to the extent that they don't want the conference to have a bad name, but they aren't in the position to be bound by any laws pertaining to the way the conference is administered (outside of normal law-abiding behavior).