In reality, there is no problem to manage here. You simply wind the incentives up until people move.
The "problem" is an airline too cheap to wind the incentives up far enough to get people to give up their seat voluntarily.
So what I'm hearing is that they'd rather be lied to at the airport, than at the time they're buying the ticket.
If you buy a ticket, then there should be no reason for the airline to deny you boarding (excepting safety issues). This is how every other service works.
If I turn up and it turns out so did everyone else who bought a ticket, then the airline should not be bullshitting about overbooking.
http://www.tvlon.com/news/how-many-people-get-involuntarily-...
http://www.huffingtonpost.com/entry/united-bump-overbooking-...
They are absolutely not forbidden from offering more if they choose to - this is actually even explicitly mentioned in the regulations. The legalese is not super easy to parse, but this link makes a decent attempt at explaining it: https://www.dailykos.com/stories/2017/4/11/1652290/-The-Wide...
Edit: The Department of Transportation's own official website also explains it quite clearly here: (https://cms.dot.gov/airconsumer/faq)
Q: Is the amount an airline must offer involuntarily bumped passengers arriving on a substitute flight over 2 hours after their original flight still 400% of the one-way fare, for a maximum of $1,350?
A: Yes, an airline must offer 400% of the one-way fare up to $1350 to involuntarily bumped passengers arriving on a substitute flight over two hours after the planned arrival time of their original domestic flight. Airlines are free to offer involuntarily bumped passengers more money than required.
The 400% minimum compensation only applies if the airline chooses not to offer enough for anyone to volunteer.
The airlines are trying to make it sounds like they are just trying to reach 100% capacity but in reality they are trying to arbitrage the fact that a few people buy non-refundable tickets and don't show up.