United knows the cheapest tickets on the flight are $200. They know DOT mandated compensation for involuntary bumping is 4x cost of ticket. Hence, its not worth it to them to offer more than $800 in compensation as they can just bump people involuntarily for the same value.
Demonstrating why the DOTs rules for involuntary bumping create perverse market incentives re overbooking.
the law can be that overbooking is allowed but airlines also cant involuntary boot anyone. They have to incentivize someone to get off. I'm sure if they went up to $2k in cash someone would have taken them up on the offer and just ubered to ($400ish if I remember what my check showed me) to their destination. For me, $800 (even cash) wouldn't have been sufficient for me to convince me to uber to my destination, even if I wouldn't have lost money on the transaction.
i.e. airlines are only allowed to purposefully overbook due to DOT rules, the same rules provide what I perceive as a perverse incentive when it comes to encouraging involuntary bumping.
The part you are missing is that airlines don't need a law that lets them overbook. They absolutely can involuntary boot anyone for any reason (other than discriminatory reasons that are otherwise illegal). Booting a person would be a breach of contract, but breaches of contracts aren't illegal.
Hell, they could update their contact and then it wouldn't even be a breach of a contract.
The law was written to reign in their behavior. Without it, they have a lot more freedom.
United knows the cheapest tickets on the flight are $200. They know DOT mandated compensation for involuntary bumping is 4x cost of ticket. Hence, its not worth it to them to offer more than $800 in compensation as they can just bump people involuntarily for the same value.
Demonstrating why the DOTs rules for involuntary bumping create perverse market incentives re overbooking.