You've offered a good explanation for how and why the "overbooking" scenario can occur, but the problem is with how United chose to solve the issue. This could have all been solved more easily by continuing to increase the offered compensation until *someone* agreed to get off the flight. If "price optimization" is used to dynamically adjust prices when purchased by passengers, the same holds true when being "purchased back" by the airline. At some $$ amount a passenger will agree to give up their seat; even at $5K or $10K it would have been fractions cheaper than what this option will cost in lost business, damaged reputation and legal fees and possible legal judgments.