Woman bumped from flight, misses 10K dream cruise

There is no need for involuntary bumping. The solution: Ask for volunteers using a bid up/bid down process.

1) Announce the maximum possible compensation lets say $800.
2) Start bidding up at $300 in $25 increments and increase until someone raises a hand, let's say $650.
3) If multiple people raise their hand, start the bid down process. Those people leave their hands up and the price goes down from $650 in $25 increments.
4) If all hands go down at the same time at $450, the person who paid the least for their ticket is selected and paid the previous price $475.

The passenger already volunteered for the process and already agreed to the $475 price.

Problem solved.