The compensation for involuntarily being bumped, doesn't matter if you have a seat assignment or not

* If you are bumped involuntarily and the airline arranges substitute transportation that is scheduled to get you to your final destination (including later connections) within one hour of your original scheduled arrival time, there is no compensation.

* If the airline arranges substitute transportation that is scheduled to arrive at your destination between one and two hours after your original arrival time (between one and four hours on international flights), the airline must pay you an amount equal to 200% of your one-way fare to your final destination that day, with a $650 maximum.

* If the substitute transportation is scheduled to get you to your destination more than two hours later (four hours internationally), or if the airline does not make any substitute travel arrangements for you, the compensation doubles (400% of your one-way fare, $1300 maximum).

* If your ticket does not show a fare (for example, a frequent-flyer award ticket or a ticket issued by a consolidator), your denied boarding compensation is based on the lowest cash, check or credit card payment charged for a ticket in the same class of service (e.g., coach, first class) on that flight.

* You always get to keep your original ticket and use it on another flight. If you choose to make your own arrangements, you can request an "involuntary refund" for the ticket for the flight you were bumped from. The denied boarding compensation is essentially a payment for your inconvenience.

* If you paid for optional services on your original flight (e.g., seat selection, checked baggage) and you did not receive those services on your substitute flight or were required to pay a second time, the airline that bumped you must refund those payments to you.

The exceptions, because there are always exceptions

* If the airline must substitute a smaller plane for the one it originally planned to use, the carrier isn't required to pay people who are bumped as a result. In addition, on flights using aircraft with 30 through 60 passenger seats, compensation is not required if you were bumped due to safety-related aircraft weight or balance constraints.

* The rules do not apply to charter flights, or to scheduled flights operated with planes that hold fewer than 30 passengers.