Allow fliers at the time of purchase to elect a contingent discount (or discount category) if the flier is willing to be bumped off the flight if it is oversold. Then, if a flight is oversold, the airline automatically bumps those fliers who checked bumpee discount, starting with those willing to be bumped for the least amount, and the bumpee collects his discount. If the airline sees that few fliers have elected a bumpee discount, it might conclude that it should limit overselling.

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