In 2011, Delta Air Lines began a practice in which they overbook some flights, using algorithms to determine how many seats to overbook based on historical data, and allow passengers checking in for the overbooked flight to state the value of travel vouchers they would be willing to accept in exchange for taking a later flight. The airline then selects the passengers who will be bumped to a later flight based on the lowest bids.[10] According to the airline, the biggest cost saving from the practice is that it improves on-time flight departures, since gate attendants are not burdened with negotiating with passengers that are considering being bumped from the flight.[10] Among the three major U.S. carriers, Delta had the highest rate of total bumped passengers (96 per 100,000 passengers vs. 95 on United Airlines and 50 on American Airlines), but the lowest rate of involuntarily bumped passengers (3 per 100,000 vs. 5 on American and 11 on United).[10]