United Airlines booted 3,765 passengers off flights last year just because it sold more tickets than there were seats on the plane, but none of those got as much attention as the man who was dragged off a plane in Chicago over the weekend.

Video posted on Facebook showed the shock on the faces of other passengers. And it created a public-relations nightmare for the airline today as news of the video spread.

Airlines are allowed to oversell flights, and they frequently do, because they assume that some passengers won’t show up. U.S. airlines bumped 40,000 passengers last year, not counting those who volunteered to give up their seats.

But there are some federal rules that apply.

VOLUNTEERS

When they know a flight is oversold, airlines will ask for volunteers to give up their seat, usually for a travel voucher or other reward, and a seat on a later flight. According to the government, 434,000 passengers voluntarily gave up seats on the country’s largest 12 airlines last year, including nearly 63,000 on United. The champion of overbookers was Delta Air Lines — about 130,000 passengers on Delta gave up their seats last year.

When voluntary offers don’t work, the airlines can deny boarding — or bump — passengers against their will. That appears to be what happened before Sunday night’s United flight from Chicago to Louisville, Kentucky. In those cases, federal rules spell out how much the airline must pay each passenger. Airlines must give bumped passengers a written statement that explains their compensation rights.

COMPENSATION

Compensation varies by how long the passenger will be delayed. If the airline can rebook the passenger and get him to his destination within an hour of his originally scheduled arrival time, no compensation is required.

If the passenger will arrive between one and two hours later than planned — or between one and four hours for an international flight — the airline must pay the passenger twice the amount of the one-way fare to his destination, up to $675.

If the passenger will be delayed more than two hours — or four hours for international flights — the airline must pay him four times the one-way fare, up to $1,350.

AVOIDING GETTING BUMPED

Airlines will usually bump people flying on the cheapest tickets because the required compensation will be lower. Carriers have other rules, too. United Airlines says that when deciding who gets bumped, it considers how long it will take for passengers to reach their destination on a later flight, it won’t break up a family group, and won’t bump minors who are traveling alone.

Airlines are most likely to oversell flights during busy travel periods such as spring break and the summer-vacation season, but bumping can happen any time there is bad weather that causes some flights to be canceled.

IF YOU WANT TO BE BUMPED

Some savvy travelers see oversold flights as an opportunity — for them. They’ll give up their seats if the airline makes a sweet enough offer. Some check their flight’s seating chart ahead of time to see if it’s sold out. If you aim to be bumped, sit near the gate agent’s desk so you can pounce before other passengers take that offer of travel vouchers, gift cards, and sometimes cash. If offered a spot on a later flight, make sure it’s a confirmed seat. And don’t check a bag.