Here's how airlines like United choose who to kick off of a flight

On Sunday, law enforcement officials forcibly removed a passenger from a United Airlines flight in Chicago.

The incident stemmed from the passenger's refusal to deplane after being bumped from Flight 3411 to Louisville.

The incident once again shines the spotlight on the practice bumping ticketed passengers from flights.

"What happened with United was exceedingly rare," aviation analyst Henry Harteveldt told Business Insider.

According to a United spokesperson, the airline needed to bump four passengers from to flight in order to make room for pilots and crew it needed to transport down to Louisville to operate flights later on that evening.

In many instances, airlines oversell their flights, using algorithm that calculate the likelihood people will cancel, not show up, or run late. However, there are times where passengers call the airlines' bluff and all show up.

In that case, airlines follow a specific procedure to try and accommodate all passengers.

A United Airlines spokesperson told Business Insider that Flight 3411 was not overbooked - in contradiction to a statement released by the airline Monday morning.

First, airlines will ask for volunteers,- through email, at check in or even at the gate. These requests for volunteers will typically come with anything ranging from large sums of cash to hotel rooms and a first class upgrade on a later flight.

According to Harteveldt, there is no federal limit to amount of money an airline can offer its passenger to deplane.

But this doesn't always solve the problem.

When there are simply not enough volunteers, an airline would then involuntarily deny boarding to any remaining passengers.

Statistically speaking, this rarely happens. According to Wichita State University and Embry Riddle University's Airline Quality Rating study, involuntary denied boardings fell to just 0.62 per 10,000 passengers.

Unfortunately for the Louisville-bound passenger, he was selected as one of the passengers to be bumped.

However, his selection wasn't random. He was chosen based on a series of criteria.

Based on United Airlines' Contract of Carriage (more on that later), passengers with disabilities and unaccompanied minors are the least likely to bumped from a flight.

For everyone else, the contract states that the airline made the decision based a passenger's frequent flyer status, the layout of his or her itinerary (whether the passenger has a connecting flight), the fare class of the ticket, and the time he or she checked into the flight.

This means passengers who are more expensive tickets, higher frequent flyer status, and checked in early are less likely to be bumped.

Delta and American both operate under similar policies as stipulated in their respective contracts of carriage.

A Contract of Carriage

Buying a plane ticket isn't so much a straight-forward purchase as it's an agreement to adhere to the airline's contract that spells out the terms of service for the flights. The agreement is called the Contract of Carriage.

"Customers do agree to a contract of carriage when they purchase a ticket with clear stipulation and it's available on United.com," an airline spokesperson told Business Insider.

Every airline has one and they are usually available on their website. They are long, complex, and filled with legalese. For instance, Delta's contract is 51 pages long.

As with any contract written by a single party in that agreement, it's heavily tilted towards the protection of the airlines' interests.

Do you airlines have the right to throw you off of their planes even if you haven't done anything wrong?

"Yes," Harteveldt said. "Remember, it is their aircraft and their seat - you're just renting it to get from point a to point b."

However, Harteveldt reiterated that what happened on board the Chicago flight was extremely rare.