The revelations this week that airlines overbook as a policy and that they can forcibly remove passengers when their calculations go awry has shocked millions from Chicago to China. But it's a problem as old as the airline industry itself.

As they expanded service in the late 1940s, airlines struggled with the problem of "no-shows" - people who reserved a seat but failed to board. This was a serious problem: A half-empty plane -- even one with a few empty seats -- could operate at a loss, or with severely diminished profits.

Overbooking was the solution, albeit one likely discovered by accident. Prior to the 1950s, airline reservations were a low-tech affair. Each airline had a "master board" at headquarters that showed all the available seats on any given flight; regional offices maintained versions of the board as well.

The clerk overseeing the master board would put a green flag next to flights that had only a few seats left, and a red flag when filled entirely. This cumbersome system, though, did not operate in real time, so it was easy to oversell a flight by mistake.

The airlines, however, quickly realized that this wasn't a problem: Virtually every flight had its share of no-shows. It didn't take long for executives to realize that overbooking was a fantastic money-making strategy.

Yet no airline has ever taken responsibility for the innovation. Indeed, executives spent years steadfastly denying that they deliberately overbooked flights.

By 1950, the practice had become widespread. So, too, did the complaints of irate passengers.

In one well-publicized incident in December, 1953, a New York businessman bumped from a flight out of Newark opted to picket the plane on the tarmac, eventually sitting on the front wheel in protest. (Airline security was nonexistent at this time). The New York Times, writing a few years later about the overbooking problem, observed that this particular passenger "was doing only what hundreds of others have felt like doing."

But the practice continued, and Congress, stirred by irate constituents, began pushing for action. In June, 1956, Republican Senator Margaret Chase Smith of Maine lambasted the airlines for their "callousness"; a month later, the Civilian Aeronautics Board (CAB, a precursor to the Federal Aviation Agency and the National Transportation Safety Board) sent out a letter warning the major carriers to curtail the practice.

The number of incidents dropped dramatically, but soared again within a few months. The CAB implemented enforcement proceedings against National (later acquired by Pan Am) and Eastern (which went bankrupt in 1991, but not before selling part of the company to Donald Trump). Both were charged with overbooking as well as what was then the illegal practice of paying customers cash for their trouble. (Because bumped passengers got a better deal than everyone else, the CAB barred the practice as "discrimination.")

The airlines fought back, claiming that any overbooking that happened was an honest mistake, not a result of policy. This, to put it politely, was highly unlikely. As Marvin Rothstein, a manager at American Airlines in 1960, later recalled, the company's director of reservations informed him "that deliberate overbooking was practiced everywhere in the system whenever the volume of traffic made it worthwhile." Top management condoned the practice; regional managers implemented it.

That same decade, the CAB lurched from one extreme to another in struggling to address the problem. In 1961, it supported a scheme by the airlines to penalize no-show passengers, but abandoned the idea two years later. Bad publicity. After studying the problem further, the CAB reversed course and sanctioned overbooking - padded as it was with euphemism. "Through 'carefully controlled overbooking,'" the agency concluded in a 1967 report, "the airlines can reduce the number of empty seats and at the same time serve the public interest by accommodating more passengers."

The CAB didn't define "carefully controlled," but it did mandate that airlines give bumped passengers a voucher equivalent to the cost of the original flight. This one-size-fits-all solution fell short, failing to recognize that passengers might want more to compensate them for their trouble (or might be willing to settle for less).

Enter the economist Julian Simon. In a short but cheeky article entitled "An Almost Practical Solution to Airline Overbooking" published in a very obscure academic journal in 1977, Simon proposed a novel solution: Airlines should conduct an auction, with passengers offering sealed bids as to what they would be willing to accept for the inconvenience of getting bumped. The lowest bidder (or bidders) would get bumped and receive a voucher; everyone else would fly on schedule. "All parties benefit, and no party loses," wrote Simon.

Simon didn't expect the article to be taken seriously. It was written in a light-hearted tone, and he speculated that airlines would reject the idea because it wasn't "decorous." "It smacks of the pushcart rather than the one price store," he wrote.

But Simon was on to something. In subsequent years, airlines gradually adopted a crude version of the auction, offering vouchers at a certain price, and if this failed to attract passengers, raising the price. In recent years, some airlines have gone even further, asking passengers when they check in how much they would be willing to accept in exchange for getting left behind.

Unfortunately, the auction system was grafted onto older regulations governing how much money passengers could be paid. Today, that figure is 400% of the original fare, up to a maximum of US$1,350.

If regulators want to solve this problem for good, they should consider the vexed history of overbooking and abolish this upper limit and then implement Simon's proposal in its entirely. In other words, airlines should be permitted to overbook their flights, but when they need to bump passengers, they should only remove people who have voluntarily given up their seats for a voucher, with the price set by auction

Perhaps that price will be US$500; it may well be US$5,000. But one imagines that after handing out some vouchers in the high four figures, the airlines may, after seventy years, finally curtail their reliance on overbooking.