"Airlines are allowed to sell more tickets than there are seats on the plane, and they routinely overbook flights because some people do not show up."
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This is obviously the problem - and there is a simple solution: our governments need to change the law.
A reasonable law would force airlines to sell ALL overbooked seats as overbooked seats.  Once the flight is full, if the airline chooses to sell additional seats, they would have to sell them as "overbooked" seats with the resulting risk attached.  No doubt, the seats would sell at a discount, but its the only honest way of doing business - any other way is dishonest.