Right. The solution is for them to immediately say: We need 3 people to take this offer of $800 in US cash (not vouchers), or 3 people will be selected randomly.
I guarantee there will be enough takers. The issue is, even though the cost of overbooking is already factored into the cost of the flight, the airline is still trying to eek out extra dollars by offering less than the cost (vouchers, starting with lowball offers, etc).
I'm not a lawyer, but pre-announcing that three unfortunate souls will be summarily booted from the plane seems like a lawsuit waiting to happen. I'm guessing they go through the whole song and dance partially to minimize the payout, partially to collect data on average payouts and equilibrium pricing, and partially to create the opportunity for volunteers to leave willingly.
Don't get me wrong; I'd love if they simply cut to the chase. But airlines are not in the business of customer service, as is often painfully obvious. They seem to take their business practices from the Ferengi Rules of Acquisition. (In particular, the dictum, "Once you've got their money, never give it back.")
I guarantee there will be enough takers. The issue is, even though the cost of overbooking is already factored into the cost of the flight, the airline is still trying to eek out extra dollars by offering less than the cost (vouchers, starting with lowball offers, etc).