WEBVTT

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Have you ever sat in a doctor's
office for hours

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despite having an appointment
at a specific time?

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Has a hotel turned down
your reservation because it's full?

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Or have you been bumped off a flight
that you paid for?

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These are all symptoms of overbooking,

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a practice where businesses
and institutions

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sell or book more 
than their full capacity.

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While often infuriating for the customer,

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overbooking happens because
it increases profits

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while also letting businesses
optimize their resources.

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They know that not everyone
will show up to their appointments,

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reservations,

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and flights,

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so they make more available
than they actually have to offer.

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Airlines are the classical example,
partially because it happens so often.

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About 50,000 people get bumped
off their flights each year.

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That figure comes at little surprise
to the airlines themselves,

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which use statistics to determine
exactly how many tickets to sell.

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It's a delicate operation.

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Sell too few, and they're wasting seats.

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Sell too many, and they pay penalties -

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money, free flights, hotel stays,
and annoyed customers.

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So here's a simplified version
of how their calculations work.

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Airlines have collected years worth
of information

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about who does and doesn't show up
for certain flights.

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They know, for example,
that on a particular route,

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the probability that each individual
customer will show up on time is 90%.

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For the sake of simplicity,

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we'll assume that every customer
is traveling individually

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rather than as families or groups.

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Then, if there are 180 seats on the plane
and they sell 180 tickets,

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the most likely result is that 162
passengers will board.

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But, of course, you could also
end up with more passengers,

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or fewer.

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The probability for each value
is given by what's called

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a binomial distribution,

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which peaks at the most likely outcome.

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Now let's look at the revenue.

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The airline makes money from each
ticket buyer

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and loses money for each person
who gets bumped.

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Let's say a ticket costs $250
and isn't exchangeable for a later flight.

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And the cost of bumping 
a passenger is $800.

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These numbers are just for the sake
of example.

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Actual amounts vary considerably.

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So here, if you don't sell
any extra tickets, you make $45,000.

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If you sell 15 extras
and at least 15 people are no shows,

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you make $48,750.

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That's the best case.

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In the worst case, everyone shows up.

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15 unlucky passengers get bumped,
and the revenue will only be $36,750,

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even less than if you only sold 180
tickets in the first place.

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But what matters isn't just how
good or bad a scenario is financially,

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but how likely it is to happen.

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So how likely is each scenario?

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We can find out by using
the binomial distribution.

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In this example, the probability
of exactly 195 passengers boarding

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is almost 0%.

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The probability of exactly 184 passengers
boarding is 1.11%, and so on.

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Multiply these probabilities
by the revenue for each case,

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add them all up,

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and subtract the sum from the earnings
by 195 sold tickets,

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and you get the expected revenue
for selling 195 tickets.

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By repeating this calculation
for various numbers of extra tickets,

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the airline can find the one likely
to yield the highest revenue.

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In this example, that's 198 tickets,

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from which the airline will probably
make $48,774,

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almost 4,000 more than without
overbooking.

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And that's just for one flight.

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Multiply that by a million flights
per airline per year,

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and overbooking adds up fast.

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Of course, the actual calculation
is much more complicated.

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Airlines apply many factors
to create even more accurate models.

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But should they?

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Some argue that overbooking is unethical.

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You're charging two people 
for the same resource.

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Of course, if you're 100% sure 
someone won't show up,

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it's fine to sell their seat.

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But what if you're only 95% sure?

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75%?

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Is there a number that separates being
unethical from being practical?