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	Film buffs huff over fest lottery fairness

				by

			Jeffrey S. Rosenthal

National Post (Toronto Section, Page 20)

Saturday, September 10, 2005

(Jeffrey S. Rosenthal is a professor in the Department of Statistics at
the University of Toronto.  His book "Struck by Lightning: The Curious
World of Probabilities" was just published by HarperCollins Canada.)

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Of the 335 films showing at the Toronto International Film Festival this
year, some are more popular than others.  Competition for precious spots
at key screenings is intense, and emotions run high.

In the festival's early days, ticket requests were processed on a first
come, first served basis, with gung-ho movie fans camping out overnight
in sidewalk queues (or paying others to line up for them) in an effort
to secure entry to their preferred flicks.

In recent years, the festival has instead used a lottery system, whereby
all of the advance ticket requests are grouped together and processed in
random order.  This new system has eased the early-hour rush, but makes
many festival goers furious.  "If they're going to make it arbitrary,
then at least make it FAIR," snapped one.  "If you're in Box 21, and
they select Box 22, you're SCREWED," wailed another.

As a professor of probability, I often find myself at the receiving end
of such complaints.  What has these patrons so worked up?

When ticket request forms are received, they are filed in a number of
different boxes (48, this year).  From there, the festival COULD decide
to process those boxes in completely random order (say, first Box 36,
then Box 21, then Box 8, then Box 45, and so on) -- just like shuffling
a deck of cards completely before dealing them out.  But this is NOT
what they actually do.

Instead, one box is selected by random draw (Box 36, this year).
The movie requests in that box are processed first.  Once that box is
empty, then the remaining boxes are processed sequentially: Box 37, then
Box 38, then Box 39, and so on up to Box 48, then back to Box 1, Box 2,
through to Box 35.  This is like taking a new deck of cards, giving
it a single cut to put a random card on top (say, the six of hearts),
and then dealing all of the cards out in sequence: six of hearts, seven
of hearts, eight of hearts, etc.  Is this fair?

Some say no.  They point out that if your request form happens to be
in Box 35, and Box 36 is picked first, then you will be ignored until
virtually all the other festival goers have been serviced.  You might then
miss out on many of your first-choice movies, and be forced to make do
with substitute films, with no recourse or refund in sight.  Outrageous!

I feel their pain.  This year, my wife and I had our ticket request
form filed in Box 31, which was opened nearly dead last -- 44th out of
48 boxes.  We obtained tickets to just three of our nine first-choice
films, a poor showing indeed.  Do we have grounds for complaint?

Not really.  If Box 31 had instead been selected in the draw, then our box
would have been opened first, and all our movie dreams would have come
true.  Or, if Box 30 had been selected, our box would have been opened
second.  If Box 29 were selected, we would have been third.  And so on.
Overall, our box had an equal chance of being opened first, second,
third, or in any other position between one and 48 -- exactly the same
as every other box and every other patron.  In terms of probabilities,
there was indeed equality for all, which is what fairness is all about.

It's the same when cutting that new deck of cards: as long as the cut is
done fairly, every individual card has an equal chance of ending up on
top, or third from the top, or on the bottom, or in any other position --
exactly as if the cards had been shuffled completely.

Of course, AFTER hearing that Box 36 was selected in the draw, my wife
and I would have preferred the festival to switch over to a completely
random draw, allowing Box 31 the possibility of still doing well.  On the
other hand, if the draw had instead selected Box 30, then we would have
been very happy to continue with the festival's sequential order system,
knowing that Box 31 would then be opened second.  And most importantly,
BEFORE the draw results were announced, our box had an equal chance of
doing well or poorly, regardless of which lottery system -- completely
random draw, or sequential processing -- was employed.

Does this mean movie fans should stop complaining about the festival
lottery system?  Perhaps not; complaining is half the fun!  But despite
the inevitable disappointments, the festival's current lottery system
really is equally fair to us all.  And if you did badly in this year's
draw, well, better luck next year.

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