Re: Risk/probability interactions with the public

["Dukelow, James S Jr" <jim.dukelow@pnl.gov>]

Charles Blue  <BLUE.CHARLES@epamail.mail.gov>  responded to my long, sorta
tedious calculation of the expected winnings from a $1 Powerball ticket
purchased earlier this week, by writing:

>  Some people just have too much time on their hands.)

Well, maybe so, but --

If we on RADSAFE are going to beat up on the press and the public about how they
think about probability and risk, it behooves us to do it correctly ourselves.

The lottery is not a bad model for more general situations in which we have very
small probabilities of very large consequences.  Previous discussions on RADSAFE
suggest that at least some RADSAFE readers are interested in how the public
thinks about these kinds of situations.

Organizations that run lotteries behaved rationally a few years ago when they
changed the rules so that the probability of a winner in each drawing was
smaller and so that the payout pools would carry over to later drawings.

Individuals may have an intuitive sense that their expected winnings increase
when this week's ticket offers a chance at not only this weeks payout pool, but
also one or more previous pools.  With some combinations of the size of the
payout and the number of tickets sold, each ticket may actually have a positive
expected winnings.  In those situations, the buyer's decision to buy a ticket is
perfectly rational.  However, if enough buyers sense this, there is a sort of
"tragedy of the commons", in that so many tickets are sold that the individual
ticket's expected winnings drops below zero again.

The Powerball lottery paid out $161.5 million on yesterday's single winning
ticket.  It took in $210.8 million on ticket sales for this drawing plus its
revenue in ticket sales for all of the previous drawings without grand prize
winners which led up to this week's big payout.  Clearly, the lottery, itself,
is the really big winner here.

Best regards.

Jim Dukelow
Pacific Northwest National Laboratory
Richland, WA
jim.dukelow@pnl.gov

These comments are mine and have not been reviewed and/or approved by  my
management or by the U.S. Department of Energy.
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