The Irrationality of Playing the Lottery

I have posted several times over the years on the irrationality of playing the lottery and on the immorality of state sponsorship and promotion (via deceptive advertising) of lotteries.  The following e-mail, however, raises an interesting question that gives me pause:

As I was reading this story of an impoverished young rancher who won $88 million net with a Powerball ticket, I was wondering whether you'd allow that a case could be made for the rationality of his gamble. The young man and his whole family were in desperate financial circumstances with no way to cover back taxes, livestock loans, etc. They faced foreclosures, eviction, etc. The young man bought one ticket. He was not a chronic heavy lotto-gambler. The one ticket did not make his situation worse. Arguably, the lottery gamble was his only hope of salvaging his situation. If you have only ONE way to save yourself, the odds don't really matter.

Actually, according to the account linked to above, the cowboy bought $15 worth of tickets.  So he bought more than one ticket.  But no matter.  Let us assume that this $15 was the only money he ever spent on the lottery.  And let's also assume that the cowpoke was at the end of his rope -- pun intended -- facing foreclosure and imminent residency on Skid Row.  We may also safely assume that the young man will never again play the lottery.  (For he seems resolved not to fritter away his winnings  on loose women and fast cars.) The question is whether it was rational for him in his precise circumstances to spend $15 on lottery tickets.

 

Now one question to ask is whether the rationality of a decision can be judged ex post facto.  I would say not.  A rational agent agent is one who chooses means that he has good reason to believe are conducive to the ends he has in view.  A rational decision is one made calmly and deliberately and with 'due diligence' on the basis of the best information the agent has available to him within the limited time he has at his disposal for acquiring information.  A rational decision cannot be rendered irrational by a bad outcome, and an irrational decision cannot be rendered rational by a good outcome.

 

So I am inclined to say that our cowboy made an irrational decison when he decide to spend $15 on a chance to win millions.  The fact that, against all odds, he won is irrelevant to the rationality of his decision. The decision was irrational because the chances of winning anything significant were astronomically small, whereas the value of  $15 to someone who is down to his last $15 is substantial. 

 

But I can understand how intuitions might differ.  Suppose we alter the example by supposing that the man will die and knows that he will die if he does not win today's lottery.  Suppose he has exactly $15 to spend and he spends it on lottery tickets.  He now has nothing to lose by spending the money.  It is perhaps arguable that, in these precise circumstances, it is prudentially if not theoretically rational for the cowpoke to blow his last $15 on lotto tickets.

 

Just what is rationality anyway?