In an article yesterday, for the Guardian on “statistical illiteracy”, Cory Doctorow wrote:
in the US, its slogan is “Lotto: You’ve Got to Be In It to Win It”. A more numerate slogan would be “Lotto: Your Chance of Finding the Winning Ticket in the Road is Approximately the Same as Your Chance of Buying it”. The more we tell people that there is a meaning gap between the one-in-a-squillion chance of finding the winning ticket and the one-in-several-million chance of buying it, the more we encourage the statistical fallacy that events are inherently more likely if they’re very splashy and interesting to consider.
Yes, I agree. You are almost unfathomably unlikely to win the jackpot in the lottery. And yes, the odds are so low, that it actually is difficult for a human being to conceive of them. But that does not mean that buying lottery tickets is stupid. A Powerball ticket is a dollar ($2 if you select the multiplier). That is not very much money. And what you buy for that money is the fantasy that in two days you might become unfathomably wealthy.
Now, that is a fantasy that many Americans have, even without the lottery. Personally, I have a fantasy of all kinds of very unlikely writing-related things happening that will gratify various social slash monetary desires. I find this fantasy to be extremely pleasurable, and I would not willingly sacrifice it.
Furthermore, I spend an incredible amount of time and money on writing to keep this fantasy alive. Some people choose, instead, to spend a few dollars every week to do the same thing…what is so stupid about that? If someone spends $10 on a movie ticket, people do not seem to find that repulsive or irrational. At the end of a movie you haven’t gotten anything tangible, other than a memory. A lottery ticket is exactly the same (only cheaper).
I actually don’t want to say mean things about Cory Doctorow, or other people who maintain these sorts of views, but I really do wonder at it. Is it so easy to believe that hundreds of millions of people are doing something just because they are stupid? Is it so easy to believe that if they were only lectured at a little bit (the title of Doctorow’s piece is “promoting statistical literacy”) then they would understand the error of their ways and stop spending their own hard-earned money on something they want? Is it so hard to believe that people do something because they gain some pleasure from it? And that the very fact that they are willing to continue to spend that money for that pleasure indicates that the pleasure is worth more to them than the money?
There’s an additional argument here, which is that it might make good sense, in terms of maximizing your happiness, to buy a $1 ticket that gives you a 1 in five million chance of winning a million dollars, if the utility you derive from having $1m is more than five million times the utility you get from having $1. This is not at all strange, if you think about it. No matter how many $1s most people save, they are never going to have $1,000,000. A million dollars represents a kind of security and safety that most Americans will never achieve. And if a person looks at their life, decides they really want that, and realizes that the only way they will ever achieve that security is by winning the lottery, then it might make good sense, economically-speaking, for them to buy lottery tickets.
Indeed, isn’t that the gamble that many of us are making, in some way? People who quit their jobs to start businesses know that they are likely to fail (and many of them do fail), but they desire what a successful business can give them so much that the risk is worth it. A dollar, by itself, is meaningless. A dollar, or a million dollars, only has the value that human beings put on it. If someone spends a dollar for something, then by definition, it is worth a dollar. In some ways, this assumption of Doctorow’s is as empty as criticizing someone for paying money to see a movie you don’t like, or a book you don’t like. Yeah, if they understood things the way you understand them, then spending that money would have been a waste. But it is precisely the fact that they did choose to spend that money which shows you that spending it was not a waste. Let’s try to have some more faith in the reasoning abilities of our fellow men.