People go nuts over the fact that most people think they’re above average. “Hilarious!” they say, “only half of the world can be above average, so how loony people must be if a majority of people think they’re above average.” Take for example the oft-cited fact that one survey found ninety-three percent of Americans believe they are above average drivers (where “average” is the median). Many articles citing this fact smugly refer to it as a “mathematical impossibility” and go on to talk about illusory superiority, to which I say “Erroneous!” or at least “Maybe erroneous!” While it’s true that it’s impossible for a majority of people to be above average (except the children of Lake Wobegon), it’s perfectly consistent for a majority of people to believe they’re above average.

An example (courtesy of an enlightening conversation with a professor (the conversation occurred like two years ago, but I haven’t stopped thinking about it)): suppose there are two kinds of drivers: above average and below average. Half of all drivers are above average and half are below but they don’t necessarily know which type they are. Further suppose that the only signal people get of their driving quality is whether or not they get a ticket; above average drivers don’t get tickets, and below average drivers get a ticket with some probability (our hardworking men and women in law enforcement can’t possibly catch every bad driver). If this is the case, anyone who doesn’t get a ticket could accurately infer that there is a greater than fifty percent chance that they are an above average driver, so the majority of people (everyone who doesn’t get a ticket) could reasonably say that they believe they are above average.

What’s really fun is that the above argument holds for any probability of getting a ticket that isn’t zero percent or one hundred percent. So, we could make the probability of getting a ticket vanishingly small (say 0.000001%) and the vast majority of people (99.999999%) would believe that there is a greater than fifty percent chance that they are an above average driver. And what’s more, no one underestimates anyone else’s ability; each driver should make the same inference about themselves as they do about other individual drivers.

I think this is great. In real life I wouldn’t advocate for an almost-no-ticket policy, but for the sake of a blog post it seems like a good point. I really mean it, though: I think this is great. It isn’t actually mathematical validation for naive self-confidence, but because I’m naively self-confident I choose to interpret it as mathematical validation for naive self-confidence. And let’s be clear: I love naive self-confidence.

I love naive self-confidence so much that I allow myself to be naive about things that I shouldn’t be naive about. I once got a ticket for an expired driver’s license and forgot about it a week later while filling out a job application. It was the best (at least for a little while; when the prospective employer ran a background check, they found out about it and called me, and I had to explain that I wasn’t deliberately lying but rather loved naive self-confidence).

Of course, allowing myself to eject negative signals breaks down the simple model laid out above, but I’m fine with that. In fact, that’s just another negative signal that I give myself the right to eject.

It’s a good system. I even get to eject the fact that that I’m ejecting things. I think this is mastery of my fate and captaincy of my soul. I highly recommend it.

Tony Ditta

Tony graduated in 2012 with majors in mathematics and economics. He now lives in Chicago and is pursuing graduate study in economics. He also has a very good cultural trivia podcast called “Here’s My Number, So Call Me Ishmael” available on Libsyn, iTunes, and Google Play.

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