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Viliam_Bur comments on What false beliefs have you held and why were you wrong? - Less Wrong Discussion
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If your idea of a "bad programmer" is someone who studied programming, but had unimpressive results, then yes, the idea that half the programmers can't do FizzBuzz is unsettling.
However, the set of "bad programmers" also includes crazy people who believe they understand programming without any good reasons; overconfident people who used Excel for a few months and now believe they know everything there is about using computers; etc. It is not so difficult to believe that these people are as numerous as the real programmers.
In other words, instead of a less skilled programmer, imagine a non-programmer with an extreme case of Dunning–Kruger effect.
By the way, I wonder how much this effect is culture-dependent. There seems to be something in the American culture that supports overconfidence, at least in job interviews.
By “programmer” in this context I meant ‘someone who applies for a programming job and makes it to the interview stage’. Which unless they outright lied on their CV means they probably have some kind of certification. In another article I read that more than half of comp sci graduates can't do FizzBuzz.
In a halfway decent world, granting a comp sci degree to someone who can't do FizzBuzz would be punishable as fraud.