There’s an amazing moment in one of Michael Sandel’s popular “Justice” classes. The Harvard philosopher is lecturing on John Rawls’s view of meritocracy, challenging the assumption that life’s playing field is ever level. Sandel even takes on the idea that we should be given full credit for our hard work. He asks the students in his large class to raise their hands if they are first-borns. About three-quarters of the hands go up. He’s been asking the same question for years and getting the same overwhelming show of hands.
But does this mean that first-borns work harder in school and are therefore more likely to attend Harvard?
Antony Millner and Raphael Calel don’t think so. In the June 2012 issue of the statistical magazine Significance, they unpack the math behind the claim and argue that it doesn’t support Sandel’s conclusion. The question, they say, isn’t whether a lot of Harvard students are first-borns—that seems to be true. The question is whether the fact that they were first-borns made it more likely that they would attend Harvard.
They calculate that, starting with the statistic that 41 percent of children born in the United States in 1991 were first-borns, it would mean that first-borns were four to five times more likely to get that acceptance letter than children born later—a figure, they write, that “stretches credulity.”
The authors offer an alternate possibility:
… perhaps the fertility rate amongst mothers of Harvard students is lower than the national average? In other words, Harvard students might come from smaller families. An intuitive reason for this might be that those who attend Harvard come from wealthy or well-educated backgrounds, and that wealthy and well-educated parents tend to have fewer children than poorer parents.
At the very least, they say, in order to begin to understand the effect of being first-born on getting into Harvard, you’d have to know the size of the families of students at Harvard. Otherwise, they write, drawing that conclusion from a show of hands is misleading: “While on the surface his survey provides a crisp demonstration of a philosophical point, in reality it may be better suited as a lesson in the subtlety of of reasoning accurately about conditional probabilities.”
Still, something is going on with first-born children, and not all of it is good. They try harder for mastery, according to one study, but they’re less trustful and cooperative. Also, they may be risk-averse, less extroverted, and more likely to develop eczema.
(Antony Millner is a postdoctoral fellow at the University of California at Berkeley. Raphael Calel is a doctoral researcher at the London School of Economics and Political Science. The Significance article is not online but a previous paper of theirs on the same topic is.) UPDATE: Here’s a link to the gated Significance article.