Are First-Borns More Likely To Attend Harvard?
Are first-borns more likely to attend Harvard?
Between 75% and 80% of students at Harvard are first-borns.
Do first-born children work harder academically, and so end up overrepresented at top universities? So claims noted philosopher
Michael Sandel. But Antony Millner and Raphael Calel find a simple fault in the statistical reasoning and give a more plausible explanation. Michael Sandel’s book Justice1 is a rewarding and accessible account of political philosophy. Based on a course he has taught at Harvard for over two decades, it contains an account of an interesting survey he has conducted with his students. Sandel was trying to demonstrate
John Rawls’s famous critique of three conceptions of distributive justice – the feudal, …show more content…
Given a population of mothers, consider the set of all their children. Let F be the subset of first-born june2012 First-borns predominate at
Harvard. But how large are Harvard families? 37
children in this set, and let H be the subset of Harvard students in this set. Let p(F | H) be the probability of being a first-born child, given that you are a Harvard student, and p(H | F) be the probability of being at Harvard, given that you are a first-born child. The Venn diagram in Figure 1 may help to visualize this.
What we are interested in is a measure of how p(H | F) differs from p(H | Fc), where Fc is the complement of F. In words, we’d like to know how a child’s chances of being at Harvard if she is first born (p(H | F)) differ from her chances of being at Harvard if she is not first born (p(H | Fc)). In order to investigate this difference, define r :=
p(H | F ) (1) p(H | F c )
to be the ratio of the two probabilities of interest. We can use Bayes’ formula to write this ratio as
p(F | H ) p(H ) p(F c | H ) p(H ) r= ÷
(2) p(F ) p(F c )
=
Harvard students by the Charles River. © iStockphoto.com/Marcio
Between 75% and 80% of students at Harvard are first-borns.
Do first-born children work harder academically, and so end up overrepresented at top universities? So claims noted philosopher
Michael Sandel. But Antony Millner and Raphael Calel find a simple fault in the statistical reasoning and give a more plausible explanation. Michael Sandel’s book Justice1 is a rewarding and accessible account of political philosophy. Based on a course he has taught at Harvard for over two decades, it contains an account of an interesting survey he has conducted with his students. Sandel was trying to demonstrate
John Rawls’s famous critique of three conceptions of distributive justice – the feudal, …show more content…
Given a population of mothers, consider the set of all their children. Let F be the subset of first-born june2012 First-borns predominate at
Harvard. But how large are Harvard families? 37
children in this set, and let H be the subset of Harvard students in this set. Let p(F | H) be the probability of being a first-born child, given that you are a Harvard student, and p(H | F) be the probability of being at Harvard, given that you are a first-born child. The Venn diagram in Figure 1 may help to visualize this.
What we are interested in is a measure of how p(H | F) differs from p(H | Fc), where Fc is the complement of F. In words, we’d like to know how a child’s chances of being at Harvard if she is first born (p(H | F)) differ from her chances of being at Harvard if she is not first born (p(H | Fc)). In order to investigate this difference, define r :=
p(H | F ) (1) p(H | F c )
to be the ratio of the two probabilities of interest. We can use Bayes’ formula to write this ratio as
p(F | H ) p(H ) p(F c | H ) p(H ) r= ÷
(2) p(F ) p(F c )
=
Harvard students by the Charles River. © iStockphoto.com/Marcio