Complaints About Ratios
Whether I’m travelling in a developed or developing country, one of the common features of news reports is the presence of ratios, often termed the “something something rate.” Often, the reports are meant to suggest to the reader that the current rate is not desirable.
A classic example is voter turnout rates. Journalists (and policymakers) often misrepresent low voter turnout to indicate voter apathy or voter nonparticipation, suggesting that a voter turnout rate of 100% would be ideal (do these same people later move to Belgium?). Older people vote in disproportionately high numbers not because people become better voters with age, but because their ability to do something economically productive during that hour is encumbered or diminished (and hence their opportunity cost is lower). So, what is the ideal rate of voter turnout? Will people really get enormously more utility from voting if it is deemed cool? The ideal rate, in these terms, is probably very low: the voting pattern that reflects the wishes of the majority with as few highly-productive people wasting time in the queue to vote as possible.
People are particularly bad at examining rates and ratios that affect people as workers or consumers. If one asks the average Londoner what the ideal unemployment rate (I’m only looking for a reasoned reply, I’m not asking laypeople to explain an equilibrium rate of unemployment or stability relative to labour and wage inflation) would be in London right now, one faces terrible odds of receiving a well-reasoned reply. If one asks whether the VAT should be higher or lower, or the income tax, or the land taxes, one is equally unlikely to hear clear reasons for the policy recommendations one receives. No wonder those in Westminster are often exasperated that they’re given little guidance on what their constituents like, but a flood of angry letters in the post describing what their constituents dislike.
One example in the papers recently is admission statistics. As a member of the Admissions Committee at the University of Chicago Booth School of Business, I am very interested in admissions statistics and how they are used by the media. David Lammy MP, a Harvard Law School graduate, wrote a piece in The Guardian noting that Merton College, Oxford has not admitted a black student in five years and that Cambridge does not employ a single black academic.
No doubt these are eye-catching statistics, but is the “right” rate one black student every three years, every year, ten each year, twenty? Should the faculty be 2% black (the percentage of blacks in the UK according to the 2001 census)? Should the faculty be 14% black (the percentage of blacks in the worldwide population)? Should blacks be overrepresented on Cambridge’s faculty relative to their representation in the population (and if so, why)? Mr. Lammy offers the usual answer given by people providing such statistics: someone should, um, do something.
In considering these statistics, consider that the acceptance rates for both whites and blacks at Cambridge and Oxford are incredibly high by American standards. From 1999 through 2009, the success rate among black applicants to read in undergraduate studies at Oxford (across all colleges and all subjects read) was 22%. This is far higher than the general undergraduate admissions rate (disregarding subject to be read and race of the applicant) at Harvard (7%), Yale (8%), Stanford (8%), and so on. As I’m sure Mr. Lammy knows from waiting for a reply from Harvard Law School (13% acceptance rate), it is difficult to gain access to top educational institutions – primarily because nearly every student applying is extraordinarily well-qualified and places are scarce.
It is relatively easy to say that a murder rate of zero would be desirable, or that a catastrophic nuclear reactor failure rate of zero would be nice. But human intuition is terrible at figuring out ratios that require some of this and some of that. This is why we have cookbooks, economics, and computer-controlled fuel injection, among other things. So, next time you read something claiming the XYZ rate is much higher/lower than it should be, think on it a bit.
