The Ups and Downs of Rankings

— The latest issue of People is on the newsstands now. In it, the magazine promises, you will discover who are the 50 most beautiful people of the year.

Julia Roberts, the star of the hit movie Erin Brockovich, is on the cover and inside are pictures of — surprise — more actors, among them Ben Affleck, Tom Cruise, Ashley Judd, Jude Law, Catherine Zeta-Jones, Denzel Washington, and Hilary Swank.

The top 50 includes singers too: Faith Hill, Tina Turner, Ricky Martin, and Shania Twain. The list also features sports figures Scott Erickson, John Michael Gambill, and Michelle Kwan as well as chef Ming Tsai, model Iman, violinist Joshua Bell, and financial analyst Alison Deans.

Fallen Facelifts? Flabby Pecs?

My hopes of being selected were dashed once again this year, but my disappointment was eased somewhat when I realized that no scientists or mathematicians appeared on the list.

Another personal reaction to the list was to wonder what happened to last year’s beautiful people. Why did so many of them suffer such a decline in looks that they’re off the list this year? Did face-lifts go bad, hair turn wispy, muscles go flabby? And what about the new entries to the list? Were they even close last year? Given that the candidates for the list are almost always celebrities of one sort or another, why such variability from year to year?

Similar objections can be raised about the ad hoc nature of many top 10 or top 100 lists — most loved people in the country, most hated, best dressed people, worst dressed, etc. The results vary wildly from year to year. For many publicly appraised traits (X), the list of the most X- ish can be determined by a simple mathematical product : a fluctuating and rough numerical measure of the trait ostensibly in question — beauty, dress, whatever — multiplied by the recognition rate of its possessor.

A celebrity can end up on the worst dressed list, for example, merely because he or she wore an odd outfit once or twice and he or she is known to tens of millions of people. The homeless person on the corner is certainly dressed worse than any celebrity, but he is known only to the people who step over him every morning.

Where Are You Going to College?

All right, enough of that. Let’s look at the ups and downs and old standbys of college rankings. Last year’s U.S. News and World Report list of the best universities had Caltech as #1 in the country, up from #9 the previous year.

Such major re-shufflings of the list take place each year and naturally increase the magazine’s circulation. Fiddling with the criteria used, the way they’re measured, and the weights assigned to the lists results in a pleasant degree of novelty. It’s tiresome to read that Harvard, Princeton, and Yale are once again tied for first and that the upstate branch campus of the Ticonderoga School of Metallurgy and Horticulture has clawed its way up from 589 to 586.

Per student spending on instruction and education-related services, for example, was weighted more last year and Caltech’s was the highest of any institution rated, contributing to its elevation in the rankings

There are more significant financial consequences of college ratings as well. They tend to affect the number of applications a school receives the following year. There is also evidence that schools sometimes successfully jockey for position in the rankings by making modifications to programs that have no impact on academic quality.

We can also criticize the phony precision and excessively changeable rankings of the best places-to-live list published by many organizations. The upshot is that colleges and cities don’t really shoot up that much in a year.

What About Your Portfolio?

And this brings me to the stock market and its gyrations and would-be prognosticators. Three of the biggest daily point gains and four of the largest point declines in Nasdaq’s history occurred this past month. The increase in volatility during the last few years has been substantial, though a bit exaggerated. (Our perceptions of gains and losses have been distorted because the numbers are so high. A 2 percent drop in the Dow when the market is at 11,000 is 220 points, whereas such a percentage drop was only 60 points when it was at 3,000 not too long ago.)

The volatility has come about as the media has fixed relentlessly on these numbers. More people than ever have started trading, many of them influenced by inconstant lists of the 50 most beautiful (er ..., undervalued) stocks. IPO’s are still incessantly hyped, spawning, up until a month or two ago, all those jealousy-inducing 20-something billionaires.

Did I use the word jealousy? As with beautiful people and distinguished universities, emotions and psychology are imponderable factors in the market’s skittish variability. Just as beauty and academic quality don’t change as rapidly as our ad hoc lists and rankings, so the fundamentals of companies don’t change as quickly as our mercurial overreactions to them.

It may be useful to imagine the market as a fine race car with an exquisitely sensitive steering wheel making it impossible to drive in a straight line. Tiny bumps in our path cause us to swerve wildly, and we zig-zag from fear to greed and back again, from unreasonable gloom to irrational exuberance and back.

The Point?

We’re capricious and easily bored and, whatever the domain, seem to prefer a lot of variety. Intentionally or not, we impose it even when it’s not there.

Our objective criteria may be bone structure, symmetry, and skin texture for beauty; graduation rates, SAT scores, and faculty publications for universities; P/E ratios, capitalization, and cash flow for businesses. Yet we can’t ignore popular psychology and the complicated, fluctuating, poorly understood way it helps produce a Julia Roberts, a Yale, or an

Professor of mathematics at Temple University, John Allen Paulos is the author of several books, including A Mathematician Reads the Newspaper and, most recently, I Think, Therefore I Laugh. His “Who’s Counting?” column on appears on the first day of every month.