 News Home
 Hot Topics
Current
 Categories
 From the Magazine

17 April 2014 12:48 pm ,
Vol. 344 ,
#6181

Officials last week revealed that the U.S. contribution to ITER could cost $3.9 billion by 2034—roughly four times the...

An experimental hepatitis B drug that looked safe in animal trials tragically killed five of 15 patients in 1993. Now,...

Using the two highquality genomes that exist for Neandertals and Denisovans, researchers find clues to gene activity...

A new report from the Intergovernmental Panel on Climate Change (IPCC) concludes that humanity has done little to slow...

Astronomers have discovered an Earthsized planet in the habitable zone of a red dwarf—a star cooler than the sun—500...

Three years ago, Jennifer Francis of Rutgers University proposed that a warming Arctic was altering the behavior of the...


17 April 2014 12:48 pm ,
Vol. 344 ,
#6181
 ScienceNow
 ScienceInsider
 ScienceLive
 About Us
A House Divided
23 February 2001 7:00 pm
SAN FRANCISCOOf all the uses of the U.S. census, the most importantto politiciansis the apportionment of congressional seats. Since 1941, Congress has assigned seats by a complicated formula that replaced a simpler approach designed in 1832 by the American statesman Daniel Webster. But Peyton Young, a senior fellow at the Brookings Institution in Washington, D.C., says Webster's system was actually better. The current method is biased, giving less populous states 3% to 4% more seats than they deserve, Young reported here on 17 February at the annual meeting of the American Association for the Advancement of Science (publisher of ScienceNOW).
Assigning House seats might seem simple: Calculate each state's fraction of the population, multiply by 435, round up the largest fractions to achieve a total of 435, and round down the rest. But no matter how you do the rounding, the simple arithmetic approach is susceptible to outcomes that mathematicians call paradoxical and politicians consider unacceptable. The most famous case occurred in 1880, when a decision to expand Congress from 299 to 300 seats caused the state of Alabama to lose a seat. Simple rounding can also cause states to lose seats when they gain population or gain seats by failing to count some of their citizens.
Webster's method avoids these paradoxes with a mathematical formula that involves multiplying the fractions by a tiny bit more than 435 and rounding to the nearest whole number. Its 1941 successor was supposed to be even better, because it minimizes differences in states' relative per capita representation. Many mathematicians, including the famous John von Neumann, endorsed the method.
But it introduced a bias, says Young, because it results in small numbers being rounded up more often than large numbers. The number 1.45 gets rounded up, for example, whereas 54.45 gets rounded down. Because every state gets two senators regardless of population, "the whole system is now rigged toward small states," Young says. He thinks Congress should switch back to Webster's method, and now is the time, he says, because the population happens to be aligned so that the new and old methods yield the same results.
Steven Brams, an expert on voting systems at New York University, doesn't foresee any surge of support for a change. But he agrees that Webster's schemeor even the older, simple rounding method"would be superior" to what's in place today.
Related sites
U.S. map showing the changes in apportionment based on the 2000 census
The Census Bureau's role in the apportionment process
Census Bureau information about computing apportionment
Peyton Young's home page at the Brookings Institution
Posted In: