Alabama Paradox
DEPARTMENT OF MATHEMATICS AND STATISTICS
Georgia State University
The Alabama Paradox is the paradox that confronted George
Washington as our founding fathers tried to devise a
means for apportioning representatives to the
Congress among the several states. The Constitution
required that a state's Congressional delegation be
proportional to the population of the state. Any
middle schooler could crunch the numbers and
establish the size of each state's delegation except
that state delegations needed to be expressed in
whole numbers.
The controversy obtained when President
Washington's numbers people decided the way to
go was first to round off the results of the initial
calculation in the usual fashion: 0.5 and above were
rounded up and 0.4 and below were rounded down.
Second, if, at this point, the total of the several
states' delegations was not equal to the preestablished
total size of The House of
Representatives, apportion additional
representatives one at a time to the states that had
the largest fractional part prior to rounding until the
desired strength of the House was met.
Under this scheme, Alabama picked up an
additional representative. Then it was decided to
increase the size of The House by one and the
algorithm was repeated. Alabama lost its additional
representative to the consternation of all. As this
turn of events was contrary to common sense, the
title Alabama Paradox was born.
President Washington vetoed the proposal and the
number crunchers went back to work.