**Apportionment: Different Reasonable Methods Yield Different Distributions of Seats**

Prepared by:

Joseph Malkevitch

Department of Mathematics

York College (CUNY)

Jamaica, New York 11451

email:

__malkevitch@york.cuny.edu__

web page:

__http://york.cuny.edu/~malk__

The example below illustrates that the 5 commonly discussed divisor methods of apportionment can all lead to different apportionments starting with the same data.

The next table widens the list of methods and shows a diversity of different apportionments.

Lowndes's Method is similar to Hamilton's but gives out undistributed seats in order of largest number of people per representative based on the initial assignment of seats (exact quota rounded down).

These examples are due to Mark Beumer.

Reference:

Beumer, M., Masters Thesis, University of Amsterdam, 2010.