Apportionment: Different Reasonable Methods Yield Different Distributions of Seats

Prepared by:

Joseph Malkevitch
Department of Mathematics
York College (CUNY)
Jamaica, New York 11451


web page:

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.


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