Methods of apportionment

This question was posed by an ACE user through the "Ask a question" function in Electoral Advice.

Original question:

I am looking for information about the methods used to allocate seats - not to parties after the election but - to the geographical areas in the country and the electoral districts before the election to guarantee fair representation of the voters in each district.

My question is: Is there any type of country comparative database with this information, or are there case studies on particular countries I could get access to?

Many thanks beforehand.

Summary of responses:

Posted on 21 March, 2007

Most of the literature about apportionment is related to the American election regulations and court cases on the fairness and constitutionality of different apportionment methods. There is to our knowledge no comparative database on the actual apportionment formulas of seats; but for a wider discussion on apportionment and reapportionment rules and practice there is a number of sources available. One book which covers many aspects of boundary delimitation in the United Kingdom in considerable depth as well as provides some comparative data from Australia, Canada, France, Germany, India, New Zealand and the United States is “Fixing the Boundaries: Defining and Redefining Single-Member Electoral Districts” by Iain McLean and David Butler from 1996. Please also find links to documents and reports both on the mathematical and political side of apportionment including country case studies.

Replies were received, with thanks, from:

• Apportionment II: Apportionment Systems. Discusses Hamilton's, Webster's, Jefferson's, Adams', Dean’s and Huntington-Hill method from a mathematical perspective and provides a reference list for more information about apportionment.
• Afghanistan: Delimiting Districts for Transitional Elections in a Post-Conflict Society
• Apportionment Methods; University of Alabama. Discusses Hamilton’s method, Jefferson’s method, Adams' method, Webster’s method, Huntington-Hill method from a mathematical and “fairness perspective”.
• The European Parliament election in the treaty on a constitution for Europe: an electorate of degressive valencies by Friedrich Pukelsheim Universität Augsburg, Germany. Apportionment and electoral system for European Parliament elections.
• The United States of America: Reapportionment and Redistricting
  
• Democratic Republic of Congo: Determining How Districts Might be Delimited in a Post-Conflict Society
  
• Australia: Using Projections to Equalize Electoral District Populations
  
• Kosovo: Delimiting Electoral Districts for a Proportional Representation System

Quote from the ACE Encyclopaedia on apportionment:

"There are usually two phases in the electoral district delimitation process. The first phase is the allocation, or apportionment, of seats in the legislature to regional entities such as states or provinces. This is usually a very mechanical process, with the number of seats assigned to each state or province usually dependent on the relative population of that state or province. In countries that do not delimit single-member districts, the reallocation of seats, or reapportionment, is the only step taken to equalize population across electoral districts."

Individual responses in full below:

The US has produced a sizeable literature on the mathematics of apportionment, since it turns out that there are various formulae one can apply, and the US has experimented with several different ones in apportioning seats in its House of Representatives to the individual states.  There is also a lengthy body of legal opinions, most recently when Utah "lost" a seat to North Carolina due in part to the fact that Mormon missionaries operating overseas are not counted for apportionment purposes while armed forces personnel are (and NC has a large number of military).  There is an interesting roundup of the math here.

The larger question, of course, regards the sorts of modifications that countries place on the apportionment process, to guarantee regions a certain minimum number of seats, for example.  This is commonly done, in Canada for example, and the UK.  I don't know of a database with cross-national comparisons, although there is an academic literature relating to varying ways of apportioning seats.

As you for sure know, in some election laws like in Germany the geographical and electoral districts should be the same. If we talk about fair representation it is of course a question about the size and the numbers of voters on one district. If you would like to guarantee that some people (minorities etc.) in all cases shall get a seat, that I think you need to write this down before. We have this case in one state in the north of Germany, where  the Danish minority gets in all cases 3 seats in the parliament. And in 2000 they had special arrangements for the Serbs in the first parliament of Kosovo.