apportionment

Apportionment is the process of distributing a fixed total amount among several groups according to a specified criterion, typically population or need. The term originates from Latin and has been used in political, administrative, and economic contexts to describe proportionate sharing of resources or representation.

In politics, apportionment determines how legislative seats, electoral districts, or other allocations are divided among defined political units such as states or provinces. After a census or similar data update, the total seats or districts are apportioned to reflect population changes, with the aim of maintaining fair representation. Disputes over apportionment can arise when division patterns produce malapportionment or encourage gerrymandering, which can distort voting power and accountability.

Mathematical approaches to apportionment fall into two broad families: divisor methods and quota methods. Divisor methods (for example Jefferson, Webster, and Sainte-Laguë) use a common divisor and specific rounding rules to assign seats. The quota method, best known as Hamilton’s largest remainder, computes exact quotas and distributes any remaining seats to those with the largest fractional remainders. The United States uses a divisor method, the method of equal proportions, to allocate House seats after each census.

In addition to political representation, apportionment is used to allocate budget shares, resources, or costs among participating entities, such as agencies, regions, or groups, according to published criteria. The goal in all forms is to distribute a fixed total fairly and transparently, while acknowledging the limitations of any single rule in capturing relative need or capacity.