Allocation of seats to regional units, or to parties under systems of proportional representation.
Territorial apportionment is usually a process of adjusting the seats allocated to each unit to reflect changes in population. Under the US Constitution, seats in the House of Representatives are divided among the states once every ten years (after each census), with no seat crossing a state line. The UK Boundary Commissions redistribute parliamentary seats every twelve to fifteen years, and normally no parliamentary seat crosses county boundaries.
Within territorial units, the apportionment process then involves the (re‐)drawing of constituency boundaries (in the US known as redistricting, in India delimitation), usually with the aim of equalizing the population (or electorate) per seat, in accordance with the principle of ‘one person, one vote, one value’. This is usually done with regard to stated constraints of administrative convenience, contiguity, geographical, and communication factors; and unstated influences of party‐political advantage. Such a process is open to political manipulation, or gerrymandering.
Alternatively, apportionment may refer to the allocation of seats according to the number of votes a party has received, particularly in the case of list proportional representation. In the Northern Ireland Assembly ministerial portfolios are apportioned according to the number of votes each party attained, according to the d'Hondt formula. Applications of apportionment have a common mathematical structure (and hence face common impossibility theorems) but this has not generally been realized by reformers who periodically reinvent systems of apportionment that are already in use under another name somewhere else. See d'Hondt; Sainte‐Lagüe; Jefferson; Webster.