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| Hare-Niemeyer method | |
|---|---|
| Name | Hare–Niemeyer method |
| Alternative names | Hagenbach-Bischoff quota (related), Largest remainder method |
| Type | Apportionment method |
| First used | 19th century (Hare), 1910s (Niemeyer refinements) |
| Region | United Kingdom, Germany, Latin America |
Hare-Niemeyer method The Hare-Niemeyer method is an apportionment procedure used to allocate seats in representative bodies and distribute divisible goods according to votes or quotas. It combines concepts from proportional representation systems and quota methods to translate vote totals into whole-seat allocations, balancing integer rounding and fractional remainders.
The Hare-Niemeyer method assigns seats by computing a quota from total votes and dividing each party's votes by that quota to obtain exact quotients, then allocating integer parts followed by largest fractional remainders. It is associated historically with proponents such as Thomas Hare and later refinements attributed to Julius Niemeyer and has parallels with the Hamilton method and the Largest Remainder method. Nations and institutions including Argentina, Brazil, Chile, Spain, and various regional assemblies have implemented variants related to the method in legislative apportionment, with legal and constitutional debates involving courts such as the Supreme Court of Argentina and electoral bodies like the National Electoral Council (Venezuela).
The procedure begins by determining a standard quota Q = total votes / total seats. For each party or list—examples include Conservative Party (UK), Liberal Democrats (UK), Socialist Party (France), Christian Democratic Union (Germany), and Workers' Party (Brazil)—compute the exact quotient v_i / Q. Allocate the floor of each quotient as guaranteed seats, then rank parties by their fractional remainders and distribute remaining seats to highest remainders until all seats are assigned. Implementation details have been debated in contexts involving the Electoral College (United States), the D'Hondt method, and regional systems like Andorra and Portugal.
Mathematically, Hare-Niemeyer is a largest-remainder method with properties including quota compliance—each party receives either the lower or upper quota—and failure of house monotonicity in some cases, producing paradoxes such as the Alabama paradox observed in apportionment debates involving the United States House of Representatives, John Quincy Adams, and works by Alexander Hamilton (Founding Father). It satisfies the quota rule but can violate population monotonicity and avoid the Sainte-Laguë bias associated with divisor methods used in Sweden and Norway. The method is analyzable using integer rounding theory from contributors like Edwin Thiele and mathematical treatments in the tradition of John von Neumann and Oskar Morgenstern.
Hare-Niemeyer and its variants have been used to apportion seats in national parliaments, municipal councils, and supra-national bodies such as the Andean Community and Mercosur-related assemblies, and have influenced quotas in proportional lists for parties like Partido Justicialista (Argentina), Partido dos Trabalhadores (Brazil), and Partido Popular (Spain). It appears in legislative reforms discussed in the Argentine Constitution debates, electoral law revisions in Chile's transition period, and municipal allocation procedures in cities such as Buenos Aires and Madrid.
Advantages cited by advocates like Thomas Hare and reformers in Germany include simple computation, intuitive fairness by honoring exact quotas, and transparency for electoral commissions such as Electoral Commission (UK) and international observers from Organization of American States. Limitations include susceptibility to paradoxes such as the Alabama paradox, inability to guarantee non-negativity of marginal seat changes under all scenarios as examined in studies by Daniel Webster-type apportionment critiques, and sensitivity to district magnitude issues raised in comparative work by Arend Lijphart and Maurice Duverger.
Origins trace to nineteenth-century proponents of proportional representation like Thomas Hare and nineteenth- to early-twentieth-century German statisticians including Julius Niemeyer. The method was discussed alongside alternatives such as the D'Hondt method (Jeffreys and Victor D'Hondt), the Sainte-Laguë method (advocated in Norway and Germany), and Hamiltonian apportionment debates in the early United States Republic. Twentieth-century electoral reformers in Argentina, Brazil, and Spain adapted the method in statutory frameworks and constitutional rulings, with academic analysis by scholars such as Kenneth Arrow and P. A. Samuelson informing normative assessments.
Related procedures include the Hamilton method, the Hagenbach-Bischoff quota, and largest-remainder systems applied in contexts like European Parliament seat distribution, United Nations commission staffing, and party-list systems in countries like Netherlands and Belgium. Divisor methods such as Jefferson method and Sainte-Laguë method offer alternative rounding schemes that contrast with Hare-Niemeyer on bias and monotonicity, while hybrid systems used in Germany's mixed-member proportional representation and New Zealand's electoral law combine list allocation rules with district seats.
Category:Apportionment methods