The Costa Rican Legislative Assembly (Asamblea Legislativa) elects its members by the largest remainder system of proportional representation with a Hare quota off of closed party lists.
Within each province, parties receive as many mandates as they win multiples of the provincial Hare quota (cociente)–valid votes divided by the number of mandates in the province. Any seats left are awarded to parties based on remainder votes–those votes that were not already used towards a full quota–in descending order. Only parties that win at least 50% of a Hare quota (subcociente) are eligible to receive remainder seats. Party lists are closed, so members gain their seats in list order.
Here is an example of the allocation process from Heredia Province in 2014:
The cociente is the Hare quota based on the total number of valid votes divided by the number of deputies to elect (diputaciones a eligir). The subcociente is 50% of the cociente or Hare quota.
In the first allocation of seats to parties for full Hare quota, two parties, Acción Ciudadana and Liberación Nacional, won one seat apiece. Each won more votes than the cociente, a single Hare quota. However, neither had enough votes for a second seat at this point in the allocation as their vote totals fell short of two multiples of the cociente.
The final four seats were distributed by on remainder votes (residuos) in descending order of votes not already used towards a full Hare quota. The fourth and final seat went to Liberación Nacional with 15,849.833 remainder votes. Note that Movimiento Libertario’s 16,682 votes exceeded the remainder votes won by Liberación Nacional but Movimiento Libertario was ineligible to receive seats because its vote total fell below the subcociente of 18,354.583.
The following table shows the apportionment of mandates to provincial constituencies:
Sources: Chapter VI, Electoral Code; Tribunal Supremo de Elecciones, República de Costa Rica.