Any system of proportional representation in which a set of representatives is chosen to supplement those chosen by some other route in such a way that the house, overall, is proportionately representative of the votes cast. The additional members are sometimes also called ‘top‐up’ members. The best‐known AMS is used for the German parliament, where voters have two votes. With the first, they elect a single constituency MP by the plurality (‘first‐past‐the‐post’) rule. With the second, they shape the overall party composition of the house. Additional members (additional, that is, to those elected in the single‐member districts) are elected in such numbers as required to ensure that the house reflects the vote shares gained by the parties in the second votes. The electoral systems in Belgium, Denmark, and Sweden also have an AMS component.
The combination of locally accountable members and a roughly proportional outcome has made AMS systems popular in new democracies across Eastern Europe, as well as in countries considering electoral reform. New Zealand voted to switch from a first‐past‐the‐post system to AMS in 1993, and in the same year Japan switched to AMS from the single non‐transferable vote. The devolved assemblies/parliaments of Scotland, Wales, and London use AMS systems.