How does the Additional Members System work?

This is a really useful system to get your head around because its one of the only examples of a hybrid electoral system. Since it is such an unusual combination, its great for bringing into questions about legitimacy and strategic voting (or even devolution). AMS is a system that uses two counting methods (which we can go over separately if you need to) and gives each person two votes each. It is used in Scotland for electing Members to the Scottish Parliament (MSPs).
Essentially each voter is a member of both a local constituency and a larger regional constituency. Within their local constituency they vote once for a candidate (as in the UK general elections) and the First Past the Post system is used in determining which single candidate gets the seat. At the same time each person is given a vote for a party within their regional constituency where a Party List system is used. Instead of a single seat given to the candidate with the most votes, regional constituencies have multiple "additional member" seats to fill. These are shared between representatives in proportion to their share of the vote and in theory balances out the disproportional nature of the FPTP system.