"The additional member system is an improvement on first past the post
because it gives greater choice to voters and results in a more
representative parliament"

Discuss this statement

One example of a Parliament that uses the AM system is the Scottish Parliament:

The voting system used by the Scottish Parliament is known as the
Additional Member System (AMS). AMS is a type of proportional
representation. This means that the share of seats each party receives
reflects its level of support among voters.
  At a Scottish Parliament election each voter has 2 votes. With the
first vote, voters choose between candidates standing in their
constituency. The candidate winning the largest number of votes will
gain the seat. There are a total of 73 constituency MSPs.
  The second vote is for a political party, or for a candidate
standing as an individual, within a larger electoral area called a
Scottish Parliament Region. There are 8 Scottish Parliament Regions.
Each region has 7 additional seats in the Parliament. Within each
region, parties are allocated additional seats dependent upon the
number of constituency seats it won. The members chosen to fill these
56 additional seats are known as 'regional members'.
  Each voter will have one constituency MSP and 7 regional MSPs. All
MSPs have equal status in the Parliament.
http://www.scottish.parliament.uk/cnPages/faq2.htm#3

There are research briefings on parliamentary systems linked from
http://www.scottish.parliament.uk/business/research/subject/parliament.htm#par

Another is the Welsh Assembly. 

The Assembly has 60 elected members and each voter has two votes. The
first vote is used to elect a local or constituency Assembly Member in
the same way as MPs are elected to the House of Commons. Forty
Assembly Members are elected on this ?first past the post? basis, one
from each constituency in Wales.

The second vote is used to elect 20 additional members, on a regional
basis, to ensure that the overall number of seats for each political
party reflects the share of the vote they receive. This is known as
the Additional Member System, a form of proportional representation.
There are five electoral regions, based on the European Parliamentary
Constituencies created in 1994, and each region returns four members
to the Assembly.
http://www.wales.gov.uk/pubinfaboutassembly/content/howelect-e.htm#top

Owain