In a list proportional representation (PR) electoral system, parties present voters with a list of candidates to elect multiple candidates in a district. In an open list PR system, you choose a particular party list and indicate your support for individual candidates on your chosen party list. The number of seats that a party wins is determined by how many times its party list is chosen. Once the seats have been allocated to the parties, the seats are then allocated to the candidates on each party list starting with the candidates that won the most individual support. If a party wins 3 district seats, then it allocates these seats to the three most popular candidates on its list. This electoral system is called "open" because voters have a say over which candidates on a party list obtain district seats; the selection of candidates is "open" to voters.
In Latvia, you can indicate your support for individual candidates on their chosen party list by placing a 'plus' sign next to the name of candidates you particularly like, by drawing a line through the name of candidates you particularly dislike, and by leaving intact the names of candidates that you do not particularly like or dislike.
To determine the most popular candidates on a party list, one computes an index score for each candidate. The index score for each candidate is equal to the number of votes won by the party as a whole plus the number of times the candidate's name was marked with a plus sign minus the number of times the candidates name was crossed out. If a party wins two seats, then the seats are allocated to the two candidates with the highest index scores.
Advantages and disadvantages:
One advantage of all proportional representation systems is that they tend to produce proportional outcomes in which parties receive district seats in rough proportion to their share of the district vote. Among list proportional representation (PR) electoral systems, one advantage of open list systems is that they provide voters with the opportunity to express their support for or against specific candidates, creating an incentive for legislators to respond to voter preferences rather than the dictates of the party leadership.
One disadvantage of open list systems is that they can generate internal party fighting due to the fact that candidates from the same party are effectively competing with each other for the same votes. A second disadvantage is that open list systems create incentives for legislators to vote with their constituency rather than their party leadership, thereby creating ill-disciplined parties in the legislature.<< Closed List Panachage & Cumulation >> For those interested in mathematics you can find more information about how votes are translated into seats here.