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 can indicate your support for individual candidates. In an open list system with panachage, you have multiple votes, often as many votes as there are seats to be filled in the district, and you can use these votes to indicate support for candidates across one or more party lists. In an open list system with cumulation, voters can give more than one vote to a single candidate.
The number of seats that a party wins is determined by the total number of votes won by all of the candidates on its list. 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 who won the most individual support. Thus, if a party wins 3 district seats, then it allocates these seats to the three most popular candidates on its list.
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 with panachage and cumulation is that they provide voters with a very high degree of flexibility when it comes to expressing their support for particular candidates. A second advantage is that a voter can increase the electoral prospects of an individual candidate by cumulating votes.
One disadvantage of this open list system is that it 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 it creates incentives for legislators to vote with their constituency rather than their party leadership, thereby creating ill-disciplined parties in the legislature.<< Open List Pan-European constituency >> For those interested in mathematics you can find more information about how votes are translated into seats here.