Typically, one of the elections is by first-past-the-post, runoff voting or bloc voting, while the other election uses some form of proportional representation.
The electoral arithmetic may not result in the overall result being fully proportional; typically the problem is that of overhang seats where a party wins more seats in the non-proportional part of the election than its overall proportion would justify as membership of the whole assembly. This can be resolved by allowing it a disproportionate representation, or by compensting other parties, and may result in the assembly being enlarged.
One of the justifications is often to ensure an element of district representation, while encouraging the overall result to be broadly proportional. This proportionality means that mixed member proportional voting is less likely to produce a decisive result than parallel voting.
It has been used in countries such as Bolivia, Germany, Hungary, Italy, Mexico, New Zealand, and Venezuela.
In terms of tactical voting, the first vote for the district representative is often much less important than the second party list vote in determining the overall result of an election; in other cases a party may be so certain of winning seats in the district election that it expects no extra seats in the proportional top-up. Some voters may therefore be able to get a double representation by voting tactically and splitting their votes, though this runs the risk of unintended consequences.