To put it rather casually, we understand that by strategic voting, a voter will not vote for his favourite party, his highest-preferred party. The motive for strategic voting consists in avoiding a wasted vote. I will concentrate here only on the first votes, because I think this would also be the important part for you.
Strategic voting in this case means that a voter will not give his first vote to a candidate who has ostensibly no chance of winning the constituency. The usual pattern here is that supporters of small parties, such as the liberal FDP in Germany, or the Greens, will vote for the constituency candidate from a big party that is closest to their own party, such as our coalition party. Whether this pattern of strategic voting is desired or not depends on the electoral system and on the normative beliefs you have. But the consequences are certainly set. The point is that it is possible to induce overhang seats by this kind of ticket splitting and strategic voting. This means that a coalition can enhance the share of seats it will get by steering some of its voters to this ticket splitting. This has been a main problem in Germany since 1990, and obviously, it increased in the last election.
There's also a case in [Inaudible--Editor] that had a dramatic influence. Imagine, for example, that you could found a party named the “Friends of Conservatives”, and then recommend that supporters of Conservatives vote with their first vote for the the Friends of Conservatives, and with their second vote for the real Conservative Party. This would mean that the constituency seats that are won for the Friends of the Conservative Party could not be accounted as party votes for the Conservative Party, and this would create a potentially huge number of overhang seats. This is the reason that we recommend you take only the one-vote solution.