Speaking of electoral systems, I once wrote up a short description of the German one for my
home page (yes, there is more to it than just my
Urbis material...

) shortly before the recent German federal elections:
"Every voter, which is every German citizen of age 18 and older (no, you don't have to register to vote here, and being an ex-felon doesn't take your right to vote away, either) gets two votes. The first one is the
Erststimme, or primary vote. With this, the voter can choose one of the candidates for the local voting district. The candidate with the most votes gets into the German parliament, or
Bundestag (with certain exceptions... more on those later).
The
Zweitstimme, or secondary vote, is actually more important. This vote goes to a specific party. If only directly elected candidates from the electoral districts could go to the Bundestag, only the biggest parties could get into the Bundestag at all (which is basically what happens in the USA and in the UK). But with the secondary votes the parties can get additional representatives from their party lists into the Bundestag until their percentage of representatives matches the percentage of their secondary votes. In other words, if a party gets roughly 8% of the votes, it will get roughly 8% of all seats in the Bundestag. (There are some arcane formulas for determining the exact number of seats, but that's the general principle...)
Not every party can get into the Bundestag, however. In the Weimar Republic, every 60,000 votes translated into one seat in the Reichstag - and predictably, the Reichstag was so full of different parties and splinter groups that it became almost impossible to form a stable government - yet another reason why that first experiment in German democracy failed so badly.
Today, a party can only get into the Bundestag if it gets at least 5% of all secondary votes, or at directly elected candidates from at least three voting districts. This means that the number of parties that can get into the Bundestag is fairly limited - unlike in Italy, where forming governments remains an art form of its own.
After the votes have been counted and the seats in the Bundestag have been distributed, someone needs to form a government. This government needs the approval of the majority of representatives in the Bundestag. In practice, this usually means that two parties that aren't too hostile to each other and have the majority of seats hammer out a coalition and distribute the various government departments among each other. Then the Bundestag votes on it, the German president (yes, we have one of those, too - though they are usually content to play "moral authority" and only rarely involve themselves into daily politics) gives it his seal of approval, and the Kanzler, or chancellor (the German head of government - as opposed to the head of state, which is the German president) can get to work.
Incidentally, readers from Florida might be interested to hear that you vote here by putting an "x" on a nationally standardized sheet of paper with the list of candidates and list of parties. The votes are then counted in the same building where the voting took place, under scrutiny of representatives from all parties that bother to send one - and nobody leaves the building until they can agree on the vote count (this is rarely later than three hours after the voting booths are closed). Mail-in votes are counted at the same time - they have to be sent in per mail in time for this."
Hope that this is interesting for your discussion...