Current electoral reform in Germany

[Casimir]

As you all know Germany uses MMP for elections to the Bundestag (national parliament).
There currently is a commission for electoral reform reviewing changes to the system. In a recent paper they propose a fundamental shift in how the MMP system works and consider approval voting and IRV as possible methods for district mandates.

As background, the current system is a mixed member proportional system. There is nothing in the constitution demanding any particular system, but this was invented in 1949 and since only changed slightly.
Voters have two votes. One for a candidate in their district and one for a party. The party vote determines the proportion of parties in the parliament. There is a 5% threshold, so it's not entirely proportional and many votes are just ignored. Proportionality is calculated both at the level of the Länder (=states) and nation wide, but I spare you the details. (The electoral law has been called "the law that makes people crazy" by an expert in a previous commission.)

A main problem with this is that a party can win more districts than they have seats to fill by the proportional vote. The solution, until now, was to increase the total size of the parliament until this isn't an issue any more. However, with this there is no limit to parliament size. In the last election there where 736 seats instead of the regular 598. Which makes the Bundestag the second largest national parliament after China. This for one costs a lot of money, it reaches the limits of what the parliament building can physically support and it slows down the work.

The commissions task is to find a solution to this problem. It also discusses lowering the voting age and ways to better represent women.

Last week they voted on a paper outlining the direction for the new voting system (pdf, German) ("Eckpunktepapier" lit.: corner point paper).

There will be exactly 598 seats and 299 districts. Voters still have two votes. The party vote determines the number of seats for each party. When a party has won more districts than seats, they only send the candidates with the best results, the leftovers don't get a seat.
E.g. Party A has won 35 districts, but is only entitled to 30 seats, therefor the 5 worst winners aren't elected.

Then the question is what happens to those left over districts. They shouldn't be vacant, because then the voters aren't directly represented and also have less of a vote than everyone else. So they list four alternatives:
a) A "replacement" vote. Voters get to mark a secondary preference, but it is only counted when the candidate with most votes isn't covered by the party vote.
b) Keep plurality voting and elect the second best candidate.
c) Implement Approval voting and elect the second best candidate.
d) Implement IRV and elect the second best candidate.

My comment on this proposal:
I would have liked to see multi member districts, but was aware that the chance for is was very small. The new rule solves the main problem but does nothing to improve the voting system or address the many other problems it has.

a) This is confusing to voters and mostly useless. In the last election, it would only have been relevant in 38 of 299 districts. So why should voters care to add another mark on the ballot. They already don't care about who wins the district.
b) Plurality voting is bad, but in this context it's even worse. You not only don't elect the candidate with the most votes, but one with no intersecting set of votes, i.e. the opponent. A right leaning district would be represented by a left candidate (or vice versa).
c) This is what I advocated for. Approval voting natively provides an ordering of candidates by popularity. It's no problem to elect the next best. I also hope that once approval has a use in Germany it will over time replace all other plurality elections and all runoff elections with approval+runoff.
d) There is no movement for IRV in Germany, but it still is the most widely known of the alternative voting methods. It doesn't provide a real ordering of candidates. The last candidate to be eliminated isn't necessarily the "second best", it very much depends on who is running and in what order they are eliminated. One object of the commission is to make the voting law simpler. With the above changes it takes a huge step towards this goal, IRV however would be detrimental to it.

In a previous petition and a recent letter (pdf, German) to the commission I advocated for the use of approval voting in the candidate vote, but also as cumulative voting in the party vote. If you would vote for four parties, each would get ¼ of your vote. I'm generally against a party vote threshold, but proposed that this could be used to reduce the number of ignored votes. In a first step count the votes and eliminate all parties that fail to reach the threshold, then count the votes again, but distribute among the remaining parties. So if you voted for 4 parties, but one got eliminated, then your votes goes with ⅓ to your remaining three parties.

[Jack Waugh]

@casimir I did not know what system Germany used and thanks for stating it.

I think that your proposals are best for meeting the stated objectives.

If some people really want to try ranking, they could use Ranked Robin. This would give an overall ranking in terms of how many other candidates a given candidate beats. Ties in that ranking could be broken based on how many voters preferred the given candidate minus how many preferred others who tied with that candidate in the first measure.