New Zealand’s Prime Minister John Key this morning announced his new ministry, after final results from the NZ electoral commission confirmed his re-election for a second term.

The team includes places for representatives of ACT and United Future, and two from the Maori Party, thus reassembling the same alliance he had before the election (not technically a coalition, since the minor parties retain their freedom of action). Their total of 64 seats is down from 69 in the previous parliament, but the National Party’s own share of that total is much improved. Key still needs the minor parties, but they will have less leverage than before.

National came away with 59 seats out of 121 — from the results on the night it looked like 60, but postal and absentee votes brought their total down slightly. Instead the Greens picked up an extra seat, going to 14 from 11.1% of the vote. No doubt psephologists are excited by some things that would leave the public cold, but I confess that for me there is something of a thrill in seeing a party win 47.3% of the vote, almost 20% ahead of its nearest rival, but still fail to win a majority in its own right.

Although New Zealanders vote for local members in geographically based single-member electorates much the same as we do (although without preferences), those votes are not what determine the make-up of parliament. Under the mixed-member proportional (MMP) system the party balance is determined by the party vote; among the parties represented in parliament their share of seats matches their share of votes almost exactly. National got a bit less than half the vote, so it won a bit less than half the seats.

As I’ve said before, it’s not rocket science. You can do it yourself in minutes with a spreadsheet: just list all the party vote totals, divide them by a common divisor, round the resulting figures to the nearest whole number, total them, and keep adjusting the divisor until that total equals the number of seats in parliament. If New Zealand can do it there’s no rational reason why we can’t.

In conjunction with the election there was a referendum on whether or not to keep MMP, which was introduced against the wishes of the political parties in 1994 … 57.8% voted to stay with it against 42.2% for change, despite the fact that Key was supporting change. It shows that voters don’t always put complete faith in the party they’re voting for but are capable of making up their own minds.

It’s quite striking how often voters return a government but turn down its referendum proposals, including cases as recent as 1974 and 1984 in Australia. Sometimes it even happens the other way around — in 1933, Western Australians voted for secession from Australia but turfed out the government that had promoted it.

For Key, it’s not a major issue. By coming so close to winning a majority on his own, he showed that MMP does not preclude single-party government — thus unintentionally refuting one of the main claims of its opponents. Holding a referendum also gave him some insurance, since voters who might otherwise have been worried that National would move to abolish MMP were able to prevent that with their referendum vote and still re-elect the government.

Instead of fundamental change, what New Zealand will get is a review of MMP to try to improve its working and clear up some anomalies. At the margin, some odd things happen: the four-party government alliance dropped only about 1.4% of the vote this time but lost five seats; the new Conservative Party comfortably outvoted ACT and United Future but failed to win any seats. (Antony Green last month provided a good explanation of these and other problems.)

So MMP can certainly be improved, and the review is all to the good. But New Zealanders have wisely decided not to throw the baby out with the bathwater.