This is a series of quantitative thoughts on the election outcome. It is based on the 2017 election night vote. Specials are likely to change precise voting shares and even seats. However potential changes do not invalidate the column’s overall conclusions.

Summary (which is less numerically challenging)

• The share of the left has returned to its long-term average after the disastrous 2014 election. National’s share is only down a little. The centre was cannibalised.
• The big change 24 years after the 1993 election is that National seems to have got 10 percentage point from, essentially, Alliance voters. The other party shares are much the same
• By ruling out a Grand Coalition, National is only as strong in negotiations as (or even weaker than) NZF, despite having many more seats.
• The threshold rule for entitlement to parliamentary seats (an electorate-seat or 5 percent of the list vote) generates paradoxes.
• The Epsom deal with Act, enabled National to filch a seat from Labour or NZF.

Long-term Trends

Basically, the left (Labour, Greens, Top) got the same share of the votes as about its long-term average (44.0%) over all the MMP elections (since 1996). The right was up 2 percentage points (46.7% over 44.4%). It has done this by cannibalising the centre.

Compared to 2014, the 2017 voter share of the left is up 6.7 percentage points, Labour share is up 10.7 percentage points at the cost of Greens. The right voter share (National, Act, Conservatives etc.) is down 6.4 percentage points since 2014 but National is down by only 1.0 percentage points.

2014 was the worst year for the left since MMP began. In some ways 2017 is to Labour as 2005 was to National - the unwinding of a disastrous earlier election performance.

The 1993 Election

My recent work in this area has focused on the MMP regime which began in 1996. Previous to that there was a Front-Runner system (often misleadingly called ‘First-Past-the Post’; there is no electorate post). Voter share under FR, which comes only from electorate counts, may reflect tactical voting. That applies today in the electorate vote – a voter may prefer A but vote for B who has a better chance of getting rid of a loathed C. However such tactical voting is less likely to happen for the list vote. (Some may switch their list vote from a preferred main party to a small party struggling to exceed the 5 percent threshold.)

I could not help noticing that Sunday’s German election is scored as a win to Angela Merkel even though her CDU/CSU party got only 32.9% of the vote. (Less than NZ Labour’s 35.8%.) The SPD got 20.6% and Die Links (a party to its left) got 9.1%. The Greens got 9.1%, the centrist FDP got 10.6%, the far right AID 13.0% and others 4.09%.

That led me to reflect on the 1993 FR election in which National got 35.1% of the vote, Labour 34.7%, the Alliance 18.2%, NZ First 8.4% and the rest 3.7%. So the left won the voter share but because of the way the system worked, National became government by itself. The big change in the subsequent 24 years is that National seems to have got 10 percentage points from, essentially, Alliance voters who were considered to be on the left of Labour (it included Greens). The other shares are much the same. Quite an achievement. Perhaps many Alliance voters of 1993 were actually covert National voters fed up with Ruth Richardson and neoliberalism and were protest voting – in the expectation that their vote would not matter?

The Banzhaf Analysis

Another feature of the German election outcome is the expectation of a ‘Grand Coalition’ between the centre right CDU/CSU and the centre left SPD – comparable to National and Labour. That option is never discussed very much in NZ.

I turned to the Banzhaf Index (sometimes coupled with Penrose or Coleman, who independently discovered it). It is used to evaluate coalition possibilities and the consequential power of the parties’ involved. I’ll avoid the mathematics and go straight to showing how it is calculated for the New Zealand 2017 election.

Given the outcome there are only four possible minimalist coalitions (in order of their parliamentary seats).

            National-Labour 103 seats

            National-NZF 67 seats

            National-Greens 65 seats

            Labour-NZF-Greens 61 seats

(These are minimalist coalitions. ACT for instance, could join them but it would not change the coalition’s domination in parliament.)

In the case of three of these four coalitions, National is necessary. But Labour, NZF and Greens can each prevent only two of the coalitions by withdrawing from them.

Add up the 3+2+2+2 = 9. The Banzhaf index is calculated by noting that of these 9 possibilities National involved 3 so its power score is 33.3% while the other three parties each have a power score of 22.2%. So National remains ahead but by not as much as its voter share. Moreover NZF and the Greens with much smaller voter shares are as powerful as Labour.

You can complicate this by assuming some coalition options are not acceptable. (Famously National was ruled out as a possible leader of a coalition in 2005 because the Maori Party considered Don Brash too racist – recall the ‘iwi vs kiwi’ billboard.)

For instance, if a Grand Coalition is ruled out, instead of

N = 33.3; L = 22.2; NZF = 22.2; G = 22.2

You get

N = 28.4; L = 14.2; NZF = 28.4; G = 28.4.

So that by ruling out a Grand Coalition, National weakens its bargaining power against NZF and Greens.

English hinted that National might be open to an approach from Greens. Were National to rule that out, they would be actually weaker than NZF for they would have only one option while Peters would have two – which is the way the public commentary presents it.

(Act is as relevant to any coalition forming as is the Maori Party.)

The Threshold Effect

To understand the actual composition of parliament it is necessary to look at the eccentricities of the threshold effect which says you have to win 5 percent of the vote or an electorate-seat to be in parliament.

The current expected composition is

Act 1, National 58, NZF 9, Labour 45, Greens 7.

Now suppose United Future had won Ohariu (which would have been an overhang electorate) and the Maori Party had won Waiariki. The outcome could well have been

Act 1, National 57, Maori Party 1, United Future 1, NZF 9, Labour 45, Greens 7 = 121.

Instead National may have to form a government with NZF despite the latter having lost, apparently, some of its vote to National. Moreover this became more possible because Labour won Ohariu and Waiariki.

Strategic Voting and Act

Had Act not won Epsom the outcome would have been:

National 58, NZF 10, Labour 45, Greens 7 = 120.

So, in effect, National filched a seat from NZF.

Suppose National had not done the deal with Act, but United Future had won Ohariu and the Maori Party had won Waiariki, the outcome could have been:

National 57, Maori Party 1, United Future 1, NZF 9, Labour 46, Greens 7 = 121.

In this case the Epsom deal with Act, enabled National to filch a seat from Labour.

(Note in all these calculations the swing (or last seat) is sensitive to particularities and to special votes.)