Several months ago I realized that the 2011 referendum in NZ on the voting system for parliamentary elections was coming soon. Geoff Pritchard and I developed a simulator with the aim of enabling voters to understand the consequences of a change to another system. In order to do this in a way that is useful to the non-expert, some simplifying assumptions must be made. We had substantial media coverage and some criticism.

Initial surprises:

• How few people bothered to read the detailed FAQ before criticizing.
• How many people thought that the simulator was trying to “back-cast” historical elections, and were certain that our results were unrealistic, without giving any evidence.
• How much the criticisms, even unfounded ones, helped to clarify my understanding of what we had actually done, and suggested further research.
• How short the attention span of internet visitors is.

In particular I want to respond to comments by David Farrar on his well-known site Kiwiblog. The relevant extract:

Now in 2002 National actually won 21 electorate seats out of 69 or 70. So this model is saying if there were 50 extra electorate seats, National would win 11 fewer seats!!

Why? Because they have come up with a formula based on the last 50 years or so of FPP elections, which they applied to the party vote figures for 2002. They ignored the actual electorate vote. It is a classic academic approach.

The more pragmatic approach, which is what others have done, is to say well if National won 21 electorate seats in 2002 out of 70, then if there 120 seats, their estimated number of seats would be 21*120/70, which is 36 seats.

In fact we did not look at any of the historical FPP elections The “formula” is based completely on the MMP party vote from the 2008 election (so yes, we did ignore the electorate vote, for what we think are good reasons).

However this got me thinking about how we might try to validate our assumptions. One way which I don’t (yet) claim is rigorous, but makes at least as much sense as the above, is to apply the simulator (the FPP part) to the historical FPP elections, and scale the 120 seats down to whatever it was historically (80 for many years, then increasing over time). The results surprised me greatly, as they are much better than expected, and this cries out for explanation (“further research”, always good for academics). Here they are. Note that these simulator results explicitly do not use any historical data, seat boundaries and parties have changed, etc.

1969: Real result was Nat 45 Lab 39; simulator scaled was Nat 46.9, Lab 37.1
1972: Real was Nat 55 Lab 32; simulator scaled was Nat 54.4, Lab 31.6
1975: Real was Nat 55 Lab 32; simulator scaled was Nat 55.1, Lab 31.9
1978: Real was Nat 51  Lab 40 SoCred 1; simulator scaled was Nat  47.5, Lab 44.5.
1981: Real was Nat 47 Lab 43 SoCred 2; simulator scaled was Nat 48.3, Lab 43.7
1984: Real was Nat 37 Lab 56 SoCred 2; simulator scaled was Nat 37 Lab 58.
1987: Real was Lab 57, Nat 40; simulator scaled was Lab 50.2, Nat 46.8
1990: Real was  Nat 67, Lab 29, NewLab 1; simulator scaled was Nat 71, Lab 26
1993: Real was Nat 50, Lab 45,  NZF 2, Alliance 2; simulator scaled was Nat 53.6, Lab 45.4