## 2011 referendum options simulator project

New Zealanders will vote in a referendum in November asking whether they want to change the current voting system used for deciding the makeup of Parliament.

Dr Geoffrey Pritchard and Dr Mark C. Wilson, members of the Centre for Mathematical Social Science at the University of Auckland, have created a simulator intended to voters to compare the 5 proposed electoral systems in a quantitative way, by allowing them to compute quickly, for a given polling scenario, the party seat distribution in Parliament under each system. It is written in Javascript and the source code is publicly available. The assumptions made are detailed in the FAQ. The authors intend to refine the model used in future depending on resources, and welcome constructive feedback. The simulator is a research tool that they hope will have some use for members of the public.

The main page of the simulator can be accessed here.

1. August 4th, 2011 at 00:11 | #1

The calculator appears to be fairly faulty when it comes to FPP (and probably others which have a FPP-base, such as SM).

Take the 2002 election. We know that the actual electorate seat breakdown was Labour 45, National 21, and one each for NZ First, Progressive and United Future. In other words, Labour received approximately two electorate seat for every one National electorate seat.

How, then, when I run the 2002 election simulator, does Labour come out at 110 seats out of 120? This is 11 Labour seats to every one National seat: a massive margin which should raise some alarm bells as being pretty far out of whack. Surely the ratio of 2:1 should apply more or less across the country, rather than somehow being skewed to 11:1.

And what about the seats for NZ First, Progressive or United Future? Why have they suddenly disappeared?

Seems like some faulty assumptions are at play.

2. August 4th, 2011 at 10:02 | #2

@Greg As stated in the documentation of the simulator, it uses only the party vote to determine results. The 2002 election electorate seats are determined by the electorate vote, which is not considered. One can debate this assumption, but it seems reasonable to me to expect that under FPP, for example, a voter is more likely to vote for a party than for a candidate. I would welcome hearing about any serious empirical research that could shed light on this assumption.

The smaller parties would not win any electorate seat if the 2002 election were held under FPP with the same voting behaviour and the same distribution of voter preferences across our hypothetical electorates as we have derived from the 2008 NZ Election Survey, as described in the documentation. We do not claim that these assumptions are 100% “realistic”, but one must start somewhere if a fair comparison between the electoral systems is to be undertaken.

3. August 4th, 2011 at 23:37 | #3

@Greg
If you look closely at the 2002 election results you will see that there were many seats won by National candidates where Labour won the party vote. Often the results were not even particularly close, as e.g. in Nelson:

Electorate vote: Nick Smith (NAT) 15779, John Kennedy (LAB) 11547
Party vote: Labour 15149, National 6517.

The voters favoured Smith, but were not nearly as keen on his party. So, what would have happened under FPP, where casting a vote for a candidate is effectively an endorsement of the party as well? It is hard to say for sure, but the simulator uses the MMP party vote to indicate how things might have gone. That’s how National ends up retaining only 10 seats out of 120 in that scenario.

It’s a similar story for the seats won by the NZ First, Progressive, and United Future parties – their candidates won only the electorate vote, so they don’t show up in the simulator result.

4. August 7th, 2011 at 23:05 | #4

Thank you both for your responses. With the greatest of respect, this appears to be a case of the statistical model ignoring reality. A further question: were any political scientists involved in the construction of your models?

I’ve briefly reviewed each election since 1914. The greatest ratios of electorate seats for a winning party over a second party are:

– 1925: 4.6 seats for Reform to every 1 seat for Labour (although if you count Liberal as well, you’re down to 2.4:1)
– 1935: 2.8:1
– 1990: 2.3:1 – widely regarded as the greatest ‘landslide’ in modern New Zealand electorate history.

The 1990 election also appears to give us the largest percentage won by a party overall – National took 69% of the available seats.

Compare this to 2002:
– Electorate seats: Labour wins 2.1 seats for every National seat, and 65% of electorate seats
– Overall: Labour wins only 1.9 seats for every National seat, and only 47.5% of all seats

Most of the FPP elections are actually fairly close. The ‘normal’ ratio of seats is well under 2:1. It seems nonsensical that under FPP, the 2002 ratios would suddenly kick up to 11:1, and 91.6%. That has never happened before, even under the most extreme circumstances.

Dr Pritchard’s mention of Dr Smith’s success would seem to support my argument: electorate seat volatility is a rare beast. Electorates are actually fairly loyal to their candidates: witness Dr Smith’s success, and that of National MP John Carter, who increased his majorities throughout Labour victories in both 2002 and 2005. The continued and lengthy support for Peter Dunne in Ohariu and Jim Anderton in Wigram – even in the face of changes of governments or their own parties – would suggest that focusing only on the party vote is too simplistic. There are far more variables at play.

5. August 8th, 2011 at 00:48 | #5

To answer the minor questions first: One political scientist was consulted in a general way. We will hold a seminar to allow for more academic feedback. I would be very keen to know whether there are any recognized methods of making the kind of “predictions” we are attempting. Refinements to this model could go on for many years, and we thought it important to start now with what looks to us to be a good first approximation. Your suggestions
will be made by others too, I am sure.

My opinion on the other points:

The success of Anderton et al is in an MMP environment. I don’t see that it is possible to predict whether such people would be elected in an FPP setting. In any case, the number of such exceptional candidates is likely very small. In other words, the qualitative comparison of the 5 election methods will not be much changed by small quantitative changes.

The Canadian parliamentary elections (http://en.wikipedia.org/wiki/List_of_Canadian_federal_general_elections) show some interesting data. The 1993 result was very extreme as far as the PC party goes, especially when you look at the two previous elections. The ratios you describe have been larger in Canada than you say they have been in NZ. This shows what can happen under FPP. It is not completely clear to me that such a lopsided result could not have happened in NZ in 2002 under FPP.

As far as the NZ data goes: the further back you go, the more chance there is of finding an election where voter preferences were very different from those in the 2008 NZ Election Study, and where correlations between party and electorate votes differ from those in the 2008 election. This simulator is not trying to “postdict” the results of historical elections in NZ. It is intended to be a tool that can be used to give a better idea of the likely consequences of using each of the 5 voting systems in modern NZ.

The 2008 Election Survey gives data which we used to infer voters’ party preferences (those they would admit to), and we assume that they would vote in a way that is consistent with those. Of course under FPP, it would have been clear to voters in 2002 that National would lose heavily, and voters not wanting to vote Labour would likely have switched to a third party. So changes in the voting system might lead to changes in expressed votes, which is another complicating factor.

6. August 8th, 2011 at 01:41 | #6

@Greg
Thanks for your interest. You are right that our simulated results for 2002 are unlike any in New Zealand’s FPP-era electoral history. But that isn’t the fault of the calculator – it is the scenario itself that is extreme. For the second-largest party to have only 21% of the vote would be unprecedented. The example of the 1993 Canadian federal election (the Progressive Conservatives won 2 of 295 electorates, on 16% of the popular vote) suggests to me that the calculator may be doing a reasonable job of representing what would happen under such an extreme scenario.

I do take your point that, had FPP been used in 2002, National might have got more of the FPP popular vote than it did of the MMP party vote. You may well be right about that. (But I don’t think the MMP electorate-vote data is a good quantitative measure to use – a popular candidate from an unpopular party will surely find it much easier to attract MMP electorate votes than FPP votes.) If the 2002 party vote is modified by shifting 5% from Labour to National (i.e. Labour 36.26%, National 25.93%) the calculator gives Labour 91 seats and National 29 – still a landslide of historic proportions, but perhaps closer to what you were looking for.

7. August 8th, 2011 at 04:09 | #7

Thank you both. This is a very interesting topic and I appreciate your responses.

As to what happens when one party collapses, I think Dr Wilson’s final paragraph in his last comment sums it up nicely: when voters are faced with an ineffective opposition party, they will seek out a new opposition party. That happened in 2002, when voters left National for New Zealand First and United Future. (Labour in fact gained only three seats from the previous election.) The same appears to have happened in Canada’s 1993 election: voters deserted PC for the Reform Party. The correct analogy is then not between Liberals and PC, but in fact Liberals and Reform (or Liberals and Reform+PC). The Liberals in that election received only 60% of all available seats, even though the result was a “landslide” – and it was held under FPP. In a similar fashion, Labour in a 2002 FPP election ought not capture 91.6% of the seats.

I note also that in none of Canada’s federal elections or those in Australia’s House of Representatives does the ratio of first party to second party seats exceed 5.275:1 (Canada, 1984) – and even there, 31 seats went to a third party.

I don’t dispute that if you model your calculator using primarily MMP data, you will get a massive swing when translating that to FPP results. My criticism is that MMP data shouldn’t be used as the primary base. It ignores the reality that under FPP, the country was divided into 99 electorates, each of which was relatively homogenous and is more likely than not to continue voting for a certain party, despite massive changes in the true swing vote seats. For example, Rodney (previously Kaipara) has been represented by National consistently since 1943. Rimutaka (previously Eastern Hutt and Hutt) has been represented by Labour since 1929. There will be a large number of seats across the country which are similar, and no matter what the nationwide swing, will generally always vote Labour/National (or, more accurately, centre-left or centre-right). This is indicated by the number of electorate seats retained by National in the 2002 election. You might argue that this is represented by the 10 seats National would retain in 2002 in your model. I would argue, that judging by the much lower actual seat transfers across all of New Zealand’s FPP elections, the real “base” for a party is somewhat higher than 8% of the available seats.

My preferred model in FPP would have, for example, a “strong National” base of 20% of available seats, a “more likely National” base of 20%, and repeating the same for Labour, leaving 20% true swing voters. The MMP data ought to affect the swing voters very heavily, the “likely” voters less, and the “strong” voters hardly at all. Granted, I haven’t looked through your FAQ and methodology to see if your models do exactly that, but if they do, I would humbly suggest there needs to be some tinkering with the effect of the MMP data.

8. August 16th, 2011 at 00:59 | #8

I think your FAQ would do well to mention that the “MMP” option in the referendum is an undefined variable. As the official web site says: “If at least half of voters opt to keep MMP, there will be an independent review of MMP in 2012 to recommend any changes that should be made to the way it works.” So objectively, a voter does not know what s/he is voting for. The simulator does allow switching on and off the threshhold exemption, but that is only one of the aspects of MMP that may, or may not, change.

1. July 21st, 2011 at 22:05 | #1
2. July 23rd, 2011 at 21:01 | #2
3. July 27th, 2011 at 01:19 | #3