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Archive for November, 2009

In the last few posts we’ve looked at polling averages and the number of electorate seats and total seats won in Parliament by the various political parties. For most people, however, when looking at political polls the main result they are interested in is which party or coalition would win an election if it was held today.

To answer this question we use the same technique as we used to calculate the distributions of electorate seats: a Monte Carlo Simulation. Based on the latest polling averages we simulate a single election, figure out which party or coalition wins, and then repeat that process 10000 times to average out the statistical uncertainties. After that it is just a simple matter of counting up the results to get the probabilities. When we do this with the polling averages from the 20th November, after the release of the latest poll from Roy Morgan Research, we get the following results.

Scenario analysis for 20th November 2009.

Scenario analysis for 20th November 2009, listing the probabilities for different possible outcomes for a NZ General Election if held on that date.

As can be seen from the table, we calculate a 99.87% chance of National attaining an outright majority, and an additional 0.13% chance of a National-ACT coalition government. It is necessary though to clarify that the 0.13% does not necessarily mean that the result of an election would be a National-ACT government, rather it simply refers to the probability that National would not have enough seats to govern alone, but National and ACT between them would. Under these circumstances National and ACT might instead choose to form a broader coalition containing other parties, such as the Maori Party and United Future; or National may choose to ignore ACT and instead form a coalition with another party such as the Green Party; or ACT may instead choose to go into a grand coalition with all parliamentary parties except National. The only reason the table refers to a National-ACT coalition instead of one of these other possible results is that it is considered the most likely outcome based on the political reality of the relationships between the parties as of the present.

The information in the above table can alternatively be summarised as a bar graph, as shown below.

Scenario analysis for 20th November 2009.

Scenario analysis for 20th November 2009. Bar graph shows the probabilities for different possible outcomes for a NZ General Election if held on that date. Results are identical to those in the table above.

This graph, however, isn’t particularly interesting, at least given the near certainty of a National Party absolute majority due to their current dominant lead in the polls. It may be more interesting to instead look at similar Scenario Analysis graphs from the dates of previous NZ General Elections.

Firstly, the predictions (retrodictions) for the 2008 General Election were (are) as follows:

Scenario analysis for 8th November 2008, the date of the 2008 NZ General Election. Bar graph shows the probabilities for different possible outcomes for a NZ General Election if held on that date.

Here the most likely outcome (approximately 75% probability) is of a National-ACT coalition, which is in fact what happened; in the 2008 NZ General Election National’s 58 seats were not enough to govern alone, and they had to rely on the 5 seats from the ACT party to attain a majority. There is also a roughly 20% probability that National and ACT between them would need additional seat(s) from United Future to form a majority; and a roughly 5% probability that National, ACT and United Future would not hold enough seats between them to form a majority, and the Maori Party would hold the balance of power in parliament, albeit with the Center-Right coalition having a numerical advantage over the Center-Left.

Next, the predictions (retrodictions) for the 2005 General Election were (are) as follows:

cenario analysis for 17th September 2005.

Scenario analysis for 17th September 2005, the date of the 2005 NZ General Election. Bar graph shows the probabilities for different possible outcomes for a NZ General Election if held on that date.

Here the near-certain outcome is for a four-way coalition between Labour, the Progressives, the Green Party and the New Zealand First Party, which again is what happened in the 2005 NZ General Election, or at least what would have happened if the parliamentary parties were on the same terms with each other then as they are now. The final results had Labour on 50 seats, Progressives with 1 seat and the Green Party with 6 seats, for a total of 57 seats – not enough to govern without the additional support of New Zealand First’s 7 seats. Of course that is not how the coalition negotiations worked out, but again that is due to looking at the 2005 results through the lens of the relationships between the parties as they are in 2009, and not a problem with the simulation itself. The ability of the simulation to correctly retrodict the overall outcomes of the 2005 and 2008 NZ General elections gives some confidence in the models it uses.

Finally, we can take the probabilities of the three major scenarios – National-led government, Labour-led government, and Maori Party balance of power – and plot them as a time series graph to show how the probabilities for each scenario have changed over the last 4 or so years. The results are shown in the figure below:

Time series for Scenario Analysis results.

Time series for Scenario Analysis results. Horizontal axis represents the date, starting 60 days before the 2005 NZ General Election, and finishing 60 days from the present. Lines show probabilities of a National-led government (blue), Labour-led government (red) and Maori Party balance of power (pink).

As you can see, Labour’s chances of holding together a winning coalition vanished rapidly within a few months of the 2005 election. The Maori Party were then predicted to hold the balance of power for most of the next two years, before National’s rise in the polls. Other than a brief and small (~5%) dip around the 2008 election, the National Party have looked certain of leading the government since about late November 2007. Ignore the small dip in National’s probability on the far right of the graph, that merely reflects the uncertainty due the errors on the polling averages blowing up because the simulation is performed too far in the future. They may vanish depending on future polling.

Due to National’s current lead in polling these graphs are unlikely to change significantly in the near future, so I won’t be writing too many front page posts on them. I will try to make the most recent Scenario Analysis graphs available on the graphs page though, so please have a look there if interested whenever new polls come out.

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The latest NZ political poll was released by Roy Morgan Research on the 19th November. It showed a relatively large drop in support for National of 4 points (from 55.5% to 51.5%) and a gain for Labour of 4 points (from 29% to 33%).

The current party vote polling averages for each party are shown in the table below along with their margins of error.

Party vote polling averages.

Party vote polling averages and margins of error.

The two graphs below summarise the polling averages for the party vote after the new poll. The horizontal axes represent the date, starting 60 days before the 2005 NZ General Election, and finishing 60 days from the present. The solid lines with grey error bands show the moving averages of the party vote for each party, and circles show individual polls with the vertical lines representing the total errors.

Party vote support for the 8 major and minor NZ political parties as determined by moving averages of political polls.

Party vote support for the 8 major and minor NZ political parties as determined by moving averages of political polls. Colours correspond to National (blue), Labour (red), Green Party (green), New Zealand First (black), Maori Party (pink), ACT (yellow), United Future (purple), and Progressive (light blue), respectively.

Party vote support for the 6 minor NZ political parties as determined by moving averages of political polls.

Party vote support for the 6 minor NZ political parties as determined by moving averages of political polls. Colours correspond to Green Party (green), New Zealand First (black), Maori Party (pink), ACT (yellow), United Future (purple), and Progressive (light blue), respectively.

Based on these polling averages we’ve determined the number of seats won by each party in parliament by use of a MC simulation. The results for each of the five biggest parties are shown in the histograms below.

Based on the current polling averages National would be expected to win 67.6 +- 2.0 (RMS) seats in parliament, almost – but not quite – a guaranteed outright majority. Labour is expected to win 39.2 +- 1.7 (RMS) seats.

Total number of seats won by National.

Histogram showing the total number of seats won by National in parliament.

Total number of seats won by Labour.

Histogram showing the total number of seats won by Labour in parliament.

Total number of seats won by the Green Party.

Histogram showing the total number of seats won by the Green Party in parliament.

Total number of seats won by ACT.

Histogram showing the total number of seats won by ACT in parliament.

Total number of seats won by the Maori Party.

Histogram showing the total number of seats won by the Maori Party in parliament.

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Time stamps

Apologies. I’ve been having a bit of trouble with the time and date stamps on posts due to mixing up time zones. This might have made some posts publish twice and others out of order. Sorry for any inconvenience if anybody is on an RSS feed.

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Yesterday I started on a general outline of how the electoral seat simulation works. Today I show the results for the number of electoral seats won by each party (the Green Party and New Zealand First are not expected to win any electorate seats, and thus are not shown.)

Histogram showing number of electorate seats won by National.

Histogram showing number of electorate seats won by National. Expected number of seats is 50.3 +- 2.0 (RMS). National are expected to win 47 or more electorate seats at the 95% confidence level.

Histogram showing number of electorate seats won by Labour.

Histogram showing number of electorate seats won by Labour. Expected number of seats is 11.8 +- 2.2 (RMS). Labour are expected to win 15 or fewer electorate seats at the 95% confidence level.

Histogram showing number of electorate seats won by the ACT party.

Histogram showing number of electorate seats won by the ACT party. ACT have a ~91% chance of picking up the Epsom seat.

Histogram showing number of electorate seats won by the Maori Party.

Histogram showing number of electorate seats won by the Maori Party. Maori party are predicted to most likely win 5 or 6 electorate seats. They are guaranteed to win Tamaki Makaurau, Te Tai Hauauru, Te Tai Tokerau and Waiariki.

Histogram showing number of electorate seats won by the Progressive party.

Histogram showing number of electorate seats won by the Progressive party. The Progressives have a ~93% chance of picking up the Wigram seat.

Histogram showing number of electorate seats won by United Future.

Histogram showing number of electorate seats won by United Future. United Future have a ~58% chance of picking up the Ohariu seat.

Also, as hinted at in the post yesterday, the electoral seat simulation is important as it influences the number of overhang seats in Parliament. Based on the simulation the total number of seats in Parliament and the number needed to form a majority are calculated, and the results are summarised in the histograms below.

Histogram showing the total number of seats in Parliament.

Histogram showing the total number of seats in Parliament. Expected number of seats is 123.0 +- 1.1 (RMS). In other words, there is expected to be an overhang of 3.0 +- 1.1 seats.

Histogram showing the number of seats needed to form a majority in Parliament.

Histogram showing the number of seats needed to form a majority in Parliament. 62 seats in Parliament is expected to probably be enough to form a majority.

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Correctly predicting the winners of the 70 electorate contests is vital for any New Zealand General Election simulation to be meaningful. There are two major reasons for this; firstly, for many of the minor political parties the electorate waiver determines eligibility to receive additional list seats in parliament, a current example being the four list seats held by the ACT Party solely because Rodney Hide won the Epsom electorate. Secondly, electorate seats can be the cause of an overhang which alters the number of seats needed to form a majority: in the 2008 New Zealand General Election the Maori Party’s five electorate seats caused an overhang of two seats in parliament, meaning the governing coalition would need 62 seats for a majority instead of the normal 61.

Unfortunately, accurately predicting the winners of the electorate seats is also quite a difficult task, mainly because they are not subject to the same level of polling intensity as the nation as a whole.  This means it is necessary to model the electorate contests by some other means.  I hope to do a series of detailed posts later about how the poll-averaging and election simulation works, but I figured the electorate seat calculation was likely to be a bit contentious, so I thought I’d get a rough explanation out of the way first.

There’s a handful of ways to predict these results:

  1. Just assume the results are unchanged from the previous General Election.  This is the zero-knowledge solution, and is used by David Farrar for his Curiablog public poll average calculations [actually, it’s a bit more complicated, see below].
  2. Calculate the results for each electorate by calibrating them against another index that you can measure.  This was the method used by David Farrar in his “Electoral Pendulum” series leading up to the 2008 election.  It is also the method used by FiveThirtyEight for their calculation of the “Partisan Polling Index (PPI)”.
  3. Try to predict the vote for an electorate by use of regression analysis on a variety of different variables. In the case of New Zealand these may include age distribution, ethnic distribution, qualifications, iwi and religious distributions, family incomes, marital and socio-economic status, occupations and others – all of which are available on the New Zealand Parliament website. This was another of the methods FiveThirtyEight used to predict the state-by-state results of the Electoral College for the 2008 US Presidential Election.

In addition to the above methods it is preferable to include electorate-level polling data where available, but it is not possible to rely on it completely due to sparsity and small sample sizes (I believe the Curiablog polling average does include electorate level polling data where available, and uses the results from the last election as a fallback position where it is not.)

For this simulation/website we’ve decided to more or less go with method #2 above. There are a few reasons for this; firstly, it’s feels intuitively correct. Secondly, there is a bit of historical data in New Zealand and overseas to indicate the swing in the electorate polling correlates with a swing nation-wide. Thirdly, it’s relatively simple (compared to method #3 above.) Fourthly, New Zealand votes under the MMP electoral system, which means that while the exact electoral results are important for determining the exact number of seats held by each party in parliament, they are of only limited importance in determining the overall result of an election. In addition to the above reasons, it is easy enough to combine this method with electorate-level polling data when it is available (most likely in the lead-up to an election,) so any unusual results should hopefully take care of themselves in the long run anyway.

Effectively the algorithm operates by assigning eight numbers to each electorate to indicate how the electorate vote in that electorate differs from the party vote in the nation as a whole. These eight numbers are determined from the results of the 2005 and 2008 NZ General Elections. For Tauranga, Epsom, Wigram, Ohariu, and the seven Maori electorates this can get a bit complicated, but for the remaining 59 electorates only one of these eight numbers is effectively meaningful; a number we denote \delta e_0, and which roughly parametrizes the swing in the vote in the electorate as viewed on a traditional left-right political scale. Positive values of \delta e_0 correspond to a swing towards the National Party, negative values to a swing towards the Labour Party, and near-zero values indicate New Zealand’s bellwether electorates. The values for some electorates are shown in the table below.

Electorate biases.

Electorate biases for a sample of New Zealand electorates. Helensville, Taranaki-King Country and Clutha-Southland are National strongholds, East Coast Bays, Ilam and Nelson are typical National-leaning electorates, Rotorua, Otaki and Hamilton West are bellwether electorates, Christchurch Central, Hutt South and Rimutaka are typical Labour-leaning electorates, and Mt Albert, Manukau East and Mangare are Labour-strongholds.

Based on the values of \delta e_0 and the current polling averages we simulate the results for each electorate if an election were held today. The probabilities for candidates from each party to win an electorate are shown below for the same electorates in the table above.

Sample electorate seat results.

Simulation results of selected electorate seats based on current polling averages. The columns denote the National Party (NAT), Labour Party (LAB), ACT, Maori Party (MAO), Progressive's (PRO), and United Future (UNF). The Green Party and New Zealand First party are not expected to win any electorate seats, and are not shown. A large swing in favour of National is expected; in the 2008 General Election the electorates of Christchurch Central, Hutt South, Rimutaka and Manukau East were all convincingly won by Labour.

Tomorrow, I’ll show graphs indicating how many electorates each party are expected to pick up in total.

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Based on the latest polling averages after the new Roy Morgan Poll was published on the 5th of November, we’ve determined the number of seats won by each party in parliament by use of a MC simulation.  The results for each of the five biggest parties are shown in the histograms below.

Based on the current polling averages National would be expected to win 69.25 +- 1.67 (RMS) seats in parliament, enough for a guaranteed outright majority.  Labour is expected to win 37.12 +- 1.45 (RMS) seats.

Total number of seats won by National

Histogram showing the total number of seats won by National in parliament.

Total number of seats won by Labour

Histogram showing the total number of seats won by Labour in parliament.

Total number of seats won by the Green Party

Histogram showing the total number of seats won by the Green Party in parliament.

Total number of seats won by ACT

Histogram showing the total number of seats won by ACT in parliament.

Total number of seats won by the Maori Party

Histogram showing the total number of seats won by the Maori Party in parliament.

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The two graphs below summarise the polling averages for the party vote after the new poll by Roy Morgan Research (published 5th November). The horizontal axes represent the date, starting 60 days before the 2005 NZ General Election, and finishing 60 days from the present. The solid lines with grey error bands show the moving averages of the party vote for each party, and circles show individual polls with the vertical lines representing the total errors.

Moving averages of party vote

Party vote support for the 8 major and minor NZ political parties as determined by moving averages of political polls. Colours correspond to National (blue), Labour (red), Green Party (green), New Zealand First (black), Maori Party (pink), ACT (yellow), United Future (purple), and Progressive (light blue), respectively.

Moving averages of party vote

Party vote support for the 6 minor NZ political parties as determined by moving averages of political polls. Colours correspond to Green Party (green), New Zealand First (black), Maori Party (pink), ACT (yellow), United Future (purple), and Progressive (light blue), respectively.

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