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, 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. 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:
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. 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.
