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Archive for July, 2010

The latest NZ political poll was the fortnightly Roy Morgan Research poll released on Tuesday, July 27. The poll shows some fairly large movements in support relative to the previous poll, but none of them appear to be statistically significant. National and Labour are both polling at roughly pre-budget levels within the margin of error.

As usual, 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 2008 NZ General Election, and finishing on the present day. 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 eight major and minor NZ political parties

Party vote support for the eight 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 six minor NZ political parties

Party vote support for the six 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.

The latest scenario analysis graph is also shown below:

Scenario analysis for 28th July 2010

Scenario analysis for 28th July 2010. The bar graph shows the probabilities for different possible outcomes for a NZ General Election if held on that date. The National Party are estimated to have a roughly 78% probability of winning an outright majority of the seats in Parliament, and 97% chance of being able to form a governement without Maori Party support.

Here we see that National have only a 78% probability of winning an outright majority in an election were it held today, with a further 19% chance of leading a National-ACT or National-ACT-United Future coalition for a total of 97%. The final 3% corresponds to the probability that the Maori Party will hold the balance of power in Parliament, albeit with a center-right numbers advantage. Part of the reason for this is the small drop in support for National in the latest poll, but it is largely due to the errors on the polling averages blowing up due the sparsity of recent polling data — a problem we’ve seen before, notably around the Xmas/New Year’s period. This time though, the implications are a bit different, as you can see from some of the additional simulation results shown on the Graphs page. In particular, the following stands out:

New Zealand First seats in Parliament

Histogram showing the total number of seats New Zealand First are expected to win in parliament if an election were held on July 28.

The above histogram shows the expected distribution of the number of seats won by New Zealand First in Parliament: most likely none, but with a small 9% probability of crossing the 5% threshold and receiving representation.

It is interesting to consider the implications of having the New Zealand First party back in Parliament, and we can determine them by simply running the election simulation as usual and then only counting up the results where New Zealand First gets seats. Under this condition the number of seats won are as follows:

Total number of seats New Zealand First are expected to win, assuming threshold

Histogram showing the total number of seats New Zealand First are expected to win in parliament if an election were held on July 28, given that they surpass the 5% threshold.

The graph resembles the right tail of a normal distribution, with a little bit of rounding error due to eccentricities charachteristic of the Sainte-Lague method which is used to decide the seats, which is more or less the behaviour that would be expected. We see that even in these cases New Zealand First are unlikely to get more than seven seats, indicating that even if they were to surpass the 5% threshold it is unlikely at this stage to be by a large margin.

When we re-plot the results of the scenario analysis study for just the above election results (where New Zealand First get seats) we get the graph below:

Scenario analysis for 28th July 2010, assuming New Zealand First pass the threshold

Scenario analysis for 28th July 2010, assuming New Zealand First surpass the 5% threshold. The bar graph shows the probabilities for different possible outcomes for a NZ General Election if held on that date. The Maori Party are estimated to have a roughly 28% probability of holding the balance of power.

This is where things start to get a bit more interesting. Labour still have virtually no chance of leading a centre-left coalition without the Maori Party. The reason for this is that New Zealand First’s seats have come roughly half from either side of the aisle, meaning that even with New Zealand First passing the 5% threshold there would still only be a 3~4 seat turnaround in favour of the centre-left. Nevertheless, the Maori Party now have a roughly 28% chance of holding the balance of power in Parliament. What are the chances of seeing a five-way coalition between Labour, the Greens, the Progressives, New Zealand First, and the Maori Party? And what are the chances the Maori Party would chose such a coalition over a centre-right coalition with National, ACT and United Future? Alternatively, it may be time for National to consider whether they would prefer to go into coalition with the Maori Party or New Zealand First if they were put into the position of having to chose one or the other.

Of course at this stage the results are largely hypothetical; all we’ve managed to show is that if an election were held today and New Zealand First were to pass the 5% threshold (two big ifs) then there is a non-negligible probability that the Maori Party would hold the balance of power. But if New Zealand First were to pick up 2% in the polls at the expense of the National party then we would be in for quite an unpredictable election.

These results are interesting given that the Roy Morgan Research polling was conducted before two important pieces of news recently came to light; firstly there were rumours of Whanganui mayor Michael Laws teaming up with Winston Peters to help get New Zealand First back into Parliament, and secondly in a recent interview Prime Minister John Key refused to rule out a coalition deal with New Zealand First like he did prior to the last election.

It will be interesting to watch New Zealand First’s polling numbers over the next twelve months.

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In a blog post a couple of months ago I discussed the January 2010 Roy Morgan political polling stocks on iPredict. Since then the April stocks have closed, so I’d like to take the opportunity to have a closer look at the results.

As with the January stocks, the data for all trades made on any of the April stocks is available through the history option on the API. Like last time, I have simply copy/pasted all the relevant data from the history function on Luke’s API application into a spreadsheet, and then moved it around a bit to get it into an manageable format. The results are available online in MS Excel format [.xlsx, 752kB]. Please feel free to use or modify the file as you like. The file contains one chart and 13 spreadsheets, please see the previous post for an explanation of the data format.

The first thing that should be pointed out is that at no point did the National stock that eventually closed at $1, NAT.APR10.LOW, trade as the most probable outcome; NAT.APR10.LOW typically traded at 27c ~ 36c below the favoured NAT.APR10.MID and NAT.APR10.HIGH stocks. In fact, the day before closing LOW was trading at just $0.0650, compared to $0.4502 for MID and $0.4174 for HIGH.

This behaviour makes an interesting contrast to many other bundles of stocks on iPredict, for example the bundle on the price of 91 Unleaded petrol, where typically one of the stocks in the bundle will trend towards $1 whilst the rest trend towards $0. Or rephrasing in terms of entropy, the entropy of the bundle of 91 Unleaded petrol stocks will trend towards zero, whilst the entropy of the bundles of Roy Morgan polling stocks will be constrained by a theoretical lower bound. The reason, of course, is that with the petrol stocks the only source of uncertainty is temporal uncertainty, whereas with the polling stocks there is also measurement uncertainty and statistical uncertainty. It is for this reason that the Roy Morgan polling stocks provide such a good laboratory to test the validity of predictions in a futures market.

Once again, the focus of the analysis here will be on the entropy of the political poll bundles over time. For an explanation of entropy in prediction markets please refer to the previous January stocks’ post.

The plot of entropy against time for the April stocks is shown in the first graph below.

Graph showing movement of the total entropy of the 10 political polling stocks

Graph showing movement of the total entropy of the 10 political polling stocks (vertical axis) as a function of date (horizontal axis,) from the opening of the stock on February 19, 2010, up to and including April 8, 2010 - the day before closing. The red series shows the calculated entropy immediately after the last trade of each calendar day (NZT), and the black line shows a linear fit to the data series.

The red series shows the total entropy of the two bundles, and the black line shows a linear fit to the data. In order to help interpret the results the entropies of three reference distributions are also shown in the graph. If the most recent trades of both the National and Labour bundles were $0.03, $0.11, $0.37, $0.37, and $0.12, then the total entropy would take the value of 2.6764, indicated on the graph by the green horizontal line. If the most recent trades were instead $0.02, $0.09, $0.40, $0.40, and $0.09, then the total entropy would take the value of 2.4894, indicated by the yellow horizontal line. Finally, if the most recent trades were $0.01, $0.07, $0.42, $0.42, and $0.08, then the total entropy would take the value of 2.3259, indicated by the purple horizontal line.

So how well did iPredict do? The answer is not so different to that from last time. Firstly, the good news is that on average the total entropy of the ten stocks shows a tendency to decline as the closing date approaches, as indicated by the negative gradient of the black linear fit to the data series. The bad news though is that the slope of the data series itself is not negative-definite, which it should be with only very rare exceptions. We can see a sharp drop and trough from March 15th, followed by a rise and plateau occurring around March 24th; a pattern similar to that seen in the January stocks. Once again it’s not obvious why this pattern is occurring, but it seems to be around the time of release of the penultimate Roy Morgan poll in the series before the stock closes, which was released on March 18. Perhaps some traders are underestimating the statistical error on the results of the penultimate poll, and then assuming that the result of the poll that decides the outcome of the stocks will be approximately the same.

Looking again at the graph, another surprise is the precipitous drop in entropy starting on April 4, 2010, approximately 3 days before the release of the relevant poll. It may just be a coincidence, but the drop looks fairly significant when compared to the daily movements over the proceeding 50 days. A similar pattern was observed two days before closing with the last stocks, and as with last time there were no other polls released around this time that could serve as a reference for the trades, so perhaps it was a trader exercising inside information.

To smooth out some of the day to day fluctuations we have combined the data from the January and April stocks together in the graph below.

Graph showing movement of the average of the total entropy of the 10 political polling stocks

Graph showing movement of the average of the total entropy of the 10 political polling stocks (vertical axis) as a function of days until closing (horizontal axis.) The red series shows the average of the calculated entropy for the JAN10 and APR10 stocks immediately after the last trade of each calendar day (NZT), and the black line shows a linear fit to the data series.

The red series shows the total entropy of the two bundles, and the black line shows a linear fit to the data. The horizontal axis now represents the number of days before the stock closes. The green and yellow horizontal lines are those from the above graph corresponding to entropies of 2.6764 and 2.4894, respectively. The additional two reference entropies are given by the blue (2.9673) and orange (2.8057) lines.

Averaging the two different time periods smooths out some of the fluctuations, but once again we can still see the dip, trough and rise lasting from approximately 30 days before closing until approximately 15 days before closing. This discrepancy indicates an interesting strategy for beginners who want to take part in the stocks: simply wait until three weeks before closing, and if the highest stock in either of the National and Labour bundles is priced over about 45c then sell it and buy the rest of the bundle. Other than the non-negative definite changes in entropy, though, the trading behaviour seems fairly reasonable.

In conclusion, traders at iPredict did a fairly reasonable job with the second set of Roy Morgan Poll polling stocks in the new format, which closed in April, although they did not correctly pick the stock in the National bundle that would eventually close at $1 at any point during the period of trading.

Analogous polling stocks for the first Roy Morgan poll to be released in June have also closed, and stocks for the first poll to be released in August will be closing soon, so I will do an similar analysis on those results and publish it here in the near future.

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The latest NZ political poll was the fortnightly Roy Morgan Research poll released on Friday, July 9 (albeit three weeks after the previous poll.)

The poll has National on 53% – their highest since the late February Roy Morgan Poll. Labour are on 29% – their lowest result in a Roy Morgan Poll since early December 2009. The updated Kiwi Poll Guy polling averages have National on 53.3% +- 1.8%, confirming a statistically significant improvement over their recent low of 50.4% +- 1.1% on the 25th of May, about the time of the 2010 budget. Labour, on the other hand, are on 30.8% +- 1.7%, their lowest average since March 31st 2010.

As usual, 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 2008 NZ General Election, and finishing on the present day. 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 eight major and minor NZ political parties

Party vote support for the eight 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 six minor NZ political parties

Party vote support for the six 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.

As always, please check the Graphs page for further simulation results.

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