The Proportional Application
Posted by Possum Comitatus on October 5, 2007
In our last Newspoll breakdown, we divvied up the seat swings according to the Newspoll estimate of three seat types, and by State for 139 seats across the country. That gave some people psephological indigestion because the results didn’t look like an election would at the margins of safe vs marginal seats. Fair enough, but it was never meant to – it was a breakdown of Newspoll to the best resolution available from the data.
This time, we’ll actually set out to create an approximation of what the Newspoll data was saying that isn’t limited by the data resolution, using basic probability theory and an assumption of uniform state swings. We’ll do today what some people thought we were doing the other day.
To start with, the TPP swing is calculated as the percentage change in vote of the two major parties. Hence if a seat moves from 50% to 55%, it’s had a 5% swing.
If we have 3 seats that are, in ALP/Coalition terms: 40/60, 50/50 and 60/40 and the average swing in these seats is 5%, if the people that are changing their vote are drawn randomly from those three seats, we would expect that the seat with a higher proportion of coalition voters will have more Coalition votes that changed, and the seat with less coalition voters would have less coalition votes that changed.
This is simply as a result of a random distribution of Coalition voters changing their votes. As a result, the 60/40 seat would have (0.05*40*2)-40 coalition voters = 36, and (0.05*40*2)+60 ALP voters = 64.
Doing this for the 50/50 seat we end up with a TPP of 55/45 and for the 40/60 seat we end up with a TPP of 46/54. The seats with a larger number of coalition voters swing more, on a given uniform swing to the ALP (here 5%) than seats with a smaller number of Coalition voters. This is played out in nearly every Newspoll marginal seat/safe government seat/safe ALP seat estimate and most elections.
If we apply the various State swings using the same methodology to the 139 seats we are looking at here, we end up with the following
|Actual Newspoll Swing||9.2||11||9.1||9.4||4.4|
The Calculated Swing is (using NSW as an example) what the average swing in NSW is calculated as after we’ve applied the Newspoll estimate to the individual seats using the methodology outlined above. Notice how it’s higher by a bit across the board? That’s the variation in the uniform swing interfering. So we can adjust the swing downward for this by multiplying the Actual Newspoll Swing by the ratio of the Actual Newspoll Swing to our Calculated Swing. This gives us our Adjusted Swing. When we apply our adjusted swing to all 139 seats, the State averages of the seats all tally up to the actual Newspoll state estimates. By doing this, we are choosing to minimise the size of the swing we use to account for the small variance in the random distribution of changing voters that Newspoll is picking up in their polling.
We can see how the minimising of the swing plays out by comparing our results in three seat types against the Newspoll results for the three seat types:
|Newspoll Swing||Our Swing|
|Marginal Seat Swing||8.3||8.14|
|Safe Government Seat Swing||11.6||10.18|
|Safe ALP Seat Swing||7.1||6.83|
We are smaller in every case of the three seat types, but bang on the State and National average swings. So now we have our conservative estimate that is actually well within the Newspoll estimates, we can apply that to the 139 seats in our list to get an approximation of how the election results would have looked had an election been held between July and September. Remember, as we are using a slightly smaller set of swings than Newspoll, this is a slightly conservative estimate. Instead of all 139 seats, we’ll just look at those seats where the ALP TPP vote was estimated to be above 48%
|Division||State||04 Election||Current TPP Estimate||Swing|
Let me also provide evidence from the last three elections on the basis of the random distribution of voter change. If we run a simple scatter against the size of the swing in seats vs the margin those seats were held by, and a run a simple regression through them, we get:
The Margin axis on the bottom is positive for Coalition seats and negative for ALP seats. So an ALP seat with a margin of 5% would be represented as -5 in the chart, and a Coalition seat on a 5% margin would be +5 in the chart. Likewise with the swing, a positive swing means a swing to the Coalition, and a negative swing is a swing to the ALP. The red line is the regression which helps show the general relationship between margins and swings. There is certainly lot’s of variance there – that’s why we adjusted our swings downward in the above estimates to accommodate for the general consequences of the variance at a state level. The scatters are also quite interesting in their own way.