We’ve all heard of the Electoral Pendulum – where seats are sorted from top to bottom according to their two party preferred margin. The beauty of the pendulum is that it provides an excellent approximation of how many seats would change hands for any given two party preferred swing – something that **Antony Green’s spiffy pendulum calculator** utilises. If we want to know what would probably happen in an election with, say, a swing of 2% toward the government, then we can count up all the Opposition seats that have a margin of less than 2% – on today’s pendulum that is 12 seats in total – and give that * number* of seats to the government. But we only give that number of seats, not necessarily those actual seats.

This is because swings are never uniform across Australia – some seats swing more than others. What this means in practice though is that for every Opposition seat on a margin of less than 2% that doesn’t swing enough to put it in the government’s column, there will generally be an Opposition seat on a margin of above 2% that will swing enough to make it a government gain.

The theoretical basis for the pendulum is derived from the assumption of swings taking an approximately normal distribution – a distribution approximating a bell curve shape. Yet, if we look back on election the history of federal elections, we can generally be a little more accurate than this by throwing the average standard deviations of federal election results into the mix.

The standard deviation is a measure of the variability around a uniform swing, and in Australia over the last few elections it has averaged 2.5%. With our assumption that swings follow a normal distribution, and with a standard deviation of 2.5% – that means that approximately 68% of all seats swing by an amount within 1 standard deviation of the mean swing, and approximately 95% of all seats swing by an amount within 2 standard deviations of the mean swing.

So if we had a uniform swing of 6% and a standard deviation of 2.5, then we would expect 68% of seats to swing between 3.5% and 8.5%, and 95% of seats to swing between 1% and 11%.

Currently we have a phone poll average showing a swing of 3.8% toward Labor. If we assume a standard deviation of 2.5% (the average standard deviation over the last 4 elections) and apply these qualities of a normal distribution to such a swing, we end up with something looking like this:

Around 68% of Coalition seats would swing between 1.3% and 6.3% (one standard deviation from the mean swing) toward Labor, while 95% of Coalition seats would experience a swing between 1.2% toward the Coalition and 8.8% toward Labor.

But there’s another thing that happens with Federal Elections – when we have swings toward a party larger than the value of the standard deviation of the swing – nearly all of the seats that sit on a margin less than the difference between the uniform swing and the standard deviation, fall.

Using our current figures – with a swing of 3.8% and a standard deviation of 2.5, we would expect that nearly all of the Coalition held seats that sit on a margin of less than 1.3% (the uniform swing of 3.8 minus the standard deviation of 2.5) would fall to Labor. We’ll call these seats the Red Zone.

Similarly, if we look at seats within 1 standard deviation of the mean swing – Coalition seats that sit on margins of between 1.3% and 6.3% – and apply the pendulum principles, we can get some broad probabilities for that middle group of seats. We’ll call this the Orange Zone. Because of the large number of Coalition seats that sit in this Orange Zone, we would expect around 1 in 3 of these seats to fall to Labor in an election that had a 3.8% swing.

Finally, we would expect a couple of seats further up the pendulum to experience swings much larger than the mean swing of 3.8%. So those seats between 1 and 2 standard deviations greater than the mean swing will be called the Yellow Zone.

If we redraw our first chart, but add the Zones, this is what it looks like:

Finally, if we then list the actual seats themselves into these Zones (including the seat on the 3.8% margin), this is what we end up with:

The thing to remember here is that for each seat that has a rock solid partisan history (for example, Goldstein and Menzies in the Orange Zone), because their probability of falling to Labor is virtually zilch, other seats around them will take the weight of probability – making in more likely that other seats within the Zone will fall.

All up, this is a pretty handy anxiety thermometer for Coalition MPs.

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