Taking the seat-by-seat swings for each Federal election since 1993, I was interested to see how they were distributed around the national swing in two party preferred voting outcomes compared with the previous election. I was conscious that a lot of financial data is not normally distributed (fat tails are common in financial distributions). I was wanting to check my use of a normal probability function in the simulation of election results.
First, let's look at the distribution of swings for each of the federal elections. The y-axis in the first graph (and the x-axis in the subsequent graphs) have the metric of percentage points.
Of note in the first plot, it is not unusual in an election to have one or two seats that buck the national swing by around plus or minus ten percentage points. In 1996, the outliers were swings of +17 and -14 percentage points compared to the national average.
These distributions can be compared with the normal curve (dashed in the next plot).
Combining the seven elections we can see in the next plot that the overall distribution of seat swings is normally distributed around the national swing. The normal curve in the next plot is super imposed with a red dashed line over the probability density function for seat-by-seat swings compared with the national swing for seven elections. Both curves have a standard deviation of 3.27459.
This means I can use a normal distribution in Monte Carlo simulations of the 2013 election result.
The data for this analysis came from the Australian Electoral Commission website.