Yesterday, I published a piece discussing a potential improvement to the venerable uniform-swing model. For those who haven’t read it, the general finding was that using electorate data from two elections back – as opposed to modelling a swing from solely the last election – improves the accuracy of seat forecasts. We suggested that this might have been due to seats which saw unusual swings either way tending to revert to their historical mean i.e., we should expect a Labor-leaning seat which suddenly swung right at the last election to shift at least somewhat back to the left at the next election.
On Twitter, we got an interesting comment on the possibility of the opposite happening from David Walsh, a councilor for Revesby:
Or in other words, what about seats which permanently re-align to one side or another, or which slowly shift over a few elections? Wouldn’t assuming that they are going to revert make your forecast less accurate?
In short: yes. However, as noted in our previous piece, assuming some reversion tends to do better than assuming no change and hence we can probably infer that most seats tend to revert towards their historical mean. Unless you have some way of predicting which seats are going to revert and which are going to realign/continue trending one way, we have to adopt a general rule for deciding how to forecast seats.
But, you’re not here for a simple two-sentence summary of our last piece, are you? Of course not! Welcome to part 2, where we look at the possibility of electorates realigning, and whether we can improve further on our last piece.
Modelling 2-party swings using Australian state data
I’ll be honest, I thought this was going to be a short follow-up. Until I began running the analysis.
To start off with – I’m going to eliminate the problem of redistribution we had to deal with in the last piece by focusing solely on the 2-party lean of each state in federal elections.
Data on each state’s two-party-preferred (2pp) at federal elections from here. I’ve opted to ignore elections prior to 1983 as the AEC did not conduct a full distribution of preferences at those elections (and in older elections, some electorates lacked a Labor or Coalition candidate so 2pp estimates can be a bit rubbery).
Let’s start off by redoing our graph from the last piece but focusing on Australian state/territory swings at the federal level instead. This basically shows you how the average 2pp error changes depending on how much weight you assign to a state/territory’s 2pp figures from 2 elections back as opposed to the last election:
The reduction in error is a little lower than for electoral divisions, going down from 1.93% for uniform swing to 1.84% for a model based on two elections’ worth of data. However, our optimal weight is not too far off from the figure we found last time (optimal weight for 2 elections back = 0.37) and it hovers around the simple 1:2 rule (last election = twice as important as two elections back, i.e. weight = 0.33). Hence, I’m fairly comfortable in concluding that this appears to validate our conclusions from the last piece on a larger (n = 13 elections) and more reliable (no redistribution-related error) dataset.
Now onto the new stuff. What if we tried to negatively weight data from two elections back? Negative weighting effectively assumes that the trend from the second-last election to the last election in each state continues at the next election, and it doesn’t appear to do good things for the error:
Analysing historical lean data to find trends
However, simply assuming the trend from e.g. 2016 to 2019 (say, QLD becoming more conservative) will continue at the next election is a pretty simplistic way to model state trends. Here’s an alternative: for each election, we could fit a line to the 2-party lean for election data going back a few years. I’ve plotted an example below using Victoria, with trendlines fitted to the last five elections’ worth of data to predict the 2-party lean for the 1993, 2004, 2010 and 2019 elections:
In some cases, this trendline method will produce a “realignment” – e.g. in 1993, 2004 and 2010, where the model predicted a trend would continue. In others, it will produce some “reversion” – e.g. in 2019 where it predicted Victoria would be more Labor-leaning than its 2016 lean, on the basis of data from the 2004 – 2013 elections.
But how many elections should be used to fit a trendline? Use too few, and you run the risk of one outlier election wrecking your forecast; use too many and your trendline will likely be unresponsive to recent shifts in 2-party lean. I ran a bunch of simulations using different numbers of elections to generate the trendlines, and compared the average error to uniform swing:
Using 7 elections to generate the trendline appears best. However, it’s worth noting that on its own, the trendline-based data does not outperform uniform swing no matter the number of elections used. That’s not a big issue in and of itself – using data from two elections back is also strictly worse than using last-election data – but it’s worth keeping in mind if you ever encounter someone trying to argue that a state or electorate is going to continue shifting left/right based on its history of doing so.
Just like with data from two elections back, we can weight the trendline predictions to see if adding it to last election’s data improves overall forecast accuracy. In addition to the weights plotted below, the trend prediction for each state at each election is also weighted by how strong the trend is (I use R² for this purpose). The idea is to minimise errors like the 1993 prediction in the graph above, where the 2-party lean barely shifts for 6 elections but suddenly swung one way or the other at one election.
Weighting electoral trend predictions from historical data
Uh-oh. That doesn’t look good. No matter the amount of weight given to the last election’s data, adding in even a sprinkle of “assume trends from the past 7 elections will continue” appears to increase error.
…and that’s where I’d normally leave it. I could stop here, conclude that assuming reversion beats assuming realignment as a general rule to use when forecasting electorate results, and get some sleep.
But I decided to keep digging. Could there be a rule for being able to predict, ahead of time, whether a district is going to revert? One avenue would be to look at how strong the trend is between the 2-party lean of each electorate and time, and only use the trend prediction if we’re looking at a fairly strong trend. As an example, I’ve plotted the trendlines for Tasmania in the lead-up to the 1996 and 2016 elections:
Note that the trendline in the lead-up to the 1996 election (the one on the left) is much stronger, and it correctly predicted that Tasmania would be even less Coalition-leaning in 1996 than it was in 1993. On the other side of the graph, the trend for the 2016 election is much weaker, and hence it’s unsurprising that the trendline prediction is further off than it was for 1996.
Here, I’m going to quantify the strength of the trend using the p-value of the slope, and build a new model where trend predictions are only used if they pass a certain cut-off for relationship strength (p < 0.05). Now, how does it compare to uniform swing and the combined-lean swing model from our last piece?
Restricting any attempts to forecast a trend to when that trend has been strongly apparent in past data somehow makes things worse. No matter which way I test it, reversion continues to be a stronger general assumption than realignment.
Of course, this is all on state-level data, and there might be realignments at the electorate level which “cancel out” at the state level. However, I am even more skeptical that we can detect realignments at the electorate level – there is more noise in electorate data due to issues with producing redistribution estimates, candidate effects etc. Furthermore, sufficiently detailed data is often not available for many past elections at the state level; in some states you’d be lucky to find five elections’ worth of archived data, let alone the seven used here!
A couple of other things I tested. First off – simply using the trendline predictions, without weighting or excluding any on the basis of trend strength can actually outperform uniform swing (but not the combined-lean swing model from our last piece):
However, this doesn’t test the realignment hypothesis very well – as you may have noticed in the Tasmania 2016 trendline, it’s entirely possible for a trendline to predict reversion if there’s no apparent trend in the data.
We can try combining the trend predictions with the combined-lean swing forecast to see if errors in the two might “cancel out” at realignment elections. Up till now, the weight which hasn’t been assigned to the trend prediction has been assigned to a uniform swing model; we can swap that out for a combined-lean swing model instead. However, adding trend predictions onto the combined-lean swing forecast provides little, if any benefit:
No matter how it’s tested, any version of assuming trends in 2-party lean will continue tends to underperform alternative rules of thumb in terms of error size.
So – is it reversion, or realignment?
Whew. That was a lot of graphs, so let me summarise the key points:
First off – the method of using data from two elections back continued to out-perform a simple uniform swing on a larger dataset (Australian state/territory voting patterns in federal elections). The effect is smaller – so a chunk of the improvement we saw last time is probably adjusting for unusual candidate effects (e.g. disendorsement, unpopularity of a particular candidate, celebrity candidate etc) which don’t have as large an impact on the state/territory level. Our rough estimate that the most recent election was about twice as important predictively as the data from two elections back continues to hold up in the state data.
Next – while realignments do happen from time to time, there appears to be no good rule to predict when they will happen ahead of time. You might be able to get slightly better results by looking at 7-8 elections’ worth of data for a trend, but by the time a trend becomes apparent in that data you’re more likely to be at the end of a realignment and hence the trend you identified is of little predictive value.
In any case, no matter how I try to isolate or predict trends in 2-party lean using historical data, “assume trends in 2-party lean will continue” rarely (if ever) out-performs uniform swing, and it doesn’t do any better than the combined-lean swing model we identified last time. If you had to predict the outcome of an electorate, assuming some reversion still looks to be the best general rule, with uniform swing as the next best alternative.