What does the swing look like? Proportional or not?

When a party's support increases in a province, how does it translate in each riding? The answer to this question is crucial as to which forecasting model to choose. So let's look at some graphs.

Let's look at the Conservatives (a party who experienced quite a lof of changes at the provincial level during the last 5 year), in Quebec (where the model usually performs at its best, both for the federal and provincial elections) during the last election (2008). The next graphs displays the swing at the riding level, sorted by the level of support during the previous election:

Remember that province-wide, the Conservatives dropped from 24.6% to 21.7%, thus a decrease of 2.9 percentage points, or -11.8%. Therefore, if the swing was uniform, we should see all the dots on the same horizontal line, at 2.9 (red line). On the other hand, if it was proportional, we should see the dots as forming a straight line decreasing (representing -11.9% of the previous level of support) (green line). As we can see, both assumptions would clearly be wrong. There is considerable amount of variation between the riding-level swings. You have an easy-to-understand graphical representation of how those two simplistic models could be wrong.

By the way, you get similar plots if you use other parties and/or provinces. Just to prove that I didn't use the one example that proved my points, here is a similar graph for the Liberals in Ontario, in 2008.

Here, I didn't bother showing the proportional change line, since it is obvious it wouldn't fit the data. Rather, I added the projection of the model. While I agree it isn't very clear that the model is performing better, what I would like you to notice is that the projected values are not on a straight line. Using regional effect, incumbency or the level of support last election, (for each party) my model is able to better forecast the outcome, without having to rely on an arbitrary assumption such as uniform or proportional changes.

Let's go back to the CPC in Quebec. Another aspect that might be surprising is the fact that the Conservatives actually increased their share of votes in some riding, despite a drop at the province-level. How to explain this? Well, first of all, individual effects could play a role, such as a new candidate or other specific events (for instance, what happenned to Maxime Bernier). Second of all, we are looking at shares of votes here, meaning that even though a party lost some votes, it could still increase its share if the other parties lost even more votes. For the model, I project every party and then make sure the percentages sum up to 100%. However, on e downside of the fact that riding sometimes go against the provincial trend is that my model could lead to weird results. Indeed, since I'm estimating my coefficients, the model could give parameters such that the support for one party would decrease in one rding when this party increases at the provincial level. This can be a potential problem but since I'm using more than one election, hopefully those weird effects will not biase the estimates.

At the end, it is really difficult to find evidence that the swing is proportional, especially in Ontario and Quebec. This is the reason the proportional swing model performs significantly worse than any other models, incuding the linear one, as shown in my methodology pdf. And this is why I find it weird when I see some websites basing their model on this assumption.

I'll post soon about how proportional models can even be worse for small of third parties.