How much uncertainty is there in this Ontario election?

Note: no new projections this morning as we didn't really get any new poll yesterday except the Mainstreet tracker (where the NDP is back in second place). Not enough change to justify redoing everything. Just refer to yesterday's projections.

Transposing polls into seats is nice and it works quite well if you have the correct voting percentages. That's a big if. We all remember the Alberta election of 2012 of the BC one of 2013 where polls were way off. This is why representing the uncertainty that exists is so important to me.

Think of the 2016 US election. Using a poll average, Hilary Clinton was clearly favourite. It is simply a fact that based on the information available before the election, she was the most likely to win the presidency. And whether you were reading 538 or another site, they all mostly agreed on the average expected outcome (Hilary Clinton winning with around 300-320 electoral vote). Where sites didn't agree was on the level of certainty they had of this outcome. 538 was the least bullish with Trump being given 28.6% chances of winning. This is way more than most other website or aggregators, some of which literally had Clinton's chances at over 99.9%!

Why am I talking US election? Because I believe we currently have a situation where some aggregators aren't representing uncertainty correctly. I'm talking here in particular of the well knwon CBC poll tracker (from Eric Grenier, previously at 308). As I'm writing this article, the CBC is saying the NDP has a 12% chance of winning the most seats (8.4% for a majority, 3.6% for a minority). My model on the other hand is currently giving the NDP around 24% chances (and that's a sharp drop compared to the >40% of a few days ago, before polls started showing a slight PC rebound).

Part of the difference come from a slight difference in our polling aggregation. The CBC has the NDP ahead by 0.7pt (37.3% versus 36.6% for the Tories) while I have the NDP ahead by around 1.5pt. This is because the CBC gives a lot more weight to very recent polls when I go with a more simple approach of giving equal weight to any poll conducted during the last week. Also, the CBC is currently giving the highest weight to the latest Forum poll... I don't think I need to add much more here.

But that's only part of the story. The CBC model has had the NDP with lower chances than me since the beginning. As a matter of fact the maximum was at 17.4% chances! I find it absolutely insane. And I truly believe this is incorrect.

Now, here comes the hard part: it literally is impossible to prove who is right here. The only way would be to have this election repeated a 100 times in 100 universes and see how many times the NDP wins. That is obviously not an option. So on election night, even after knowing the actual outcome, it wouldn't prove one model right or wrong (unless the outcome was one given 0% chances by us). In other words, even if the NDP wins, we wouldn't know how big of a surprise it was.

So I won't really try to convince you of who is right and who is wrong. Instead, I want to show how I come up with the chances of winning.

First of all, a probabilistic model must be properly calibrated with respect of the average polling accuracy. I have already written about this topic here. The summary is that polls in Canada have been decent but not perfect in the last few years. In average they are 1.92 points off (1.25% if we exclude the big two mistakes of Alberta and BC but then it becomes cherry picking). Beyond the average, the actual margins of error of the polling average have been 5.68%! Or 3.19% if we remove the two outliers. In other words: polls aren't bad but even after averaging them, there is still considerable uncertainty.

So right there we see that based on the average accuracy, we can have the following outcomes (NDP first, PC second): 37-37, 39-34, 35-38, etc. And based on the margins of error, we can't exclude a scenario where, for instance, the NDP is at 42% and the PC at 32%. It's not likely but absolutely possible (2-3% chances of this happening).

Let's focus on the NDP 39% (so underestimated by 1.5 points roughly in the polls) and PC at 34% (so overestimated by 1.8 pts). This scenario wouldn't even count as a surprise on election night. Or it shouldn't if you know anything about polls. At around a 5 points lead, I think it might be enough for the NDP to win (the current simulator shows a close race with these numbers however. I would call it a too close to call situation). With the collapse of the Liberals, my estimations show that the necessary lead for the NDP to win is increasing. Also, let's realize that when a party moves from 23.75% in 2014 to 39% in 2018, projection models like mine aren't the most accurate. This is a massive shift of the electoral map. So it is absolutely possible that the model is underestimating the vote efficiency of the NDP.

So, given the polling average, what are the odds of the NDP winning the popular vote by 3, 4 or 5 points? Using simulations calibrated to the average polling accuracy, we can easily answer this question. The table below shows these odds based on my polling average:

Probabilities that the NDP will win the popular vote by
3 points 36%
4 points 28%
5 points 21%

The graph below shows the possible outcomes for the popular vote. Specifically, it shows the difference between the % for the NDP and the % for the PC. and yes I'm aware it isn't a very pretty graph but you get the meaning.

So now the question really becomes: how inefficient is the NDP vote? Can the NDP really win by 4 points and still lose? The answer appears to be yes, as crazy as it sounds. The collapse of the Liberals has opened so many seats to the PC in the 905 and increased the vote efficiency of the Tories.

Right now, my most recent estimations show that the NDP probably needs 4-4.5 points lead in order to win the most seats. This is pretty crazy. It used to be 2 points but that was when the Liberals weren't as low as 20%. At the same time my simulations show that it is possible for the NDP to win if this party is only winning the popular vote by 1 points. It's unlikely but possible. If the NDP is ahead by 3 points, the chances of a NDP government are roughly 12%.

If we take into account the possibility that the polls will be off and the fact that the distribution of the vote will have a big influence (and could be mostly unknown after such a massive change in the Ontarian political landscape), I think it is fair to say the NDP has some chances. This party is clearly not favourite at this point but a NDP victory shouldn't be seen as a crazy unlikely event. In particular are these chances as low as 12%? I don't believe so. I already think that the 24% chances my model is giving the NDP are too low.