Red State, Blue State? It's Marginal
Andrew Elliott
The campaigns of the 2020 United States presidential election are now in full cry, and there is much talk of red states (the ones expected to go to Trump and the Republicans) and blue states (tending to Democrats and Biden). If you look at the forecast chances of each party winning each state, you see some states that look like they’re in the bag for the red Republicans (states like Oklahoma, Utah, Indiana) and some states that are clearly destined for the blue Democrats (like California, Illinois, or New Jersey).
The real focus of the election is on a relatively small number of so-called battleground states (examples: Georgia, Iowa, Ohio), where the balance is really uncertain, and where the eventual outcome will be decided. Because of the USA’s electoral college system, it only matters which state each candidate wins, and not by how much. So there is no point in campaigning hard in California (Biden will win it, almost certainly), or West Virginia (it’s surely going to Trump).
Here’s how Sam Wang, of the Princeton Election Consortium sees the map of electoral prospects in late September 2020 (https://www.270towin.com/maps/2020-princeton-election-consortium). A couple of different shades of blue and red, with a few disputed beige territories. This looks like a country divided between (crudely speaking) urban liberals, and rural conservatives.
You might be forgiven for thinking that, apart from the battleground states, the United States might as well be two different countries, the blues and the reds, and that this division on state lines was a reflection of the split in the country between Republicans and Democrats, conservatives and liberals. You’d not be entirely wrong, but neither would you be completely right.
Let’s look at what’s up with one of those “clearly-red” states: Indiana. Here’s how rival poll-aggregators FiveThirtyEight.com see Indiana’s prospects (https://projects.fivethirtyeight.com/2020-election-forecast/indiana/).
You can see why that is marked as a solid red. They give Biden just 4% chance of taking Indiana. You might imagine that being a Democrat in Indiana is a very lonely thing, that you would be heavily outnumbered by Republicans. Let’s see what the numbers say.
Oh! Trump has just 56% support there, and Biden has well over 40%. Indiana Democrats are not so lonely after all. That 13% edge, though, makes all the difference. A small but significant margin makes the outcome all but certain.
It works in the opposite direction, too. In New Jersey, Biden has a 58% - 40% margin over Trump, and this translates to a 98% chance of a win.
In Texas, where FiveThirtyEight.com reckon that Trump has a 70% chance of victory, the margin is very thin indeed: 51.3% vote share to Trump, 47.7% to Biden. Texans are almost as likely to vote for Biden as Trump. But that doesn’t mean Biden is almost as likely to win as Trump is. The percentage support in the state is a very different thing from the chance of winning, even though both are expressed as percentages.
Let’s explore this effect through a simulation. We’ll assume there are just 100 undecided voters in the election (and an unspecified but equal number of definitely committed red and blue voters - they don’t really affect our logic here). We don’t, of course, know how each of the undecideds will vote but we reckon that for each of them, there is a 52% chance of them breaking to the Reds, and a 48% chance of going to Blue, so Reds have a slim majority of 4%. Here’s one scenario of how the the undecideds in this election might turn out, one square for each vote.
Don’t bother to count: I can tell you that in this case, Red won by 55 votes to 45. The red candidate “overperformed their polls”. Run the simulation again, though, and the result may be different, just by chance. Blue might win, or there may even be a tie.
In fact, let’s see the range of different outcomes that could result from those same probabilities. We’ll run that election simulation fifty times over. In the grid below, each row is a simulation of one possible outcome of the undecided votes in our election.
Ok: it’s not very easy to see what’s happening there. Perhaps we can convince ourselves that we see more red than blue there, but we can’t be sure. How can we make that clearer? If we shift all the red to one side, and the blue to the other and then sort the rows by how well red has done, we get the following:
That’s better. I’ve marked the winning line in black. Where red extends to the right of that line, that’s a win for red, and you can see, as expected, that red wins more often than blue. For THIS batch of 50 simulations, red wins 31 times out of 50 and there are eight ties. Red’s best performance was a 61:39 victory, and their worst was a 41:59 defeat to the blues, one of 11 times that blue were the winners. It’s not hard to see how a 4% margin in probability among the undecideds can turn into a 70% chance of winning. For larger electorates, the effect is even more pronounced.
But even if our fake state looks pretty red on the basis of these possible outcomes, those probabilities do not reflect accurately the make-up of the population who live there. That’s not to say that the divisions in the United States are not real. They are, but the divisions do not run cleanly along state lines. The nature of the voting system is to amplify difference. Historically, a lot of voting systems are inherently disproportionate, and are designed to give decisive results rather than reflect the diversity of opinion within the population.
The battleground states are those where the margins are wafer-thin. Today, for Ohio, FiveThirtyEight.com give Biden 49.7% of the vote and Trump 49.3%, and their model translates that to a 52% chance of a win for Biden. On the other hand. while Indiana Democrats, like New Jersey Republicans, may not be lonely, they certainly can claim that their vote does not carry the same weight as those of voters in more marginal states like Texas, Florida or Ohio.
© Andrew C. A. Elliott 2020
What are the Chances of That? is a new book by Andrew C. A. Elliott, to be published by Oxford University Press in 2021. It explores the way in which we understand (and sometimes fail to understand) the operation of chance and uncertainty.
The simulations shown above come from the website http://whatarethe.chancesofthat.com/chance/ which allows you to explore probability in a variety of ways.