Putting vaccine trials in boxes
Election visuals 2: informative and playful

Election visuals: three views of FiveThirtyEight's probabilistic forecasts

As anyone who is familiar with Nate Silver's forecasting of U.S. presidential elections knows, he runs a simulation that explores the space of possible scenarios. The polls that provide a baseline forecast make certain assumptions, such as who's a likely voter. Nate's model unshackles these assumptions from the polling data, exploring how the outcomes vary as these assumptions shift.

In the most recent simulation, his computer explores 40,000 scenarios, each of which predicts a split of the electoral vote, from which the winner of the election can be determined. The model's outcome is usually summarized by a winning probability, which is just the proportion of scenarios under which one candidate wins.

This type of forecasting was responsible for the infamous meltdown in 2016 when most of these models - Nate's being an exception - issued extremely confident predictions that Hillary Clinton wins with 95% or higher probability. Essentially, the probability distribution collapses to a point. This is analogous to an extremely narrow confidence band, indicating almost zero uncertainty about the event. It was as if almost all of the 40,000 scenarios predicted Clinton to be the winner.

The 538 data team has come up with various ways of visualizing the outputs of the model (link). The entire post is worth reading. Here, I'll highlight the most scientific, and direct visual representation, which is the third display.


We start by looking at the bottom of the two charts, showing the predicted electoral votes won  by Democratic challenger Joe Biden, in each of the 40,000 scenarios. Our attention is directed to the thick line that gives the relative chance of Biden's electoral-vote tally. This line is a smoothed summary of the columns in the background, which show the number of times the simulation produces each electoral-vote count.

The highlighted, right side of the chart recounts scenarios in which Biden becomes President, that is to say, he wins more than 270 electoral votes (out of 538, doh). The faded, left side represents scenarios in which Biden is defeated and Trump wins a second term.

The reason I focused on the bottom chart is that the top chart is merely a mirror image of this one. Just reflect the bottom chart around the vertical axis of 270 electoral votes, change the color scheme to red, and swap annotations related to Trump and Biden, and you get the other chart. This is because the narrative has excluded third-party and write-in candidates, leaving us with a zero-sum situation.

Alternatively, one can jam both charts into one, while supplying extra labels, like this:


I prefer the denser single chart because my mind wanders away searching for extra meaning when chart elements are mirrored.

One advantage of the mirrored presentation is that the probability profiles of the potential Trump or Biden wins can be directly compared. We learn that Trump's winning margins are smaller, rarely above 150, and never above 250.

This comparison is made easier by flipping left side of the chart onto the right side:


Those are three different visualizations using the same chart form. I'd have to run a poll to figure out which is the best. What's your opinion?


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Jerome Duran

The mirrored chart has the advantage of less clutter, and the opportunity to add commentary on the relative margins of victory with the additional white space this view provides.

Jon Peltier

I prefer the single chart, your second one. Like you, I hunt for added meaning when the chart is duplicated.


Overall I prefer the first, because election polling is often misunderstood, so I'd put clarity at the highest priority. The mirrored positive axis in the second will confuse some people. In the third graph that bars get lost.

But as a personal preference, I like the second because it's easier to compare the odds of a Trump win to a Biden win than the 538 version.


Second one

Florian Laws

Does the "Trump wins" in the top chart have the arrow in the wrong direction? That confused me a lot.


The second and third both provide for a direct comparison of the heights of the bars (the attribute that encodes the data), which is good, but the third has the downside that the axis puts "Biden wins" and "Trump wins" in the same direction. I don't think anyone cares about whether the winner wins big without also caring who wins, so I would think it's much better to preserve the intuition of a range of potential results from a huge Biden win to a huge Trump win.


FL: I went through that phase too.

Thanks for all the comments. Good to hear of different user experiences. Keep them coming!

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