The above animation shows a single ball representing Biden’s current total electoral votes dropped through a Plinko board whose height roughly matches the uncertainty in the Economist’s election prediction model before any votes were counted. How surprised would you feel to see this outcome if you dropped a ball into a real Plinko board of the same size?
For more information about how the Plinko board represents uncertainty, or for predictions made from polling data before election day, see below.
Pre-election day predictions
Drop one ball | Drop all balls
What will the outcome of the 2020 US Presidential Election be? Forecasters build models on top of polling data and historical voting patterns to produce probabilistic predictions: predictions with uncertainty. But really internalizing that uncertainty is hard. Presidential Plinko takes that uncertainty and translates it into Plinko boards with similar uncertainty, so that you can experience just how uncertain predictors’ forecasts are.
How certain would you be in the outcome if you dropped a ball from a Plinko board the height of the one for the Economist’s prediction? How about 538’s? Try dropping one ball a few times and see how you feel about the uncertainty.
How does this work?
The short version is, I determine the height of each board based on how uncertain each forecaster is about how many electoral votes Biden will get. I then drop a number of balls through the board to illustrate that uncertainty:
The slightly longer (more technical) version is, I approximate each forecaster’s predictive distribution with a scaled-and-shifted binomial distribution, which determines the height of each board. I then determine plausible paths through the board that could have led to the final predictive distribution, which is shown as a quantile dotplot. Thus, while the output looks random, the final distribution is exactly the forecaster’s published distribution, down to the resolution of the dotplot. Full details of the methodology and source code are on Github.
Why did you make this?
I seem to be one of the few people that liked the infamous New York Times election needle.1
The Needle was a valiant attempt to show uncertainty in the final vote margin in the 2016 presidential election in real time as votes came in. The needle itself moves randomly within the central 50% most likely outcomes (according to the prediction at that time).
I think the Needle got one thing right and another thing wrong. What it got right was that this kind of animation can help people experience uncertainty.2 This makes the visualization more powerful, and the uncertainty harder to ignore. The visualization made people anxious, because they were uncertain about something they cared about. But if you’re uncertain about something you care about, you should be anxious.
However, I think the Needle also fell victim to a deterministic construal error:3 many people more readily associate the mechanism of a needle with some deterministic measurement, not an uncertain quantity.4 Those people understandably thought the rapid movement of the needle reflected that the forecast itself was changing just as rapidly.
During OpenVisConf 2018, where Amanda Cox and Kevin Quealy gave a talk on NYT visualizations and I gave a talk on uncertainty visualization, I starting thinking about alternatives to the Needle that do evoke randomness in the way they work. That’s when I started thinking about Galton boards:
A Galton board whose height changes according to the variance of a predictive distribution could display a distribution and a plausible, uncertain mechanism that could give rise to it. Michael Corey on Twitter later made the connection to Plinko, and I decided Presidential Plinko would be a good name for this site.5
Are you affiliated with 538 or the Economist?
No. I am faculty at Northwestern University, where I study uncertainty visualization, amongst other things. You can learn more about me here or check out the Midwest Uncertainty Collective, a lab I co-direct with Jessica Hullman.
I am fortunate to be able to take advantage of the fact that both forecasters release their model outputs publicly. For more details on each forecaster’s model and predictions, see 538’s forecast or the Economist’s forecast.
These forecasters have put an immense amount of work into their models and visualizations. Both have done an excellent job this year in their uncertainty communication. I recommend checking out other posts and discussions about their visualizations or their models. I am merely experimenting with one less-used visualization approach here.
Author
Matthew Kay, Assistant Professor, Computer Science and Communication Studies, Northwestern University
I talk more about the Needle in my Tapestry talk.↩︎
Jessica Hullman (a frequent collaborator of mine) dubs such animated uncertainty visualizations hypothetical outcome plots (HOPs).↩︎
See Susan Joslyn’s work on deterministic construal errors.↩︎
To the consternation of statisticians everywhere, the act of measuring something evokes certainty, not error, for many people.↩︎
Besides which, Sir Francis Galton was a noted eugenicist, so naming fewer things after him seems reasonable to me.↩︎