Has Election Night—not just the election—been modeled adequately?

Kurt Gödel famously found solutions to Albert Einstein’s equations of general relativity that allow trajectories to loop through time.

Today, early on Election Day and a usual time for our posts on Gödel, I talk about the trajectory of counting votes after tomorrow’s polls close and time-warp effects that everyone watching the returns will see.

I am picking up the vein of ethical algorithms in yesterday’s post, but with a different take about ethical modeling in novel situations where reliable training data is unavailable. I believe there is a responsibility for running simulations not just of tomorrow’s election, such as FiveThirtyEight conducts, but also of tomorrow’s count as it may unfold hour by hour and stretch over many following days.

Gödel also famously believed he had found a logical flaw in the U.S. Constitution that allowed a mechanism for legally instituting a dictatorship, but his argument was never reported. We discussed this at length in 2013, including noting a 2012 paper by Enrique Guerra-Pujol of the University of Central Florida College of Business, who is a frequent reader of this blog. Guerra-Pujol offers a detailed construction of a mechanism based on self-reference applied to the short Article V on amending the Constitution. This topic has been addressed several times since, but what stands out to us is a 2019 paper by Valeria Zahoransky and Christoph Benzmüller. This paper attempts to find a proof of Guerra-Pujol’s mechanism by automated logical inference using the Isabelle/HOL proof assistant. They found a model that satisfies the argument.

Election Evolution Over Time

My post on Election Day 2016 contrasted the relatively stable time evolution of polls in 2012 with the gyrations of 2016. That post began by defending Nate Silver of FiveThirtyEight and his 30% likelihood for Donald Trump against those who had Hillary Clinton over 90%. At the time of our 2012 post on Barack Obama versus Mitt Romney, I had thought Silver’s error bars were too wide, but in 2016 they looked right on the basis of last-minute decision making by impulse that my chess model also registers.

This year, the polls have been even steadier than in 2012, and undecided voters are found to be scarce. Of course, the pandemic has been the greatest factor in the poll numbers, but my first point is that election forecasting uses only the numbers as primary. The algorithms do not have an input that could take values Covid 19, Covid 23, Covid 17… In a normal election, the polling numbers would seem to point to an easier call than in 2012. Silver has, however, expressed caution in explaining why his odds stay just short of 90% for Joe Biden as I write at midnight. My first point of further disquiet begins with a simple fact:

The models have been trained on data from past elections.

A major difference on our flight path to Election Day is the upsurge in early voting and turnout overall. Texas reports that it has already registered more early votes than total votes cast in 2016. We are not saying this difference has been overlooked—of course, models are being adjusted for it every hour. What we are doubting is the existence of a basis for making those adjustments with high confidence. Before we discuss the major issue of the flight path after the polls close, let me insert an analogy from my current chess work.

My Own Ethical Interpolation

My statistical chess model is trained on millions of moves from games at the hours-long pace of standard in-person chess. The pandemic has led to chess moving online where fast time controls are the norm. For instance, the hallowed US Championships were just held in a format of three games per day at a pace of 25 minutes for the whole game plus 5 seconds for each move played, which equates to G/30 (game in 30 minutes) under a simplification used also here. The Online Olympiad held in August by the International Chess Federation (FIDE) gave only 15 minutes plus 5 seconds per move, equating to G/20. I have been asked for input on games at paces all the way down to 1-minute “Bullet” chess.

My solid estimates of how less time affects skill come from the annual FIDE World Rapid and Blitz Championships, which are contested at equivalents of G/25 and G/5, respectively, by hundreds of elite male and female players. For time controls in-between I face twin problems of scant data from in-person chess—basically none for player below master level—and online chess having evident contamination from cheating, as I discussed in a post last June. Hence I interpolate to determine model settings for other time controls.

This diagram shows internal evidence supporting the orange curve obtained via Aitken extrapolation, in that inverse polynomial curves based on other reasoning converge to it. The curve has been supported by recent field tests, including a restricted invitational tournament recently run by Chess.com at G/3 and a large junior league in Britain at G/15 equivalent. Still, the ethical status is:

1. The pandemic has injected me into online fast chess ahead of the year-long timeframe that would be needed to clean the available large data and rebuild my model directly for all the gamut of different time controls.
2. So it is ethical for me to give my best estimates, as supported by field tests and cross-checks in my model, but with caveat of their being “an extrapolation of an interpolation.”
3. But in principle there are more-reliable ways to do the modeling.

My second point is that this year’s election models are in similar boats: The pandemic forces their cantilevered use in new situations. As with chess the data needed for direct training may not be available. As we’ve said in the post, this year’s election task may be “Ethics-Hard.” Now we come to my third and main point about responsibility.

A Night of Waves and Blue/Red Shifts

The new dimension of time is the order in which all the following categories of votes will be counted, in the states that variously allow them:

1. Early votes cast in-person, such as my wife and I did on the first possible day in New York.
2. Early votes sent by mail.
3. In-person votes on Election Day.
4. Regular votes by mail in states that vote that way.
5. Absentee ballots, which are the only non-Tuesday option in some states.

This is approximately the order in which votes will be counted, again with state-by-state differences, which especially may lead to votes in category 2 being counted later. The issue is that the Democratic and Republican shares are expected to vary greatly across the categories, enough to cause large shifts in the perceived leader over real time.

Geoffrey Skelley of FiveThirtyEight has an article showing how a 5-point win for Biden in Pennsylvania might still present as a 16-point lead for President Trump on Election Night, when all in-person votes are counted but only some of the votes by mail. Here are the article’s key graphics, the left one showing actual proportions from Pennsylvania’s June primary.

Composite of two figures from FiveThirtyEight Skelley article

Other states that allow early tallying of early votes may show an initial Biden lead before a red-shift toward Trump on Election Night, with more of Biden’s vote share remaining to be counted. Still others are less clear. FiveThirtyEight on Saturday posted a useful state-by-state guide.

Why Important to Model the Count?

Awareness of the time-shifts is important not only for perception but also for the timing of legal challenges that are expected to arise. For instance, there is a continued specter of invalidating 127,000 early votes already cast by a novel drive-up system in Harris County Texas; despite its rejection by a district judge today, it has been appealed higher. There is expectation of legal battles nationwide over procedures that have been altered by measures to cope with the pandemic.

Public perception, however, is the most immediate concern. President Trump stated in a flagged Tweet that we “must have final total on November 3rd” and followed up by saying, “…instead of counting ballots for two weeks, which is totally inappropriate, and I don’t believe that’s by our laws.” Justice Brett Kavanaugh wrote in a formal opinion that states “want to avoid the chaos and suspicions of impropriety that can ensue if thousands of absentee ballots flow in after Election Day and potentially flip the results of an election.” Note his phrase “flip the results”—a sure sign that perception is reality.

Of course many outlets besides FiveThirtyEight are aware of the new election-reporting physics and have published their own guides. They are adjusting their election-night projection models accordingly. Our main question goes further in terms of responsibility:

Has anyone been running simulations of how Election Night vote-counting may unfold?

We believe such simulations are just as important as the ones they have run of a timeless election. Showing them is not only important to inform the many who will be watching, it would be a vaccine against pressure that exploits unexpected perception.

Yet it must be acknowledged that there is neither hard data nor sure knowledge of county-level vote-tallying policies and schedules on which to train such simulations. Nor may there be as many cross-checks as my chess interpolation situation.

This may be another “Ethics-Hard” problem. But it is one already involved in adjusting the projection models that definitely are being deployed. Aside from the many novel and vital modeling problems from the pandemic, it may be the most important one of our near future. And we are thinking of this less than 48 hours—now less than 24 hours—before the first polls close.

Open Problems

How do you think Election Night results will unfold, apart from your estimate of the time-independent “ground truth” of the electorate’s intentions?