Election predictions are too noisy to tell if Harris or Trump wins

The problem is similar to a jury hearing testimony from two witnesses — each with known biases. You think both are basically truthful, but one is a friend of the defendant and will shade testimony to protect her friend. The other is at risk of being charged in related offenses and will shade testimony so he appears more innocent. Neither is entirely consistent, and the two conflict on some points.

You try to remove the biases from each witness’ testimony, then find the version of the truth most consistent with the two adjusted stories. This version could be radically different and is not necessarily the truth. It only represents your best judgment about what their evidence means for the case. Similarly, I’m not trying to consider all the evidence for election probabilities, only to interpret what Silver’s predictions and PredictIt’s prices tell us.

For impatient readers, I’ll jump to the end with my “filtering” (the mathematical term for estimating an underlying signal from multiple reports contaminated with different forms of noise) of the election probability.

It shows Trump entering the summer with a strong lead, but gradually losing ground until the debate with President Joe Biden on June 27 turned things around. Trump continued to gain as Biden first remained in the race, then dropped out. Starting in late July, we see a crash in Trump’s chances that was dubbed Kamalamania by the press. The Democratic party and its major donors rallied smoothly behind Harris, and various imagined hurdles to replacing Biden evaporated. Trump, however, weathered the storm without ever becoming an underdog, and now seems to hold about a 70 percent win probability, the highest aside from a brief peak immediately after Biden dropped out.

Remember, I don’t claim these are the true probabilities, only what Silver and PredictIt are telling us, if we interpret them properly. Put another way, if no news came out for a couple of weeks, Silver and PredictIt would converge to near the current filtered estimate of 70 percent. We should take that seriously — Silver is a smart guy with an impressive track record, and markets can harness the wisdom of crowds, but neither is infallible.

My filtering resembles Silver’s numbers, moved a little in the direction of PredictIt’s until the beginning of Kamalamania. At that point, the numbers suggest Silver and PredictIt suffered “flash crashes.” Both models have strong momentum components that are normally balanced by mean reversion. But when a large sudden move occurs, both are overwhelmed by momentum and exaggerate the crash, like panicked investors fleeing a falling market. My filtering shows a 20 percent gain for Harris from Kamalamania, while Silver sees 26 percent and PredictIt shows 31 percent. The filtered model follows Silver’s estimate of Trump’s recovery from his low, but PredictIt thinks Trump clawed back only $0.05 versus Silver’s 14 percent estimate.

What do I mean by momentum? Silver’s forecasts move an average of 0.19 percent each day in the same direction as the previous day’s move — that’s out of a 0.96 percent average daily absolute move. Roughly 20 percent of the information in his forecast is based on stale rather than new information. PredictIt prices also move, on average, in the same direction as the previous day’s move. My filtering estimates the amount of momentum and other flaws in the forecasts that I discuss later and backs them out to derive the underlying signal.

Experts build momentum into their forecasts to appear more confident. True probabilities are random walks, like a drunkard’s meandering, and are hard to explain. Adding momentum creates trends, like a sober person walking home, making for simpler stories. Hedge fund managers and especially private equity managers do the same thing, smoothing the ups and downs of returns to make their performance seem steadier, with more skill and less luck.

Betting and financial markets have momentum for different reasons. First, information leaks slowly into prices. Second, bettors and traders are apt to treat favourable price movements as validation, a reason to increase bets, rather than as less attractive betting opportunities.

By itself, momentum has the potential to drive prices to extremes. Betting and financial markets tend to offset this with longer-term mean reversion. In the case of PredictIt, the model moves every day 2 percent closer to a $0.48 price for Trump. This represents a medium-term value anchor for bettors. But Silver, like most experts, does the opposite. Every day he moves 2 percent away from the value anchor of 48 percent. Experts who predict what everyone else expects get no respect. By exaggerating their differences, they get more attention and rewards.

The next points are features, not bugs. Silver’s forecasts move 9 percent of the way toward PredictIt’s prices every day, and PredictIt prices move 4 percent of the way toward Silver’s. I don’t mean Silver is watching the PredictIt site and mechanically adjusting forecasts. He could be doing that, or using prediction market data in general, or looking at the same factors that drive bettor behaviour. PredictIt bettors could be reading Silver, or reacting to the same information that influences him. Either way, adjusting for these tendencies helps the filter combine the information in the two forecasts.

PredictIt anticipates Silver’s momentum. Its prices move toward Silver’s forecasts augmented by the average momentum. So, if Silver says Trump’s chances moved from 60 percent to 61 percent, PredictIt bettors seem to treat that as a move to 61.19 percent, since we expect Silver to add another 0.19 percent tomorrow if there is no news. Silver does the opposite, treating PredictIt’s momentum as overreaction to be subtracted. He subtracts 0.12 times PredictIt’s move from yesterday to today. So, if PredictIt goes from $0.60 to $0.61, Silver treats it as a rise to $0.6088.

Many people, including me, have griped about these flaws since 2016 when interest in presidential election forecasts took off — and accuracy took a nosedive. It's always puzzled me why Silver, a top poker player and serious quant, would allow momentum and mean avoidance into his forecasts — especially in the face of widespread criticism. I just finished his new book, On the Edge (which I recommend highly), and it may hold the key.

To an extent that’s hard to understand, Silver is frustrated by uninformed criticism of his probabilistic forecasts. It reminds me of Cliff Asness, co-founder of AQR Capital Management, where I worked for 10 years. He was once railing about how crazy and irrational the market was, when his wife Laurel asked, “Don’t you make your money betting against crazy?” You’d think Cliff and Silver would smile with quiet satisfaction at people misunderstanding probability — like hearing someone at a poker table saying, “I never fold if there’s any card in the deck that could make my hand.”

What do I think is the actual probability that Trump will win? The filtered version of Silver and PredictIt’s information — what I think is the most likely underlying reality behind both their predictions — indicates 70 percent, which should carry a lot of weight. But I think forecasts and prices have bounced around too much this summer given both the chaos in the race and the amount of electioneering still to come.

I don’t believe Kamalamania created a 20 percent or greater change in probabilities. A 20 percent change is a big deal. In last year’s World Series, the single most consequential play, a one-out, two-run homer in the bottom of the ninth by Corey Seager to tie the game, increased the Rangers’ chance of winning the series by less than 15 percent. I don’t see early August events as Trump throwing or Harris hitting a two-run, bottom of the ninth homer to tie the game.

There’s a lot of campaigning to go, a lot of events that could turn the election into a landslide for either candidate. If nothing much happens, the result could turn on a handful of Pennsylvania voters who are on the fence about voting, or on the fence between Trump and Harris, who likely aren’t following the news much and won’t make up their minds until just before voting. I buy that Trump has a substantial lead, but it’s the third inning, not the bottom of the ninth.

Credit: Bloomberg