There’s been a bit of concern lately about political consultants or pundits offering some mix of private and public forecasting and advance, and also making side bets on elections. I don’t know enough about these stories to comment on them in any useful way. Instead I’ll share my own perspectives regarding betting on elections.
In June 2020 I wrote a post about an opportunity in a presidential election prediction market—our model-based forecast was giving Biden an 84% chance of winning the election, whereas the market’s implied odds were 53% for Biden, 40% for Trump, 2% for Mike Pence, 2% for Hillary Clinton (!), and another few percent for some other possible longshot replacements for Biden or Trump.
Just to be clear: Those betting odds didn’t correspond to Biden getting 53% of the vote, they corresponded to him having a 53% chance of winning, which in turn basically corresponded to the national election being a tossup.
I thought seriously about laying down some $ on Biden and then covering it later when, as anticipated, Biden’s price moved up.
Some people asked why I wasn’t putting my money where my mouth was. Or, to put it another way, if I wasn’t willing to bet on my convictions, did I really believe in my own forecast? Here’s what I wrote:
I agree that betting is a model for probability, but it’s not the only model for probability. To put it another way: Yes, if I were planning to bet money on the election, I would bet using the odds that our model provided. And if I were planning to bet a lot of money on it, I guess I’d put more effort into the forecasting model and try to use more information in some way. But, even if I don’t plan to bet, I can still help to create the model as a public service, to allow other people to make sensible decisions. It’s like if I were a chef: I would want to make delicious food, but that doesn’t mean that I’m always hungry myself.
Ultimately I decided not to bet, for a combination of reasons:
– I didn’t quite know how to do it. And I wasn’t quite sure it would be legal.
– The available stakes were low enough that I couldn’t make real money off it, and, if I could’ve, I would’ve been concerned about the difficulty of collecting.
– The moral issue that, as a person involved in the Economist forecast, I had a conflict of interest. And, even if not a real conflict of interest, a perceived conflict of interest.
– The related moral issue that, to the extent that I legitimately am an expert here, I’m taking advantage of ignorant people, which doesn’t seem so cool.
– Asymmetry in reputational changes. I’m already respected by the people that matter, and the people who don’t respect me won’t be persuaded by my winning some election bets. But if I lose on a public bet, I look like a fool. See the last paragraph of section 3 of this article.
Also there’s my article in Slate on 19 lessons from the 2016 election:
I myself was tempted to dismiss Trump’s chances during primary season, but then I read that article I’d written in 2011 explaining why primary elections are so difficult to predict (multiple candidates, no party cues or major ideological distinctions between them, unequal resources, unique contests, and rapidly changing circumstances), and I decided to be careful with any predictions.
The funny thing is that, in Bayes-friendly corners of the internet, some people consider it borderline-immoral for pundits to not bet on what they write about. The idea is that pundits should take public betting positions with real dollars cos talk is cheap. At the same time, these are often the same sorts of people who deny that insider trading is a thing (“Differences of opinions are what make bets and horse races possible,” etc.) It’s a big world out there.
Real-world prediction markets vs. the theoretical possibility of betting
Setting aside the practical and ethical problems in real-world markets, the concept of betting can be useful in fixing ideas about probability. See for example this article by Nassim Taleb explaining why we should not expect to see large jumps up and down in forecast probabilities during the months leading up to the event being forecast.
This is a difficult problem to wrestle with, but wrestle we must. One challenge for election forecasting comes in the mapping between forecast vote share and betting odds. Small changes in forecast vote shares correspond to big changes in win probabilities. So if we want to follow Taleb’s advice and keep win probabilities very stable until shortly before the election (see figure 3 of his linked paper), then that implies we shouldn’t be moving the vote-share forecast around much either. Which is probably correct, but then what if the forecast you’ve started with is way off? I guess that means your initial uncertainty should be very large, but how large is reasonable? The discussion often comes up when forecasts are moving around too much (for example, when simple poll averages are used as forecasts, then predictable poll movements cause the forecasts to jump up and down in a way that violates the martingale property that is required of proper probability forecasts), but the key issue comes at the starting point.
So, what about future elections? For example, 2024. Or 2028. One issue that came up with 2020 was that everyone was pretty sure ahead of time, and also correct in retrospect, that the geographic pattern of the votes were aligned so that the Democrats would likely need about 52% of the vote to win the electoral college. So, imagine that you’re sitting in 2019 trying to make a forecast for the 2020 presidential election, and, having read Taleb etc., you want to give the Democrats something very close to a 50/50 chance of winning. That would correspond to saying they’re expected to get 52% of the popular vote. Or you could forecast 50% in the popular vote but then that would correspond to a much smaller chance of winning in the electoral college. For example, say your forecast popular vote share, a year out, is 0.50 with a standard error of 0.06 (so the Democratic candidate has a 95% chance of receiving between 38% and 62% of the two-party vote), then the probability of them winning at least 52% is pnorm(0.50, 0.52, 0.06) = 0.37. On the other hand, it’s been awhile since the Republican candidate has won the popular vote . . . You could give arguments either way on this, but the point is that it’s not so clear how to express high ignorance here. To get that stable probability of the candidate winning, you need a stable predicted vote share, and, again, the difficulty here isn’t so much with the stability as in what’s your starting point is.
Thinking about hypothetical betting odds can be a useful way to understand uncertainty. I’ve found it helpful when examining concerns with my own forecasts (for example here) as well as identifying problems with forecast-based probability statements coming from others (for example here and here).
Actual betting is another story. I’m not taking a strong moral stance against forecasters also making bets, but I have enough concerns that I’m not planning to do it myself. On the other hand, I’m glad that some low-key betting markets are out there; they provide some information even if not as much as sometimes claimed. Rajiv Sethi discusses this point in detail here and here.