Classroom Talking Points About Election Polling and Probability
Why Election Polls Don't Predict Outcomes
No AI post this week. I’ve been thinking a lot about the election and about polling. As a mathematician, I love data, making election polling a particularly fascinating subject of study. I’m not going to dive very deep into it. My goal is just to provide educators with a few talking points about election polling, specifically what it does and doesn’t tell us. This is not a political post; it’s really just about math.
Many of our students are encountering polling data and probability forecasts for the first time. As school leaders, we have a unique opportunity to help them understand what these numbers really mean – and what they don't.
The Misconception About Probability
When we see that a candidate has an 80% chance of winning (which is not the case in this election), our brains typically translate this to "they're going to win." But an event with a 20% chance of occurring is about as likely as:
Rolling a six on a die
Drawing a heart from a deck of cards
Having your birthday fall on a weekend
We wouldn't be shocked if any of these happened. Yet when an election "upset" occurs, we often act as if something impossible has happened.
What Probability Really Tells Us
At its core, probability isn't about predicting single events – it's about understanding patterns that emerge over many repetitions of an event in the long run. This is a crucial distinction that often gets lost in election coverage.
Probabilities don’t help us much when it comes to predicting the next outcome of an event. They help us understand the long-term behavior of an event that is repeated many times.
Let's consider weather as an example to understand this: A 70% chance of rain doesn't tell us whether it will rain tomorrow. Instead, it tells us that if we looked at 1,000 days with similar atmospheric conditions, it would rain on about 700 of them. This doesn’t help me know if I should carry an umbrella today or not. But it does help me create an effective long-term strategy. If I carry an umbrella every time there is a 70% chance of rain, I’ll be better off in the long run, even if I sometimes carry it unnecessarily.
Knowing that the probability tells us nothing definitive about what will happen today is the key. When you wake up to a 70% chance of rain, you cannot know if today will be one of the 700 rainy days or one of the 300 dry ones. The probability describes the pattern of many events, not the outcome of this one case.
This is why election polling probabilities are so tricky. When we see a candidate has a 55% chance of winning, this doesn't really give us any information about whether they will win. It doesn't even imply that they're "likely" to win in any meaningful sense. It just means that if we could somehow run this same election 1,000 times (which we can't), this candidate would win in about 550 of those alternate realities. But we only get one reality, one election, one outcome.
Today's Even Tighter Race
Current election polling makes this conversation even more relevant. With most forecasts showing probabilities much closer to 50-50 between the candidates, the limitations of polling as a predictive tool become even more apparent. When probabilities are this close, they're telling us something crucial: the outcome is highly uncertain.
Think about it this way: If you had to bet on whether a fair coin would come up heads, and you could only make this bet once in your life, knowing it's a 50% probability doesn't help you predict what will happen in your one flip. The next flip is always uncertain, regardless of the probability. Rather, the probability tells you something about the long-term behavior of the coin.
The Swing State Coin Flip Experiment
To understand just how unpredictable this election could be, consider this thought experiment: There are seven key swing states that could determine the outcome. If the race in each state is essentially a toss-up (50-50), it's like flipping a fair coin seven times. Here's what the probability distribution looks like for getting different numbers of heads:
0 heads: 0.78% (about 1 in 128)
1 head: 5.47% (about 1 in 18)
2 heads: 16.41% (about 1 in 6)
3 heads: 27.34% (about 1 in 4)
4 heads: 27.34% (about 1 in 4)
5 heads: 16.41% (about 1 in 6)
6 heads: 5.47% (about 1 in 18)
7 heads: 0.78% (about 1 in 128)
This tells us something fascinating: with close races in seven states, getting five or more “wins” (about 1 in 6 chance) isn't that unusual. Neither is losing most states. The most likely outcome is a close split (3 or 4 wins), but even that only happens about half the time. When races are this close, almost any outcome is plausible.
This tells us that wildly opposing outcomes are all very likely! It is very possible that either candidate could sweep the election or that the election will be very close. All three possibilities are likely.
Helping Students Understand the Numbers
When discussing polling with students, here are key points to emphasize:
Probability is About the Long Run, Not a Single Event: Probability tells us very little about the outcome of a chance event. Rather, it tells us what to expect in the long run if that event were repeated many times.
Probability isn't Destiny: In a race that is as close as this one, multiple opposing outcomes are all quite likely. So, when one of those outcomes occurs, we should resist the urge to say “we were right!” or “they were wrong!” about the polling data.
Data isn't Useless, Just Misunderstood: This doesn't mean polling data and statistics are worthless – far from it. Their primary value isn't in predicting the winner on election day, but rather in helping us understand how public perception of candidates might be shifting over time. Polls can reveal how different events or policy positions affect voter sentiment, how different demographic groups are responding to campaigns, and how the overall political landscape is evolving. Think of polls less as crystal balls and more as snapshots of public opinion at a particular moment in time.
Beyond Predictions
As educators, we're in a unique position to help the next generation understand that uncertainty isn't a flaw in our polling systems – it's a fundamental feature of probability itself. When we teach students that a 55% or 80% chance of winning doesn't guarantee victory, we're not just teaching them about elections. We're teaching them how to think critically about data, understand uncertainty, and make informed decisions in an increasingly complex world. The real power of probability isn't in predicting winners – it's in understanding the nature of uncertainty itself.