Why Probability is Misunderstood

Most people think probability predicts the future; in reality, it measures our ignorance about the present.

People love to talk about elections in probabilities: “There’s a 70% chance Candidate X wins.” But when the less likely outcome happens, they react as if the prediction was broken. To them, 70% sounds like a guarantee rather than a statement of uncertainty. The misunderstanding isn’t about politics; it’s about what probability actually means.

Probability is not a property of the world: it’s a model of our uncertainty (let’s disregard quantum physics for now).

Probability for One-Off Events

The key issue with the election example is wanting to assign a probability to the winner of a single election as if it’s a coin flip. A coin flip’s probability is grounded in repeatable experiments, whereas elections aren’t repeatable; we can’t sample the 2024 election 10,000 times. So from a frequentist view, election predictions aren’t probabilities; they’re belief distributions over unknown variables (like polling error, turnout, etc.).

When a model says “Candidate A has a 70% chance,” it means “based on current data and assumptions, in 70% of possible worlds consistent with the model, A wins.”

And no, this isn’t a sci-fi argument or a stance on the many-worlds interpretation in quantum physics. In probability modeling, the “worlds” are a hypothetical idea, not a literal physical thing. But importantly, the math is identical to thinking in many-worlds quantum physics. The difference is:

In quantum systems, probability arises from superposition (the system actually exists in a blend of states).
In everyday uncertainty, probability arises from ignorance (we don’t know the true state).

Let’s use the election prediction example:

Let’s say we run 10,000 simulations of how the election might turn out, taking into account sentiments on social media, demographic details, economic trends, and what not. Importantly, each simulation yields an outcome that’s consistent with how our model of elections works. In most of the simulations, it’s one of the two most popular candidates that wins. But every once in a while, the simulation generates a scenario where a third candidate, an underdog, wins. After the simulations, we have real elections, and most importantly, only one outcome out of all the possible outcomes will happen.

All the possible outcomes could have happened (with different degrees of likelihood), but only one did, which is the world we end up living in.

What Probability Really Is

Probability is a mathematical way of describing our uncertainty about reality; it’s not reality itself.

How you choose to describe this uncertainty depends on your point of view. We already looked at the distinction, but let’s put it more formally:

Frequentist probability describes uncertainty in repeatable experiments.
Bayesian probability describes uncertainty in knowledge.
Quantum probability describes uncertainty in the underlying physical state.

Elections cannot be handled in a purely frequentist framework because there is no notion of sampling repeated elections under identical conditions. Therefore, any probability applied to a single election is necessarily Bayesian in nature. Sometimes we unintentionally confuse the two. Say you were applying for a job. You could think: “What’s the chance that I’ll get this job?” In doing so, you are assigning a degree of belief given limited information. But ten minutes later you might say: “Well, it’s either going to be a yes or no,” treating it like a coin flip.

Let’s take another example:

What’s the probability that Shakespeare wrote a poem we haven’t discovered?

First of all, a poem either was or was not written by Shakespeare, but we don’t know which. There’s no coin to flip or dice to throw; we can’t run an experiment to sample “alternate timelines.” The probability we assign is entirely about our uncertainty, not about the world itself generating randomness.

Interestingly, I think LLM hallucination risk follows the same pattern. We could say “the model hallucinates 5% of the time,” and it’s not like there’s literally a randomizer inside the model deciding “This time I hallucinate.” Instead, we’re describing our uncertainty about the model’s behavior on future, unseen prompts, based on observations of the past. It’s exactly like asking the Shakespeare question but about a model’s future output instead of authorship.

The common mistake in both of these cases is that they treat the probability as if it were describing a physical random event, like rolling a die, obeying frequentist principles. In reality, they are Bayesian: the number is about our knowledge, not about an inherent frequency. Even if the world is fully deterministic, Bayesian uncertainty still applies whenever you don’t know the true state.

How To Think About Probability

So how can you turn the words from this blog into something actionable? Let’s do some Bayesian updating on our mental models, shall we?

Instead of thinking in terms of “what will happen?”, think: “given what I know, how should I bet?”

Additionally, don’t think about probability as some sort of prophecy. It’s a tool for decision-making under uncertainty. Every statement about probability will be based on your assumptions about reality; understand those assumptions and question them.