The Probabilistic Ambiguity Principle

A New Rule in Probability

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Probability theory has long been the backbone of how we understand and quantify uncertainty. Whether it’s predicting the weather, calculating risk in finance, or even determining the likelihood of a machine learning model’s success, we rely on probabilities to help us make decisions.

Traditionally, these probabilities are treated as precise numbers between 0 (impossible) and 1 (certain), with a clear answer about the likelihood of an event occurring. But what if this traditional view of probability isn’t enough? What if the world around us is far more uncertain than we realize?

This is where the Probabilistic Ambiguity Principle (PAP) comes in. It challenges the idea of assigning exact probabilities to events and instead suggests that we should think about probabilities in terms of ranges. Let’s break this down in simpler terms and look at how it could change the way we approach uncertainty in everyday situations.

What is the Probabilistic Ambiguity Principle?

The Probabilistic Ambiguity Principle (PAP) tells us that the probability of an event isn’t always a fixed number. Instead, it could be a range of possible probabilities — an interval that represents the uncertainty we have about the outcome.