"There's a 70% chance of rain tomorrow," says the weather app on your phone. "There's a 30% chance my flight will be delayed," posts a colleague on Slack. Scientific theories also include chances: “There's a 50% chance of observing an electron with spin up,” or (less fundamental) “This is a fair die — the probability of it landing on 2 is one in six.”

We constantly talk about chances and probabilities, treating them as features of the world that we can discover and disagree about. And it seems you can be objectively wrong about the chances. The probability of a fair die landing on 2 REALLY is one in six, it seems, even if everybody in the world thought otherwise. But what exactly are these things called “chances”?

Readers on LessWrong are very familiar with the idea that many probabilities are best thought of as subjective degrees of belief. [...]

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Outline:

(02:23) Two Ways to Deal with Chance

(03:45) The Key Insight: Symmetries in Our Beliefs

(05:09) The Magic of de Finetti

(06:50) De Finetti in Practice

(06:59) 1. Weather Forecasting

(07:36) 2. Clinical Trials

(09:18) 3. Machine Learning

(11:33) Why This Matters

(12:27) Common Objections and Clarifications

(13:24) Quick Recap

The original text contained 8 footnotes which were omitted from this narration.

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First published:
January 13th, 2025

Source:
https://www.lesswrong.com/posts/auSfqhbMKEvzt4unG/chance-is-in-the-map-not-the-territory

Narrated by TYPE III AUDIO.