---
title: "degrees of belief"
type: concept
related: [Probability, Probability Theory]
source: https://www.jemoka.com/posts/kbhprobability_theory/
confidence: high
status: active
---

degrees of belief help us quantify how much we believe some event \(A\) is more/less plausible than some event \(B\).
Let us take two statements:
\(A\) Taylor gets Nobel Prize in Literature \(B\) Han shot first For instance, if we want to express &ldquo;I think its more likely that Taylor gets the prize than Han shot first&rdquo;:
\begin{equation} A \succ B \end{equation}
axioms of degrees of belief universal comparability for two statements \(A, B\), only three states can exist:
\(A \succ B\) (A more likely) \(A \prec B\) (B more likely) \(A \sim B\) (equally likely) transitivity if \(A \succeq B\) and \(B \succeq C\), then \(A \succeq C\)
language of probability using this framework, we can then describe the events in terms of probability
\(P(A) &gt; P(B) \Leftrightarrow A \succ B\) \(P(A) = P(B) \Leftrightarrow A \sim B\) See also axiom of probability
