The modesty argument is the claim that when two or more rational agents have common knowledge of a disagreement over the likelihood of an issue of simple fact, they should each adjust their probability estimates in the direction of the others'. This process should continue until the two agents are in full agreement. The name comes from the idea that rational agents should not privilege evidence they have gathered over evidence gathered by others, i.e. agents should be modest about their own estimates.
The Modesty Argument is inspired by Aumann's agreement theorem, which shows that genuine Bayesians cannot agree to disagree.
The Modesty Argument was at least partially refuted by Eliezer Yudkowsky in the article: The Modesty Argument