Restricting legitimate models of common knowledge of rationality to those with cautious beliefs conflates rationality under certainty with rationality under uncertainty, as Savage's expected utility framework permits degenerate probability-one beliefs as a limiting case.
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Beliefs that you're absolutely certain about—so certain that mathematically, the probability of being wrong is zero.
Savage's expected utility framework(as used in game theory and decision theory)
A decision-making method developed by statistician Leonard Savage that helps people choose between options by calculating the value they'd get from each choice, weighted by how likely each outcome is to happen.
common knowledge(Condition for the formation of a joint commitment)
A state in which each party knows the relevant fact, knows that the others know it, and so on — used here as the threshold condition for a joint commitment coming into force.
knowledge(Distinguished from mere true belief, which may be the product of indoctrination and need not exercise deliberative capacities.)
Justified true belief — true belief that has been arrived at through the exercise of deliberative capacities, including comparison of and deliberation among alternatives.
rationality(Traditional conception being challenged by epistemic relativists)
A cognitive virtue and hallmark of the scientific method, intimately tied to requirements of consistency, justification, warrant, and evidence for beliefs.