An expected utility maximizer's preferences between two bundles contingent on event 1 happening must be independent of what he will get if event 2 happens.

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This statement is a basic assumption of expected utility theory and is known as the independence axiom or the independence of irrelevant alternatives. The idea is that an individual's preferences between two options should not be influenced by the existence or non-existence of irrelevant alternatives.

An Expected Utility Maximizer's Preferences Between Two Bundles Contingent on Event