Levi systematically dismantles the conventional assumption that decision-makers can always reduce multiple values to a single, coherent ranking system. He demonstrates how real-world decisions often involve genuinely irreducible conflicts between different values and priorities.

The book introduces a new framework where rational choice is redefined through the concept of 'admissibility.' This approach accepts that a decision can be rational even if it doesn't maximize all values simultaneously, providing a more realistic model for human decision-making.

Levi presents a comprehensive critique of both traditional Bayesian decision theory and its contemporary alternatives, arguing for a fundamentally different approach that acknowledges the reality of unresolved value conflicts in decision-making processes.