Utility functions are used to calculate EMV. perform sensitivity analysis. encode risk attitudes. implement Bayes' rule.

Utility functions are primarily used to: 1. **Calculate EMV (Expected Monetary Value)**: Utility functions help in determining the expected utility of different outcomes, which can be used to calculate EMV in decision-making scenarios. 2. **Perform Sensitivity Analysis**: They can be used to analyze how sensitive the outcomes are to changes in the input variables, helping to understand the robustness of decisions. 3. **Encode Risk Attitudes**: Utility functions are designed to reflect an individual's risk preferences, whether they are risk-averse, risk-seeking, or risk-neutral. 4. **Implement Bayes' Rule**: While utility functions themselves do not implement Bayes' rule, they can be used in conjunction with Bayesian analysis to evaluate the expected utility of different decisions based on prior probabilities and new evidence. In summary, utility functions are versatile tools in decision theory, particularly in the context of risk and uncertainty.