core Estimated learning time: 4 h

4.20 Rational decisions: utility and decision networks

You can compute expected utility, explain why a rational agent maximises it rather than expected money, and extend a Bayesian network with decision and utility nodes.

Before:01a. Linear Algebra01b. Calculus and Optimisation01c. Probability01d. Statistics and Inference02. Python — Basics to Advanced

The rational agent at the start of this module is defined by a performance measure, and this is where that measure is finally made precise. Preferences that obey a short list of reasonable conditions can always be written as a utility function, and the agent that maximises expected utility is the one the whole approach has been pointing at. It also explains a good deal of ordinary human behaviour that looks irrational when it is measured in money.

Work through these

  • State the preference conditions that make a utility function exist

    A short list of reasonable conditions on preferences, from which a single number per outcome can always be constructed. The result is why maximising one quantity is not an arbitrary modelling choice.

  • Compute expected utility, and choose the action that maximises it

    Weighting the value of each outcome by how likely it is, and taking the best total. That one line is the formal content of acting rationally under uncertainty.

  • Explain risk aversion, and why utility is not money

    The second thousand rupees is worth less than the first, so a curve rather than a straight line fits real preference. Insurance and lotteries both make sense once value and money are separated.

  • Extend a Bayesian network with decision and utility nodes

    Adding what you may choose and what you care about to a network that already says what is likely. The result answers what to do, rather than only what is true.

  • Compute the value of information, and decide whether a test is worth running

    The gain in expected utility from learning something before deciding, which puts a price on a measurement. It is the calculation that says when to stop gathering evidence and act.

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Links last checked 29 Aug 2026.

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