Expected-utility information example

This synthetic example compares a safe action with a risky action under logarithmic utility and clairvoyant information. It demonstrates the experimental contract; it is not a real-world recommendation or evidence that the method has reached stable maturity.

The decision-maker starts with 10 USD. The risky action pays 5 USD in the favourable state and loses 9 USD in the adverse state; the safe action has a zero payoff in both states. The favourable and adverse state probabilities are 0.8 and 0.2. Clairvoyance reveals the state before the action is selected.

State	Probability	Safe payoff	Risky payoff
Favourable	0.8	0 USD	5 USD
Adverse	0.2	0 USD	-9 USD

Run the checked-in example from the repository root:

uv run python examples/expected_utility_information.py

It reads the normative request, executes the Rust-backed Python surface, and prints labelled JSON. The expected approximate values are:

Field	Value	Interpretation
EUI	0.3244 utility units	Gain on the declared log-utility scale
CEI	3.8316 USD	Difference in certainty equivalents
BPI	3.7522 USD	Maximum sure price paid for the information
SPI	3.4085 USD	Minimum sure compensation for surrendering it
PPI	0.1235	Utility gain relative to the declared floor anchor

The unequal CEI, BPI, and SPI values are expected under nonlinear utility. Their labels and units convey different indifference questions; do not treat them as interchangeable monetary estimates.

The example also requests the VoC presentation with BPI selected. The returned method remains expected_utility_information, showing that VoC did not invoke a second kernel. It intentionally does not request the evpi alias because log utility is nonlinear. Only a verified positive-affine clairvoyant request can use that alias.

When adapting the example, inspect these result fields rather than reading only the selected number:

• current_policy and informed_policies, including ties and domain exclusions;
• bpi_root or spi_root, including convergence status, residual, bracket, evaluation history, and policy transitions;
• comparability, before any ranking or cross-problem comparison; and
• input_digest, provenance, backend, and method_maturity for reporting.

See Expected-utility information pricing for the measure definitions and assurance boundary.