# Technical question
How does a predicted probability become a choice between actions?
# Mechanism
For a binary action:
EV(act) = p × value_if_success - cost_of_action
EV(do_nothing) = alternative_value
The action changes when the difference in expected utility crosses zero.
# Why the obvious explanation is incomplete
A high probability does not imply that action is worthwhile. The correct threshold depends on outcome value, action cost, alternatives and constraints.
# Working argument
Prediction and decision are separate mathematical objects. A decision rule cannot be derived from probability alone without specifying what outcomes are worth.
# Public experiment
Simulate equipment inspections:
each machine has failure probability p;
inspection has cost c;
an undetected failure has loss L;
inspection prevents a fraction q of failures.
The expected benefit is:
EV(inspect) = p × q × L - c
Vary:
calibration error;
inspection cost;
failure loss;
intervention effectiveness.
Compare a fixed probability threshold with the value-optimal threshold. Plot realised utility and action rate.
# Mathematical or decision structure
Act when:
p × q × L > c
or:
p > c / (qL)# Decision changed
Model evaluation must include probability quality in the regions where the value function changes action.
# Connection and guardrails
Source: Inspired by moving from prediction-score improvements toward understanding the downstream optimisation objective.
Abstraction: Standard abstraction.
# Queue
- Stage: Next
- Next investigation: Implement the inspection simulator and identify cases where the best-AUC and best-utility models differ.