Choose research and actions

A probability is an input to a decision, not the decision itself. The preferred action depends on the consequences of each outcome and on the cost of learning more.

decision::Action specifies utility if the event occurs and if it does not. Expected utility is p*if_yes + (1-p)*if_no. best_action returns the zero-based index and utility of the highest-value action. Exact ties select the first action in the supplied order.

extern crate supercast;
use supercast::{Probability as P, decision::{Action, best_action}};

let actions = [
    Action { if_yes: 10.0, if_no: -10.0 },
    Action { if_yes: 0.0, if_no: 0.0 },
];
let (index, utility) = best_action(&actions, P::new(0.8)?)?;
assert_eq!(index, 0);
assert!((utility - 6.0).abs() < 1e-12);
Ok::<(), supercast::Error>(())

Utilities must share a scale. They can represent money, a scored objective, or another explicitly justified utility measure. The library does not determine an organization’s values or infer utilities from a probability.

Expected value of information

An indicator can be observed before choosing an action. The value of that observation is the expected best utility after observing it, minus the best utility available now. Subtract research cost to obtain net value.

extern crate supercast;
use supercast::{Probability as P, decision::{Action, value_of_information}, decompose::Indicator};

let actions = [
    Action { if_yes: 10.0, if_no: -10.0 },
    Action { if_yes: 0.0, if_no: 0.0 },
];
let perfect_signal = Indicator { chance: P::HALF, if_yes: P::ONE, if_no: P::ZERO };
assert_eq!(value_of_information(&actions, perfect_signal, 1.0)?, 4.0);
Ok::<(), supercast::Error>(())

The calculation uses the indicator’s implied prior. Its branches must therefore represent a coherent joint model. Research cost is nonnegative and uses the same utility units as the actions. A negative net value can be the correct answer.

Rank useful work

Use probability sensitivity to identify important assumptions, information gain to measure expected belief change, and decision value to assess whether resolving uncertainty could change an action. They answer different questions.

An indicator can carry information while having zero decision value because the same action is optimal in both branches. Conversely, a modest probability change near a decision threshold can be valuable. Do not rank research by how dramatic its narrative sounds.

This primitive assumes the observation arrives in time to act and has the supplied reliability. It does not model the causal effect of acquiring the information, a changing action set, or the opportunity cost of delay beyond the declared research cost.