Elicitation
The FRI method begins with an ultimate outcome and uses structured interviews to discover events that would change an expert’s probability assessment. Turn vague indicators into independently resolvable questions.
Ask both branches. “If C happens, I become worried” is incomplete without P(C) and the forecast if it does not happen. A dramatic but nearly impossible indicator can have little expected informational value.
| Ask for upstream and downstream indicators but do not mistake temporal order for causation. Conditional association P(U | C) is not an intervention effect P(U | do(C)). |
Coherence gate
| Let c=P(C), a=P(U | C), b=P(U | not C). The implied prior is u=ca+(1-c)b. Compare to the stated prior with a declared numerical tolerance. If materially inconsistent, ask which inputs should change or label alternatives; do not silently “repair” expert beliefs. |
For an impossible branch c=0 or c=1, a conditional on the zero-probability branch is not identified by data. The helper weights that branch by zero; interpret it only as an elicited hypothetical.
Information gain
Use Bernoulli entropy h(p)=-pln(p)-(1-p)ln(1-p), with 0*ln(0)=0.
For coherent inputs: IG=h(u)-ch(a)-(1-c)h(b).
Equivalently, IG=cKL(Bern(a)||Bern(u))+(1-c)KL(Bern(b)||Bern(u)). This equivalence is an expectation identity, not a guarantee that every single branch has positive entropy reduction.
With natural logs, units are nats. Divide by ln(2) for bits. For 0<u<1, percent-of-maximum information is 100*IG/h(u). If h(u)=0 it is undefined, not 0/0=0.
FRI’s VOI metric in this report is information-theoretic. Decision-theoretic value of information additionally requires actions, consequences and utilities. Do not attach a monetary value to IG without a decision model.
Multiple indicators
Two indicators can convey the same information. Do not add marginal IG values as if every bit were unique. Elicit joint/conditional models for combinations or report overlapping candidate indicators separately. Distinguish the value of resolving a question from confidence that the conditional estimates are correct.
Preserve individual coherent assessments before computing group summaries. Averaging various conditional probabilities from different respondent subsets can create incoherence.
Helper
python3 scripts/conditional_tree.py --prior 0.3 --p-indicator 0.4 --p-u-if 0.6 --p-u-if-not 0.1
Returns implied prior, coherence gap, information gain and percentage of maximum. It rejects incoherent inputs. The helper uses standard library Python 3 and does not model multi-node dependence.
Limits
The source is a working paper/case study with small samples and long-horizon judgments. Indicator ratings are not verified predictive success on an ultimate event that has not resolved. Treat this skill as structured research prioritization.