Blackwell Garbling and Decision Risk
Compare experiments by the decision risk incurred after degrading their signals.
Free theory articleCompare experiments by the decision risk incurred after degrading their signals.
Concept & interpretation
Consider a setup where the hidden state H has prior probability P(H=1) = 0.5. A signal S provides accuracy a = 0.8. We garble this signal with error e = 0.25, and evaluate decisions with false-positive cost c = 2.
Experiment
You can interact with this model in the Blackwell Garbling and Decision Risk module.
- Set Signal accuracy to 1 (perfect signal) and observe the original risk drop to 0.
- Increase the Garbling error to 0.5. The effective accuracy drops to 0.5, representing a completely uninformative signal, causing the risk to match the "No Signal Risk".
- Change the Prior state one to 0.9. At extreme priors, the optimal decision rule might ignore the signal entirely, meaning garbling does not strictly increase risk.