## Problem 234 — rank:35

**Title:** Quantitative self-tolerance

**Added binding assumptions (LaTeX):**

```latex
Define decision regions by minimizing conditional expected loss, and define their boundaries by equality of competing conditional risks with a stated tie rule. Multiclass probability vectors do not determine one unique boundary without the loss. A reduction in Bayes risk from extra signal history is distinct from reducing estimation error. State target-population sampling and censoring assumptions before making a uniform excess-risk guarantee.
```

**Direct edits:** 0. **Fresh external checks:** None; supplied sources retained as provenance.