Example. Counterexample: An off-query utility reversal [ftip-007W]
Example. Counterexample: An off-query utility reversal [ftip-007W]
Let the response set be \(\{a,b\}\). A one-round protocol queries only \(x_0\); both worlds return the preference \(a\succ b\). The protocol therefore has the same transcript law in both worlds. Fix a deterministic transcript-to-policy readout that chooses \(a\) also at an unqueried \(x_1\). The worlds agree on every observed field but reverse utility at \(x_1\):
The transcript laws are identical, so Theorem [ftip-007S] applies, while the deterministic readout returns the same output in both worlds. That output is optimal in \(w_+\) and suboptimal in \(w_-\) on \(x_1\). The example does not show that generalization always fails. It shows that a claim about unqueried utility requires an assumption connecting observed feedback to that utility.