Question: In your own words, explain why a system can still output Sout even when the scoring function ScoreA gives a higher score to S* than to Sout. What does this reveal about the roles of the scoring function versus the search algorithm?

Sample answer: The scoring function ScoreA is only responsible for ranking possible outputs; it does not itself select the final output. The search algorithm (e.g., beam search) is an approximate method that searches over the space of possible outputs to find the one that maximizes ScoreA(S). Because it is approximate, it can fail to find the true maximum and instead settle on Sout, even though S* would have scored higher. This shows that a well-designed scoring function is not sufficient for correct behavior; the search procedure must also be capable of finding the output that the scoring function actually favors.

Key points:

• Scoring function ranks outputs but doesn't select the final one
• Search algorithm is approximate and can fail to find the true maximum
• ScoreA(S*) > ScoreA(Sout) rules out an objective/scoring problem
• The failure is attributed to the search procedure, not the scorer

Rubric: Full credit: clearly distinguishes the role of the scoring function from the search algorithm and explains the failure as a search limitation, not a scoring limitation. Partial credit: mentions one of the two roles but not the distinction. No credit: does not address the two components or misattributes the failure to the scorer.