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Prompt

# The Meridian Audit: An Adversarial Reasoning Challenge You are an independent analyst reviewing a memo that makes three claims: 1. “Program Q is causally superior to Program R.” 2. “Every person who tests positive should receive the protective action.” 3. “All six calendar tasks can be completed without overlap.” Your job is to determine exactly which claims follow from the evidence. Treat this as a closed-world problem: use only the facts given below. Do not browse, invent missing facts, or confuse an assumption with a conclusion. Do not reveal hidden chain-of-thought. Instead, provide concise calculations, a checkable proof, and clearly labeled assumptions. If a requested conclusion is not identifiable from the evidence, say so and show why. ## Exhibit 1 — Program outcomes The table reports observed successes: | Risk stratum | Program Q | Program R | |---|---:|---:| | High risk | 9 successes out of 10 | 80 successes out of 100 | | Low risk | 1 success out of 100 | 0 successes out of 10 | The assignment mechanism is not described. No claim of randomization is provided. Answer all of the following: - Compute each program’s success rate within each stratum. - Compute each program’s overall success rate by pooling its counts. - Audit claim 1. Separate the descriptive comparisons from any causal conclusion. - State the weakest additional assumption that would make a causal comparison defensible, and explain why stratifying by the listed risk group alone may still be insufficient. ## Exhibit 2 — Diagnostic test and decision losses For the same target population, assume the disease prevalence is exactly 1%, test sensitivity is exactly 99%, and specificity is exactly 95%. A protective action has these losses: - Loss 0 if an infected person receives the action. - Loss 0 if an uninfected person does not receive it. - Loss 4 if an uninfected person receives it. - Loss 30 if an infected person does not receive it. Ignore all other costs. The test is calibrated for this population. Answer all of the following: - Compute the probability of infection after a positive result and after a negative result. - Derive the probability threshold above which the protective action minimizes expected loss. - Decide whether to act after a positive result and after a negative result. - Audit claim 2, stating the assumptions needed for your decision to apply to every person in the target population. Show a calculation using a hypothetical cohort of 100,000 people as a cross-check. ## Exhibit 3 — Calendar intervals Each task occupies a positive-duration half-open interval `[start, end)`. Two tasks are compatible exactly when they do not overlap; a task may begin at the instant another ends. | ID | Interval | |---|---| | A | [0,4) | | B | [1,2) | | C | [2,3) | | D | [3,5) | | E | [4,6) | | F | [5,7) | | G | [6,8) | | H | [7,9) | | J | [7,8) | Among schedules with the maximum number of tasks, the preferred schedule is the one whose task-ID sequence, listed chronologically, is lexicographically smallest. Use the order `A < B < C < ... < J`. Answer all of the following: - Find **every** maximum-cardinality compatible schedule. - Identify the preferred schedule under the tie-break rule. - Audit claim 3. - Give a general algorithm for any `n` intervals, including a recurrence, a correctness argument, and time and space complexity. Your algorithm must implement the lexicographic tie-break, not merely find some maximum schedule. ## Final adjudication For each of the memo’s three claims, return exactly one label: - **SUPPORTED** - **REFUTED** - **NOT IDENTIFIABLE** Then give the strongest conclusion warranted by the exhibits. Explicitly distinguish the observational program comparison from the diagnostic decision and the calendar optimization; do not let evidence from one exhibit silently justify a claim in another. ## Calibration and self-audit End with: 1. A confidence score from 0–100 for each exhibit. 2. The single most fragile assumption in your analysis. 3. Two plausible mistakes a careless solver might make, and a brief check showing whether you avoided each one. ## Scoring rubric (100 points) - Exhibit 1 calculations and causal reasoning: 25 - Exhibit 2 Bayesian calculations and decision threshold: 25 - Exhibit 3 complete optimum, tie-break, algorithm, and proof: 30 - Correct separation of supported, refuted, and unidentifiable claims: 15 - Calibration and self-audit: 5 A polished answer that skips a proof, silently assumes randomization, or reports only one optimal schedule cannot receive full credit.