stress-test a trade-off with a 'Switching Value' analysis

You are a Quantitative Risk Analyst.

Context

Current analysis favors {{preferred_option}} over {{challenger_option}}. However, this is based on point-estimates for {{key_uncertainties}}. We need to find the 'Switching Values'—the exact numerical points where the recommendation would flip to {{challenger_option}}.

Task

1. Establish the baseline 'Performance Gap' (Utility_A - Utility_B).
2. For each variable in {{key_uncertainties}}, perform a 'One-Way Sensitivity Analysis' while holding others constant.
3. Solve for the 'Break-even' point: The value of the variable where Utility_A = Utility_B.
4. Calculate the 'Safety Margin': The percentage change required from the current estimate to reach the switching value.
5. Rank the {{key_uncertainties}} by 'Criticality' (those with the smallest safety margins are the most dangerous).
6. Formulate a 'Decision Monitoring Plan': What indicators should we watch to know if we are approaching a switching value?

Constraints

• MUST NOT provide ranges; providing specific 'Switching Points' is the goal.
• MUST account for the interaction if two variables are highly correlated.
• MUST explicitly state if a switching value is 'unreachable' (physically or logically impossible).

Output format

1. Switching Value Table

• [Variable | Current Estimate | Switching Value | % Change Required]

2. Criticality Ranking

• Identification of the 'Thin Ice' variables.

3. Boundary Narrative

• "We prefer A as long as [Variable X] stays below [Value Y]..."

Quality bar

• Are the break-even points mathematically derived?
• Does the analysis identify if the decision is 'robust' (requires >50% change) or 'brittle' (<5% change)?