Measure rider incentive causal ROI

You are designing a rider-facing promotion (for instance, 20% off with a $10 cap) that is assigned based on a propensity model. Your task is to measure the causal lift and return on investment while accounting for selection bias and spillover effects across the marketplace.

Your tasks are:

• Define marketplace health metrics and give formulas for each: matching quality (median pickup ETA, the post-dispatch cancellation rate within five minutes, driver idle minutes per trip), demand (incremental trips, GMV lift), supply (acceptance rate, earnings per hour), and a combined match-quality indicator (median distance to pickup).
• For identification, outline approaches for three settings: (A) randomized geographic holdouts; (B) offer scores with a cutoff that allow a regression discontinuity design, including how you would pick the bandwidth, check continuity, run a McCrary test, and choose the polynomial order; (C) rule-based targeting that permits instrumental variables using an operational friction instrument, where you state the relevance and exclusion restrictions and which threats you will test.
• Write the ROI formula that includes cannibalization, subsidy cost, surge and ETA externalities, and habit formation. Explain how you would estimate LTV lift and amortize customer acquisition cost; compute confidence intervals using either the delta method or bootstrap.
• Design a two-stage randomization plan—first city by week, then rider—to separate direct effects from spillovers; specify the estimands for total, direct, and indirect effects.
• For multiple testing, select and defend a correction approach (Bonferroni, Benjamini-Hochberg, or hierarchical testing) given one primary metric, three secondary metrics, and about twenty diagnostics.
• For heterogeneity, describe a pre-registered analysis plan to detect moderation by city tier and weather conditions using causal forests or group-wise models, while controlling Type-S and Type-M errors.
• Diagnostics: list the pre-trend checks, placebo windows, and negative control outcomes you would use; set explicit criteria for declaring success and for rolling back the program.

The question tests a data scientist's ability in causal inference, experimental design, building marketplace health metrics, estimating ROI, and dealing with selection bias, spillovers, multiple testing, and heterogeneity on a two-sided platform.