Diagnose and fix selection bias in experiments

Define selection bias and diagnose it in this scenario: users can opt into seeing a discount banner (treatment), and treated users show higher conversion. (a) List at least three plausible selection mechanisms and the directions of bias they induce. (b) Propose two fixes that produce unbiased (or less biased) causal estimates—e.g., randomized encouragement, regression discontinuity (thresholded eligibility), front‑door adjustment, or IV with assignment instrument—and state the assumptions each requires and how you would test them. (c) Provide a small numerical example where naive differences are biased but a corrected method recovers an unbiased or less biased estimate.