Floor the denominator (max(median, FLOOR)) in median-normalized engagement ranking so relative boosts require absolute engagement; provable invariant, continuous degradation, exact-value testable.
When ranking content by engagement normalized against a per-source median (e.g. Reddit post comments/points vs the subreddit's weekly median), pure ratios are gameable by dead sources: a post with 4 points in a sub whose median is 2 computes as '2x median' and jumps the queue, ranking equal to a 400-point post in a sub with median 200.
Fix: floor the denominator, not the numerator — ratio = count / max(median, FLOOR), capped at RATIO_CAP.
This yields a provable invariant: a ratio can exceed 1.0 only when the absolute count exceeds FLOOR, regardless of how dead the source is (denominator >= FLOOR always). Relative popularity is only trusted once absolute engagement clears the bar; below it the score degrades smoothly toward count/FLOOR instead of cliff-edge gating.
Worked example with FLOOR_points=25, FLOOR_comments=10, weights 0.7 comments / 0.3 points:
Advantages over alternatives: (a) additive smoothing (x+prior)/(median+prior) shrinks ratios but still allows small-count boosts and is harder to explain; (b) absolute gate (if count < N: ratio = min(ratio, 1.0)) creates a discontinuity at the gate. The denominator floor is one expression, continuous, and testable with exact expected values.
Pick floors relative to existing domain bars: if the system already treats score<5 as dead content, set the normalization floor 2-5x above that so a boost demands unambiguous engagement. Zero/empty medians are also automatically safe (denominator never below FLOOR, no ZeroDivisionError).