Your scenario · Human authority
Remaining authority under a constant conditional loss hazard at each transition.
Each transition represents a consequential test of human control. The result uses the rates you select.
The mechanism in words
With a 0.1% conditional chance of permanent authority loss at each transition, a system preserves authority with 99.9% probability each time. Across 1,000 transitions, multiplying those conditional retention chances gives about 36.8%.
Change the pattern and the result changes. Risk that keeps shrinking sufficiently fast can leave a positive chance of indefinite retention. Ending exposure stops additional losses in this model.
Show the calculation
For conditional hazards q₁ through qₙ, retention is the product of (1 − qᵢ). The constant-rate case is (1 − q)ⁿ. The shrinking case uses qᵢ = q × 0.5^((i − 1)/50). The closed case sets future hazard to zero after 20 transitions.
Using conditional probabilities does not require a claim that events are independent. It does require defensible conditional rates. Here they are illustrative inputs. This small tool models irreversible authority loss only, with no recovery, extinction, direct catastrophe, or competing risks.