Laplace's Rule of Succession
Updated 2026-08-01
INTRODUCTION
English translation pending.
CORE DEFINITION
Formulated by Pierre-Simon Laplace in the late eighteenth century as an answer to the sunrise problem. Given n successes and no observed failures, the rule assigns the next trial a probability of (n+1)/(n+2). It follows from placing a uniform prior over the unknown success probability under Laplace's principle of indifference. The rule guarantees that no outcome receives probability zero or one, so even a million consecutive successes leave room for a first failure.
SCAFFOLDING EFFECT
Reduce cognitive load
- Stress-test certainty: when a model claims an event cannot occur, check whether a smoothing prior is missing - Price rare events: use (n+1)/(n+2) to estimate a first-ever failure in a spotless record - Calibrate language: reserve absolute words like never and always for mathematical limits, not for track records
Anchor fast decisions
Raw counting assigns zero probability to unseen outcomes, and a single zero erases an entire product of likelihoods. Adding one to every count is equivalent to starting from a weak uniform prior, so the estimate stays strictly between zero and one. As evidence accumulates, the prior's influence shrinks and the estimate converges toward the observed frequency.
MINIMUM ACTION
In progress 0/1Practice this model in one real situation:
account_treeGenealogyexpand_more
menu_bookReferencesexpand_more
Source support: Explicit
- en.wikipedia.orghttps://en.wikipedia.org/wiki/Rule_of_successionverified
PRIVATE NOTES · Only visible to you
SAVED Q&A
ENTRY Q&A · Private saving available
Ask with a clear boundary
thinkingmodels answers from published entry context only.
Your question is sent to thinkingmodels. The answer uses public entry context only.
RELATED MODELS