Definition
The Equal Probability Assumption (also known as the Principle of Indifference) states that if there is no known reason to predicate of any one case rather than another, then all cases should be assigned an equal probability. It is the foundation for defining a “Uniform Distribution” in the absence of specific evidence.
Why It Matters
This assumption is the “maximum entropy” starting point for reasoning under total ignorance, allowing us to build non-informative priors for Bayesian updating. It is the foundation for designing fair systems and games, ensuring that our initial estimates are logically symmetric when no evidence favors one outcome over another.
Core Concepts
- Symmetry of Ignorance: If you have mutually exclusive and exhaustive possibilities and no evidence favoring any one of them, the probability of each is .
- How to read: “The probability P equals one over N for each of the N outcomes.”
- Meaning: Uniform prior when you have no information to break symmetry—the principle of indifference and maximum-entropy starting point.
- Prior Probability: In Bayesian statistics, the equal probability assumption is often used to set a “Non-Informative Prior” before any data is collected.
- Sample Space: The assumption requires a clearly defined set of all possible outcomes. A change in how you “partition” the sample space can change the probabilities (Bertrand’s Paradox).