Equipossibility is a
philosophical
Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Som ...
concept in
possibility theory
Possibility theory is a mathematical theory for dealing with certain types of uncertainty and is an alternative to probability theory. It uses measures of possibility and necessity between 0 and 1, ranging from impossible to possible and unneces ...
that is a precursor to the notion of
equiprobability
Equiprobability is a property for a collection of events that each have the same probability of occurring. In statistics and probability theory it is applied in the discrete uniform distribution and the equidistribution theorem for rational num ...
in
probability theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...
. It is used to distinguish what ''can'' occur in a probability experiment. For example, it is the difference between viewing the possible results of rolling a
six sided dice as rather than .
The former (equipossible) set contains equally possible alternatives, while the latter does not because there are five times as many alternatives inherent in 'not 6' as in 6. This is true even if the die is biased so that 6 and 'not 6' are equally likely to occur (equiprobability).
The
Principle of Indifference
The principle of indifference (also called principle of insufficient reason) is a rule for assigning epistemic probabilities. The principle of indifference states that in the absence of any relevant evidence, agents should distribute their cre ...
of
Laplace
Pierre-Simon, marquis de Laplace (; ; 23 March 1749 – 5 March 1827) was a French scholar and polymath whose work was important to the development of engineering, mathematics, statistics, physics, astronomy, and philosophy. He summariz ...
states that equipossible alternatives may be accorded equal probabilities if nothing more is known about the underlying
probability distribution
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomeno ...
. However, it is a matter of contention whether the concept of equipossibility, also called equispecificity (from equispecific), can truly be distinguished from the concept of equiprobability.
In
Bayesian inference, one definition of equipossibility is "a
transformation group
In mathematics, the automorphism group of an object ''X'' is the group consisting of automorphisms of ''X'' under composition of morphisms. For example, if ''X'' is a finite-dimensional vector space, then the automorphism group of ''X'' is t ...
which leaves invariant one's state of knowledge". Equiprobability is then defined by normalizing the
Haar measure of this symmetry group. This is known as the
principle of transformation groups.
References
{{reflist
External links
Book Chapter by Henry E. Kyburg Jr.on equipossibility, with the 6/not-6 example above
in classical probability
Probability interpretations
Possibility