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Equipossibility is a philosophical concept in possibility theory that is a precursor to the notion of equiprobability in probability theory. 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 {1,2,3,4,5,6} rather than {6, not 6}.^[1] 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 of Laplace states that equipossible alternatives may be accorded equal probabilities if nothing more is known about the underlying probability distribution. 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^[2].

In Bayesian inference, one definition of equipossibility is "a transformation group which leaves invariant one's state of knowledge". Equiprobability is then defined by normalizing the Haar measure of this symmetry group^[3] . This is known as the principle of transformation groups.

References

^ "Socrates and Berkeley Scholars Web Hosting Services Have Been Retired | Web Platform Services". web.berkeley.edu. Retrieved 2022-05-29.
^ Wright, J. N. (January 1951). "Book Reviews". The Philosophical Quarterly. 1 (2): 179–180.
^ Jensen, A.; la Cour-Harbo, A. (2001). The Discrete Wavelet Transform via Lifting. Berlin, Heidelberg: Springer. pp. 11–24. {{cite book}}: Unknown parameter |booktitle= ignored (help)

External links

Book Chapter by Henry E. Kyburg Jr. on equipossibility, with the 6/not-6 example above
Quotes on equipossibility in classical probability

[1] "Socrates and Berkeley Scholars Web Hosting Services Have Been Retired | Web Platform Services". web.berkeley.edu. Retrieved 2022-05-29.

[2] Wright, J. N. (January 1951). "Book Reviews". The Philosophical Quarterly. 1 (2): 179–180.

[3] Jensen, A.; la Cour-Harbo, A. (2001). The Discrete Wavelet Transform via Lifting. Berlin, Heidelberg: Springer. pp. 11–24. {{cite book}}: Unknown parameter |booktitle= ignored (help)

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 The [[Principle of Indifference]] of [[Laplace]] states that equipossible alternatives may be accorded equal probabilities if nothing more is known about the underlying [[probability distribution]]. 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<ref>{{cite journal |last1=Wright |first1=J. N. |title=Book Reviews |journal=The Philosophical Quarterly |volume=1 |issue=2 |date=January 1951 |pages=179–180 |url=https://doi.org/10.2307/2216737}}</ref>.
-In [[Bayesian inference]], one definition of equipossibility is "a [[transformation group]] which leaves invariant one's state of knowledge".  Equiprobability is then defined by normalizing the [[Haar measure]] of this symmetry group{{Citation needed|date=May 2022}}.  This is known as the [[principle of transformation groups]].
+In [[Bayesian inference]], one definition of equipossibility is "a [[transformation group]] which leaves invariant one's state of knowledge".  Equiprobability is then defined by normalizing the [[Haar measure]] of this symmetry group<ref>{{cite book |last1=Jensen |first1=A. |last2=la Cour-Harbo |first2=A. |year=2001 |title=The Discrete Wavelet Transform via Lifting |booktitle=Ripples in Mathematics |publisher=Springer |location=Berlin, Heidelberg |pages=11-24 |url=https://doi.org/10.1007/978-3-642-56702-5_3}}</ref>
+.  This is known as the [[principle of transformation groups]].
 ==References==