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- Title
A Maximum Entropy Resolution to the Wine/Water Paradox.
- Authors
Parker, Michael C.; Jeynes, Chris
- Abstract
The Principle of Indifference ('PI': the simplest non-informative prior in Bayesian probability) has been shown to lead to paradoxes since Bertrand (1889). Von Mises (1928) introduced the 'Wine/Water Paradox' as a resonant example of a 'Bertrand paradox', which has been presented as demonstrating that the PI must be rejected. We now resolve these paradoxes using a Maximum Entropy (MaxEnt) treatment of the PI that also includes information provided by Benford's 'Law of Anomalous Numbers' (1938). We show that the PI should be understood to represent a family of informationally identical MaxEnt solutions, each solution being identified with its own explicitly justified boundary condition. In particular, our solution to the Wine/Water Paradox exploits Benford's Law to construct a non-uniform distribution representing the universal constraint of scale invariance, which is a physical consequence of the Second Law of Thermodynamics.
- Subjects
BENFORD'S law (Statistics); SECOND law of thermodynamics; ENTROPY; PARADOX; WINES
- Publication
Entropy, 2023, Vol 25, Issue 8, p1242
- ISSN
1099-4300
- Publication type
Article
- DOI
10.3390/e25081242