Order-distance and other metric-like functions on jointly distributed random variables
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- by Ehtibar N. Dzhafarov and Janne V. Kujala PDF
- Proc. Amer. Math. Soc. 141 (2013), 3291-3301 Request permission
Abstract:
We construct a class of real-valued nonnegative binary functions on a set of jointly distributed random variables. These functions satisfy the triangle inequality and vanish at identical arguments (pseudo-quasi-metrics). We apply these functions to the problem of selective probabilistic causality encountered in behavioral sciences and in quantum physics. The problem reduces to that of ascertaining the existence of a joint distribution for a set of variables with known distributions of certain subsets of this set. Any violation of the triangle inequality by one of our functions when applied to such a set rules out the existence of the joint distribution. We focus on an especially versatile and widely applicable class of pseudo-quasi-metrics called order-distances. We show, in particular, that the Bell-CHSH-Fine inequalities of quantum physics follow from the triangle inequalities for appropriately defined order-distances.References
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Additional Information
- Ehtibar N. Dzhafarov
- Affiliation: Department of Psychological Sciences, Purdue University, West Lafayette, Indiana 47907
- Email: ehtibar@purdue.edu
- Janne V. Kujala
- Affiliation: Department of Mathematics, University of Jyväskylä, Jyväskylä, Finland
- Email: jvk@iki.fi
- Received by editor(s): October 26, 2011
- Received by editor(s) in revised form: November 18, 2011
- Published electronically: May 15, 2013
- Additional Notes: The first author’s work was supported by AFOSR grant FA9550-09-1-0252
The second author’s work was supported by Academy of Finland grant 121855 - Communicated by: Edward C. Waymire
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 3291-3301
- MSC (2010): Primary 60B99; Secondary 81Q99, 91E45
- DOI: https://doi.org/10.1090/S0002-9939-2013-11575-3
- MathSciNet review: 3068981