Version 1
: Received: 16 December 2020 / Approved: 17 December 2020 / Online: 17 December 2020 (11:23:32 CET)
Version 2
: Received: 27 December 2020 / Approved: 28 December 2020 / Online: 28 December 2020 (15:31:31 CET)
Version 3
: Received: 19 February 2021 / Approved: 23 February 2021 / Online: 23 February 2021 (15:26:35 CET)
Version 4
: Received: 21 April 2021 / Approved: 22 April 2021 / Online: 22 April 2021 (21:14:09 CEST)
Lesage, A.; Victor, J.-M. To
Be or to Have Been Lucky, That Is the
Question. Philosophies 2021, 6, 57.
https://doi.org/10.3390/
philosophies6030057
Lesage, A.; Victor, J.-M. To
Be or to Have Been Lucky, That Is the
Question. Philosophies 2021, 6, 57.
https://doi.org/10.3390/
philosophies6030057
Lesage, A.; Victor, J.-M. To
Be or to Have Been Lucky, That Is the
Question. Philosophies 2021, 6, 57.
https://doi.org/10.3390/
philosophies6030057
Lesage, A.; Victor, J.-M. To
Be or to Have Been Lucky, That Is the
Question. Philosophies 2021, 6, 57.
https://doi.org/10.3390/
philosophies6030057
Abstract
Is it possible to measure the dispersion of ex-ante chances (i.e. chances “before the event”) among people, be it gambling, health, or social opportunities? We explore this question and provide some tools, including a statistical test, to evidence the actual dispersion of ex-ante chances in various areas with a focus on chronic diseases. Using the principle of maximum entropy, we derive the distribution of the risk to become ill in the global population as well as in the population of affected people. We find that affected people are either at very low risk like the overwhelming majority of the population but still were unlucky to become ill, or are at extremely high risk and were bound to become ill.
Keywords
ex-ante chances; dispersion of chances; maximum entropy principle; chronic diseases; gambling; statistical test; twin studies
Subject
Biology and Life Sciences, Biochemistry and Molecular Biology
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received:
23 February 2021
Commenter:
Jean Marc Victor
Commenter's Conflict of Interests:
Author
Comment:
Extensively rewritten version with an important new result that is relevant to the field of complex genetic disorders. We here derive the expression of the risk distr ibution to become ill using the maximum entropy principle (see section 4, lines 364-388). We also derive the risk distribution among affected people, which turns out to have two narrow peaks, one close to p=0 and the other one close to p=1 (see figures 4 and 5 and lines 389-408). The consequences of this functional form are highlighted.
Commenter: Jean Marc Victor
Commenter's Conflict of Interests: Author