I will have to look at Magnitude Based Inference (aka Magnitude Based Decisions) a bit more carefully, but Jeffrey Blume has developed an approach that is superficially similar called Second Generation P values. His approach is derived from likelihood theory, and has attractive properties I don’t think the MBI/MBD people are cognizant of yet.
I have not yet proven to myself Blume’s Second Generation P values and MBI are equivalent. It may be the case that these scholars stumbled upon Blume’s good idea, but do not have enough background statistical knowledge to demonstrate correctness.
I’m adding for reference an openly published paper that examines the method in light of known statistical principles by Welsh and Knight (referenced by Sander below).
Magnitude-based Inference: A Statistical Review (link)
The Vindication of Magnitude-Based Inference (link)
The statistical reviewer was Kristin L. Sainani, PhD from Stanford, who is critical of MBI/MBD:
https://web.stanford.edu/~kcobb/
Her critique is here. It looks like a thorough analysis. I managed to find freely available copy below:
The Problem with “Magnitude-based Inference” (link )
I am somewhat concerned that there are no references to the statistical literature in my scan of the PDF you linked to. For example:
I forgot to add Dr. Blume’s American Statistician paper on Second Generation P values, where he goes into a bit more theory.
An Introduction to Second-Generation p -Values (link)