fiducial on a string

A very short note in arXiv today by Gunnar Taraldsen and Bo Henry Lindqvist (NTU, Norway). With the above title. I find the note close to unreadable, I must say, as the notations are not all or well- defined. The problem starts from Teddy Seidenfeld [whom I met in Harvard around Dutch book arguments] arguing about the lack of unicity of fiducial distributions in a relatively simple setting. Actually the note is also inspired from Bayes, Fiducial and Frequentist, and comments from Teddy, a talk I apparently missed by taking a flight back home too early!

What I find surprising in this note is that the “fiducial on a string” is a conditional distribution on the parameter space restricted to a  curve, derived from the original fiducial distribution by a conditioning argument. Except that since the conditioning is on a set of measure zero, this conditional is not only not-unique, but it is completely undefined and arbitrary, since changing it does not modify the properties of the joint distribution.