Thanks Private User
Yes, I wasnt really expecting anyone except Geni staff to be able to see the link to my support request but just added it for reference.
While what you say is true in general, and I accept all your arguments regarding complexity, performance and alternative paths, but my lengthy interaction with support revealed that the algorithm is supposed to favour and return the relationship path with the shortest number of steps.
If my shortest path relationship to a cousin profile is n steps, then by definition the maximum number of steps to their offspring can be n+1 steps. There could be a shorter path of course via the other parent, but it can never be more than 1 step greater than the least number of steps to either parent.
There are situations where this can be discovered to not be true for a given profile at a point in time but Geni Support did say that you can "force" re-evaluation of the path by tree-walking to take the relationship to the parent (or child) into account.
I discovered that most of the time, tree-walking appears to help Geni to re-evaluate the shortest path using a path which is consistent with that of the parent when there are multiple paths with a different number of steps.
It also seems to usally help when there are multiple paths with the same number of steps, so that a preference for a particular pathway can be adopted (ie direct relationship instead of a relationship by marriage) which would be a logical approach.
However, there are some instances, such as the one I documented, where this is inexplicably not working and Geni's choice of the multiple paths with the same number of steps for the parent is different to Geni's choice of the multiple paths with the same number of steps for the child, even when the immediate ancestry returned for both parent and child is the same.
I accept that in the big scheme of things this is not a huge deal, but I think it is illogical to present a parent as 16th cousin 6 times removed and then their offspring as 18th cousin four times removed when logically this should be 17th cousin five times removed and the same pathway is being used for the immediate ancestry above the 2 profiles (ie not as a result of a legitimate different choice being made for the offspring which resulted in a lower number of steps).
And I dont understand why in this case the tree-walking approach doesnt fix the mistake - almost as if the preference of pathway for this specific relationship (from myself) to the offspring is "hardwired" into the array of pathways and cant be replaced?