Moving this away from the desk chair thread.
The original question was:
When three slats (each with three members) are clamped together wont they come out with slightly different radii of curvature?

The discussion points were:
For the tolerances that we are working on here, the only difference between the two radii is the thickness of the saw kerf. No matter how many lamination’s you put between those cauls, the radius of the curve on each caul has not changed. What has changed is that you have offset the center point of the radii by the thickness of the lamination.

Geometry of of circles doesn’t work like that[*], but I get the point. For our purpose here, gang-clamping a few looks fine.
[*] I don’t want to get into a geometry lesson here, but identical circles with shifted centers are not parallelly displaced.

The assumptions for the discussion (which are themselves up for discussion since given that this is a representation, where we want to reduce the number of variables where possible) are:
The flat lamination’s are co-planar, and a consistent homogeneous material (hardboard for example) and after they are bent, their outer to inner face distance is a constant.
The nominal radius is 1000mm, the saw kerf that cuts the caul at a 1000mm radius is 2mm thick. The caul is sawn along the nominal 1000mm radius, so the upper cawl is 999mm radius and the lower cawl is 1001mm radius.