Key points are not available for this paper at this time.
We propose a combinatorial framework to analyze quantitative Helly-type questions. Using this framework, we prove a Quantitative Fractional Helly Theorem with Fractional Helly Number 3d and a stability version of the Quantitative Helly Theorem of Bárány, Katchalski, and Pach.
Attila Jung (Fri,) studied this question.