  Discontinuities can be fairly arbitrary but also cause a significant impact
on outcomes in larger systems. Indeed, their arbitrariness is why they have
been used to infer causal relationships among variables in numerous settings.
Regression discontinuity from econometrics assumes the existence of a
discontinuous variable that splits the population into distinct partitions to
estimate the causal effects of a given phenomenon. Here we consider the design
of partitions for a given discontinuous variable to optimize a certain effect
previously studied using regression discontinuity. To do so, we propose a
quantization-theoretic approach to optimize the effect of interest, first
learning the causal effect size of a given discontinuous variable and then
applying dynamic programming for optimal quantization design of discontinuities
to balance the gain and loss in that effect size. We also develop a
computationally-efficient reinforcement learning algorithm for the dynamic
programming formulation of optimal quantization. We demonstrate our approach by
designing optimal time zone borders for counterfactuals of social capital,
social mobility, and health. This is based on regression discontinuity analyses
we perform on novel data, which may be of independent empirical interest.
