Unit Selection with Nonbinary Treatment and Effect

The unit selection problem aims to identify a set of individuals who are most likely to exhibit a desired mode of behavior or to evaluate the percentage of such individuals in a given population, for example, selecting individuals who would respond one way if encouraged and a different way if not encouraged. Using a combination of experimental and observational data, Li and Pearl solved the binary unit selection problem (binary treatment and effect) by deriving tight bounds on the "benefit function," which is the payoff/cost associated with selecting an individual with given characteristics. This paper extends the benefit function to the general form such that the treatment and effect are not restricted to binary. We then propose an algorithm to test the identifiability of the nonbinary benefit function and an algorithm to compute the bounds of the nonbinary benefit function using experimental and observational data.