  The problem of individualization is recognized as crucial in almost every
field. Identifying causes of effects in specific events is likewise essential
for accurate decision making. However, such estimates invoke counterfactual
relationships, and are therefore indeterminable from population data. For
example, the probability of benefiting from a treatment concerns an individual
having a favorable outcome if treated and an unfavorable outcome if untreated.
Experiments conditioning on fine-grained features are fundamentally inadequate
because we can't test both possibilities for an individual. Tian and Pearl
provided bounds on this and other probabilities of causation using a
combination of experimental and observational data. Even though those bounds
were proven tight, narrower bounds, sometimes significantly so, can be achieved
when structural information is available in the form of a causal model. This
has the power to solve central problems, such as explainable AI, legal
responsibility, and personalized medicine, all of which demand counterfactual
logic. We analyze and expand on existing research by applying bounds to the
probability of necessity and sufficiency (PNS) along with graphical criteria
and practical applications.
