  We study the probabilistic assignment of items to platforms that satisfies
both group and individual fairness constraints. Each item belongs to specific
groups and has a preference ordering over platforms. Each platform enforces
group fairness by limiting the number of items per group that can be assigned
to it. There could be multiple optimal solutions that satisfy the group
fairness constraints, but this alone ignores item preferences. Our approach
explores a `best of both worlds fairness' solution to get a randomized
matching, which is ex-ante individually fair and ex-post group-fair. Thus, we
seek a `probabilistic individually fair' distribution over `group-fair'
matchings where each item has a `high' probability of matching to one of its
top choices. This distribution is also ex-ante group-fair. Users can customize
fairness constraints to suit their requirements. Our first result is a
polynomial-time algorithm that computes a distribution over `group-fair'
matchings such that the individual fairness constraints are approximately
satisfied and the expected size of a matching is close to OPT. We empirically
test this on real-world datasets. We present two additional polynomial-time
bi-criteria approximation algorithms that users can choose from to balance
group fairness and individual fairness trade-offs.
  For disjoint groups, we provide an exact polynomial-time algorithm adaptable
to additional lower `group fairness' bounds. Extending our model, we encompass
`maxmin group fairness,' amplifying underrepresented groups, and `mindom group
fairness,' reducing the representation of dominant groups.'
