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We study the probabilistic assignment of items to platforms that satisfiesboth group and individual fairness constraints. Each item belongs to specificgroups and has a preference ordering over platforms. Each platform enforcesgroup fairness by limiting the number of items per group that can be assignedto it. There could be multiple optimal solutions that satisfy the groupfairness constraints, but this alone ignores item preferences. Our approachexplores a `best of both worlds fairness' solution to get a randomizedmatching, which is ex-ante individually fair and ex-post group-fair. Thus, weseek a `probabilistic individually fair' distribution over `group-fair'matchings where each item has a `high' probability of matching to one of itstop choices. This distribution is also ex-ante group-fair. Users can customizefairness constraints to suit their requirements. Our first result is apolynomial-time algorithm that computes a distribution over `group-fair'matchings such that the individual fairness constraints are approximatelysatisfied and the expected size of a matching is close to OPT. We empiricallytest this on real-world datasets. We present two additional polynomial-timebi-criteria approximation algorithms that users can choose from to balancegroup fairness and individual fairness trade-offs.  For disjoint groups, we provide an exact polynomial-time algorithm adaptableto additional lower `group fairness' bounds. Extending our model, we encompass`maxmin group fairness,' amplifying underrepresented groups, and `mindom groupfairness,' reducing the representation of dominant groups.'

Individual Fairness under Varied Notions of Group Fairness in Bipartite Matching - One Framework to Approximate Them All