The maximin share guarantee (MMS) is a common fairness notion in the field of fair division of indivisible goods. Since MMS is not guaranteed to exist in general, many approximation schemes have been studied. One attractive notion called Optimal-MMS maximizes the minimum approximation received by all agents. We show that in the worst case, Optimal-MMS allocations only allocate a constant number of agents their full MMS value. This research was done with Dr. Hadi Hosseini of Penn State.
Searns, A., & Hosseini, H. (2020). Fairness Does Not Imply Satisfaction (Student Abstract). Proceedings of the AAAI Conference on Artificial Intelligence, 34(10), 13911–13912. https://doi.org/10.1609/aaai.v34i10.7228