SCS Undergraduate Thesis Topics
|Elias Szabo-Wexler||Ariel Procaccia||Staying Fair|
Fairness in the context of the allocation of goods is a universal construct whose violation elicits extremely strong reactions. It has nonetheless historically been mathematically ill-defined. In recent years, the situation has improved as economists, mathematicians, and computer scientists have tackled the issue of an axiomatic treatment of fairness. These axioms enable researchers to qualify algorithms for fair allocation and to meaningfully compare different mechanisms. None have yet extended this axiomatic approach to fairness over time: there is no axiomatic treatment of situations with multiple allocation events whose outcomes are linked beyond the naive iterated application of existing (ill-suited) axioms. I have extended the current core axioms for time invariant fair allocation to account for time. In particular, I have extended the axioms of strategyproofness, envy-freeness, and efficiency to be historically aware. Using the extended axioms, I have generalized the seminal probabilistic serial allocation mechanism of Bogomolnaia and Moulin to attain a strictly superior allocation mechanism in the canonical and iterated fair allocation settings. There may be better constructions of the axioms, and there are likely better mechanisms. My work lays the foundation for continued research in this space, and suggests that it is interesting, feasible, and worth pursuing.