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Recent empirical work demonstrates that online advertisement can exhibit biasin the delivery of ads across users even when all advertisers bid in anon-discriminatory manner. We study the design of ad auctions that, given fairbids, are guaranteed to produce fair outcomes. Following the works of Dwork andIlvento (2019) and Chawla et al. (2020), our goal is to design a truthfulauction that satisfies ``individual fairness'' in its outcomes: informallyspeaking, users that are similar to each other should obtain similarallocations of ads. Within this framework we quantify the tradeoff betweensocial welfare maximization and fairness.  This work makes two conceptual contributions. First, we express the fairnessconstraint as a kind of stability condition: any two users that are assignedmultiplicatively similar values by all the advertisers must receive additivelysimilar allocations for each advertiser. This value stability constraint isexpressed as a function that maps the multiplicative distance between valuevectors to the maximum allowable $\ell_{\infty}$ distance between thecorresponding allocations. Standard auctions do not satisfy this kind of valuestability.  Second, we introduce a new class of allocation algorithms called InverseProportional Allocation that achieve a near optimal tradeoff between fairnessand social welfare for a broad and expressive class of value stabilityconditions. These allocation algorithms are truthful and prior-free, andachieve a constant factor approximation to the optimal (unconstrained) socialwelfare. In particular, the approximation ratio is independent of the number ofadvertisers in the system. In this respect, these allocation algorithms greatlysurpass the guarantees achieved in previous work. We also extend our results tobroader notions of fairness that we call subset fairness.

Individual Fairness in Advertising Auctions through Inverse Proportionality