Optimal Bounds on the Price of Fairness for Indivisible Goods

Abstract

In the allocation of resources to a set of agents, how do fairness guarantees impact social welfare? A quantitative measure of this impact is the price of fairness, which measures the worst-case loss of social welfare due to fairness constraints. While initially studied for divisible goods, recent work on the price of fairness also studies the setting of indivisible goods.In this paper, we resolve the price of two well-studied fairness notions in the context of indivisible goods: envy-freeness up to one good (EF1) and approximate maximin share (MMS). For both EF1 and 1 /2-MMS we show, via different techniques, that the price of fairness is O( √ n), where n is the number of agents. From previous work, it follows that these guarantees are tight. We, in fact, obtain the price-of-fairness results via efficient algorithms. For 1 /2-MMS our bound holds for additive valuations, whereas for EF1, it holds for the more general class of subadditive valuations. This resolves an open problem posed by Bei et al. (2019).

I Will Have Order! Optimizing Orders for Fair Reviewer Assignment

“…Existing work on fair allocation of indivisible items is also relevant. Bei et al [7] and Barman et al [5] study the price of fairness, the ratio between the maximum utilitarian welfare and the maximum utilitarian welfare for any fair allocation, for various fairness definitions. Caragiannis et al [13] find the price of envy-freeness to be Θ(n) for n agents, when an envy-free allocation exists.…”

“…Caragiannis et al [13] find the price of envy-freeness to be Θ(n) for n agents, when an envy-free allocation exists. Bei et al [7] show that the worst-case price of round-robin is O( √ n log(mn)) for n agents and m goods, while Barman et al [5] conclusively determine the price of EF1 is Θ( √ n) [5]. Barman et al [6] show that maximizing the utilitarian welfare subject to EF1 is not polynomial-time approximable.…”

EEF1-NN: Efficient and EF1 allocations through Neural Networks

“…In further related work, papers [3,9] explore, PE and EF1 allocations, [28,29] explore PE and EQ1 allocations, [6] explore PE and Prop1 allocations for various items (goods or/and chores). There will always be a tradeoff between fairness and efficiency, corresponding to the study of the price of fairness [7,10]. Alongside, Researchers have also studied how likely it is that a fairness notion will not exist [23,38,39].…”

“…We are training the network for 10 × 20 and 13 × 26. however, we show our test results for various 𝑛 ×𝑚. We test for network performance for 𝑛 ∈ [7,15]. Further, we also train a individual network over different distributions such as Gaussian (𝜇=0.5,𝜎=1), Log-normal (𝜇 = 0.5,𝜎 = 1), and Exponential (𝜆 = 1), with 150𝑘 training samples for 𝑛 = 10.…”

“…Our network will not run when 𝑛 < 10, given the four 3 × 3 Convolution-UpConvolution. Hence to report performance for 𝑛 ∈ [7,9], we reduce a Convolution-UpConvolution layer from our network and train accordingly with 7 × 14 and 10 × 20 valuation profiles. EEF1-NN scales appropriately across 𝑛; however, if we test the network performance of 𝑛 = 14 and 𝑛 = 20, the network performs better for 𝑛 = 14, solely because we trained just using 10 × 20 and 13 × 26.…”