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Fair and Truthful Mechanisms for Dichotomous Valuations

AAAI 2021 · Learning theory and algorithms › Submodular and game algorithms · approach: Fair division of indivisible goods · 53 citations (OpenAlex)

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Measured effects reported in the paper

What was changedWhereMeasuredEffect
Use prioritized egalitarian (PE) allocation with a fixed priority orderSubmodular dichotomous valuations · Submodular dichotomous valuationsWelfare maximizationHelped
Use prioritized egalitarian (PE) allocation with a fixed priority orderSubmodular dichotomous valuations · Submodular dichotomous valuationsLorenz domination and fairness guaranteesHelped
Randomize agent priorities before running PESubmodular dichotomous valuations · Submodular dichotomous valuationsEx-ante envy-freenessHelped
Randomize agent priorities before running PESubmodular dichotomous valuations · Submodular dichotomous valuationsEx-post EFXHelped
Extend dichotomous valuations to XOS valuationsTruthful allocation mechanisms · XOS valuationsWelfare maximizationHurt
Allow desired item values to vary in [1, 1 + ε] for submodular valuationsTruthful allocation mechanisms · ε-dichotomous submodular valuationsWelfare approximation ratioHurt
Require a deterministic truthful mechanism to be approximately welfare maximizing and give an agent at least one desired item when she desires twoAllocation mechanisms · Three items, two ε-leveled agentsFeasibility of the stated welfare and fairness guaranteesHurt
Require a randomized truthful-in-expectation mechanism to always be reasonableAllocation mechanisms · Two items, two ε-leveled agentsEx-post Lorenz domination, min-square, NSW, lex-min, or EFXHurt
Round reported ε-leveled values down and use randomized mechanism ℳᴸAdditive ε-dichotomous valuations · ε-leveled valuationsWelfare approximation: ρ = 1/(1 + ε)Helped
Use randomized mechanism ℳᴸ with rounded valuations and held-out itemsAdditive ε-dichotomous valuations · ε-leveled valuationsTruthfulness in expectationHelped
Use randomized mechanism ℳᴸ with rounded valuations and held-out itemsAdditive ε-dichotomous valuations · ε-leveled valuationsMaximin share and EF1 guarantees: ρ = 1/(1 + ε)Helped
Use PE for additive dichotomous valuationsAdditive dichotomous valuations · Additive dichotomous valuationsMaximin shareHelped

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