Abstract
In fair division of indivisible goods, l-out-of-d maximin share (MMS) is the value that an agent can guarantee by partitioning the goods into d bundles and choosing the l least preferred bundles. Most existing works aim to guarantee to all agents a constant fraction of their 1-out-of-n MMS. But this guarantee is sensitive to small perturbation in agents' cardinal valuations. We consider a more robust approximation notion, which depends only on the agents' ordinal rankings of bundles. We prove the existence of l-out-of-floor((l+1/2)n) MMS allocations of goods for any integer l greater than or equal to 1, and present a polynomial-time algorithm that finds a 1-out-of-ceiling(3n/2) MMS allocation when l = 1. We further develop an algorithm that provides a weaker ordinal approximation to MMS for any l > 1.
Keywords
- Game Theory and Economic Paradigms: GTEP: Fair division
- Game Theory and Economic Paradigms: GTEP: Other
- AI Ethics, Trust, Fairness: ETF: Fairness and diversity
