On picking sequences for chores
Uriel Feige, Xin Huang

TL;DR
This paper improves the guarantees of picking sequences for allocating indivisible chores among agents, achieving better disvalue ratios than previous methods and introducing new share notions and envy considerations.
Contribution
It introduces improved picking sequences with tighter disvalue ratios for chores, new share concepts like the chore share, and ex-ante envy notions, advancing fair division methods.
Findings
Achieves disvalue ratio of 1.733 for arbitrary entitlement
Achieves disvalue ratio of 8/5 for equal entitlement
Provides lower bound of 3/2 on ratio for large n
Abstract
We consider the problem of allocating indivisible chores to agents with additive disvaluation (cost) functions. It is easy to show that there are picking sequences that give every agent (that uses the greedy picking strategy) a bundle of chores of disvalue at most twice her share value (maximin share, MMS, for agents of equal entitlement, and anyprice share, APS, for agents of arbitrary entitlement). Aziz, Li and Wu (2022) designed picking sequences that improve this ratio to for the case of equal entitlement. We design picking sequences that improve the ratio to~1.733 for the case of arbitrary entitlement, and to for the case of equal entitlement. (In fact, computer assisted analysis suggests that the ratio is smaller than in the equal entitlement case.) We also prove a lower bound of on the obtainable ratio when is…
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Taxonomy
TopicsAuction Theory and Applications · Logic, Reasoning, and Knowledge · Optimization and Search Problems
