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Simultaneous Envy and Equitability Guarantees

Author

Listed:
  • Hadi Hosseini
  • Shraddha Pathak
  • Lirong Xia
  • Chengkai Zhang

Abstract

Recent work in fair division has focused on either simultaneously satisfying closely related fairness notions or achieving a single notion across the ex-ante and ex-post worlds. We study the compatibility of two fundamentally different fairness notions: envy-freeness and equitability. For indivisible goods-only and chores-only settings, we study the existence and complexity of simultaneously satisfying their relaxations, revealing sharp contrasts between the two settings. We show that EF1+EQ1 may fail to exist even for normalized, additive valuations. Our main algorithmic result computes an EF1+EQ1 allocation for normalized binary goods with at most seven agents. In sharp contrast, binary chores admit the stronger EFX+EQX guarantee for any number of agents, even without normalization. We further initiate the study of cross-notion ex-ante--ex-post guarantees, asking whether randomized allocations can provide ex-ante guarantees for one notion while preserving ex-post guarantees for another.

Suggested Citation

  • Hadi Hosseini & Shraddha Pathak & Lirong Xia & Chengkai Zhang, 2026. "Simultaneous Envy and Equitability Guarantees," Papers 2608.26410, arXiv.org.
    • Handle: RePEc:arx:papers:2608.26410
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    File URL: https://arxiv.org/pdf/2608.26410
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