Work

Non-Existence of PMMS Allocations and a $4/3$-PMMS Guarantee for Additive Chores

Year: 2026

Type: preprint

Abstract: We study pairwise maximin share (PMMS) fairness for indivisible items with additive preferences. We give a polynomial-time reduction from chores to goods that preserves the existence of a PMMS allocation. Together with known nonexistence results for chores, this yields nonexistence for additive goods. In addition, we show that deciding if a given instance admits a PMMS allocation is NP-hard. We also give explicit instances whose PMMS factors are $226/227$ for goods and $1.102065$ for chores, certified by exact enumeration. Complementing these impossibility results, we prove that every additive-chore instance admits a $4/3$-PMMS allocation.

Source: arXiv (Cornell University)

Authors: Bei, Xiaohui, Lin, Zehan, Liu, Shengxin, Luan, Rong, Tao, Biaoshuai

Institutions: Nanyang Technological University, University of Macau, Harbin Institute of Technology, Shanghai Jiao Tong University

Language: English

Topic: Game Theory and Voting Systems

Subfield: Economics and Econometrics

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

OpenAlex ID: W7212325921

Cites: 12

Cited by: 2

Related to: 10