# Repeated Fair Allocation of Indivisible Items

arXiv: https://arxiv.org/abs/2304.01644 · HTML: https://mlsanity.com/paper/2304.01644/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Apr 2023.

## Built on by (most cited first, 11 of 11)

- [Temporal Fairness in Multiwinner Voting](https://mlsanity.com/paper/2312.04417/) (2023)
- [Temporal Elections: Welfare, Strategyproofness, and Proportionality](https://mlsanity.com/paper/2408.13637/) (2024)
- [Temporal Fair Division of Indivisible Items](https://mlsanity.com/paper/2410.14593/) (2024)
- [Online Fair Division with Additional Information](https://mlsanity.com/paper/2505.24503/) (2025)
- [Not in My Backyard! Temporal Voting Over Public Chores](https://mlsanity.com/paper/2508.08810/) (2025)
- [Fairness in Repeated Matching: A Maximin Perspective](https://mlsanity.com/paper/2510.04624/) (2025)
- [Resource Allocation under the Latin Square Constraint](https://mlsanity.com/paper/2501.06506/) (2025)
- [Bandit Max-Min Fair Allocation](https://mlsanity.com/paper/2505.05169/) (2025)
- [Credit Fairness: Online Fairness In Shared Resource Pools](https://mlsanity.com/paper/2601.17944/) (2026)
- [Temporal Panel Selection in Ongoing Citizens' Assemblies](https://mlsanity.com/paper/2602.16194/) (2026)
- [Temporal Fair Division in Multi-Agent Systems: From Precise Alternation Metrics to Scalable Coordination Proxies](https://mlsanity.com/paper/2605.14879/) (2026)

## Abstract (arXiv)

The problem of fairly allocating a set of indivisible items is a well-known challenge in the field of (computational) social choice. In this scenario, there is a fundamental incompatibility between notions of fairness (such as envy-freeness and proportionality) and economic efficiency (such as Pareto-optimality). However, in the real world, items are not always allocated once and for all, but often repeatedly. For example, the items may be recurring chores to distribute in a household. Motivated by this, we initiate the study of the repeated fair division of indivisible goods and chores, and propose a formal model for this scenario. In this paper, we show that, if the number of repetitions is a multiple of the number of agents, there always exists a sequence of allocations that is proportional and Pareto-optimal. On the other hand, irrespective of the number of repetitions, an envy-free and Pareto-optimal sequence of allocations may not exist. For the case of two agents, we show that if the number of repetitions is even, it is always possible to find a sequence of allocations that is overall envy-free and Pareto-optimal. We then prove even stronger fairness guarantees, showing that every allocation in such a sequence satisfies some relaxation of envy-freeness. Finally, in case that the number of repetitions can be chosen freely, we show that envy-free and Pareto-optimal allocations are achievable for any number of agents.