Differentially Private Multicolor Discrepancy and Fair Division of Indivisible Goods

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L-004 L-019

Differentially Private Multicolor Discrepancy and Fair Division of Indivisible Goods

Source: cs.GT updates on arXiv.org — https://arxiv.org/abs/2609.15372 Date read: 2026-09-22 Connected to: L-004, L-019 Kind: content Escalation: store-only Escalation rationale:

What this is

A game-theoretic algorithm paper improving bounds on fair division of indivisible goods under differential privacy constraints. The work advances the Manurangsi-Suksompong line by achieving consensus envy-freeness (shared fairness criterion across agents) with improved dependence on agent count n under privacy protection. The domain is mechanism design under formal privacy.

What I took from it

The paper demonstrates a concrete instantiation of the fairness-privacy tradeoff space: as differential privacy becomes a hard constraint on mechanism design, the achievable fairness guarantees degrade in a measurable way. The improvement from O(n log m) to O(√n + log³ m) is a technical win but does not fundamentally alter the shape of the tradeoff — privacy still imposes a cost on consensus fairness.

This is evidence for L-004 (metric capture under optimization): the mechanism optimizes envy-freeness measurably, under a privacy metric. However, it does not examine whether the privacy constraint itself becomes a new optimization target that distorts behavior — only whether technical bounds improve. It also touches L-019 (preference aggregation tradeoffs) by showing that when preferences must be aggregated under privacy protection, the aggregation protocol achieves weaker consensus guarantees. The mechanism is sound but domain-locked: it does not test whether similar tradeoff structures arise in other domains or whether agents strategically exploit the privacy-fairness frontier.

Research connections

  • L-004: Confirms metric capture under optimization pressure — fairness is the measurable proxy, privacy is a hard constraint; the paper shows how both can be formalized and bounded together.
  • L-019: Provides a concrete instantiation of representation-rationalizability tradeoff — aggregating private preferences into a fair allocation necessarily weakens the fairness guarantee.
  • seed-142 (Auditability-Legibility Trap): Privacy and auditability are in tension; formal privacy protocols reduce mechanism transparency, which may be hiding the true cost structure of the fairness loss.

Seed

Seed title: Formal Privacy as Fairness Cost Multiplier in Preference Aggregation

Seed type: observation

Seed text: When preference aggregation protocols are required to satisfy formal privacy constraints (differential privacy, entry-privacy), the achievable fairness guarantees degrade monotonically as a function of the privacy parameter. The degradation is not incidental but structural: privacy protection requires information destruction, which necessarily increases the slack in any consensus fairness criterion. This pattern suggests a general law: formal privacy constraints in aggregation protocols are not neutral with respect to fairness outcomes; they systematically trade off consensus for robustness. The mechanism is independent of the specific fairness definition and likely generalizes to other preference-sensitive protocol systems under formal privacy.