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arxiv: 2502.17869 · v3 · submitted 2025-02-25 · 💻 cs.GT

Maximum Welfare Allocations under Quantile Valuations

Haris Aziz , Shivika Narang , Mashbat Suzuki This is my paper

Pith reviewed 2026-05-23 03:05 UTC · model grok-4.3

classification 💻 cs.GT
keywords quantile valuationsutilitarian welfareegalitarian welfareindivisible goodsapproximation algorithmsbalanced allocationscomputational complexityfair division
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The pith

The complexity of maximizing welfare under quantile valuations depends on whether allocations must be balanced.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a quantile valuation model in which each agent applies their own quantile to the sorted individual values of items in a bundle, capturing preference patterns that additive models miss. It then studies the computational task of finding allocations that maximize either total welfare or minimum welfare. The central result is that both problems become easier or harder in qualitatively different ways once the allocation is required to assign the same number of items to every agent. Near-optimal approximation algorithms are supplied for the total-welfare objective, while exact polynomial-time algorithms exist for the minimum-welfare objective under the balance constraint in the cases examined.

Core claim

Under quantile valuations an agent's value for a bundle equals the quantile of the values of the items it contains. Maximizing utilitarian welfare admits near-optimal approximations regardless of balance, yet the same objective is harder without the balance requirement. Maximizing egalitarian welfare admits exact algorithms precisely when allocations are required to be balanced and becomes intractable otherwise.

What carries the argument

The quantile valuation function that returns the q-quantile of an agent's item values inside the bundle.

If this is right

  • Near-optimal total-welfare allocations can be computed even when exact solutions are intractable.
  • Exact minimum-welfare allocations become feasible once every agent must receive the same number of items.
  • The model distinguishes agents who agree on single-item values yet disagree on bundle values.
  • Complexity results directly dictate when approximation versus exact methods should be deployed.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same quantile lens could be applied to dynamic or repeated allocation settings where agents revise their quantiles after observing outcomes.
  • Empirical tests could fit quantiles to observed bundle choices and measure how often the resulting allocations differ from additive predictions.
  • The balance-dependent complexity pattern may recur in other non-additive valuation families used in fair division.

Load-bearing premise

The quantile model is assumed to represent agent perceptions of bundles in ways additive valuations cannot.

What would settle it

A single polynomial-time algorithm that computes an optimal utilitarian allocation without any balance requirement would falsify the claimed complexity separation.

Figures

Figures reproduced from arXiv: 2502.17869 by Haris Aziz, Mashbat Suzuki, Shivika Narang.

Figure 1
Figure 1. Figure 1: Quantile-wise tractability or intractability of max ESW. Red das [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
read the original abstract

We propose a new model for aggregating preferences over a set of indivisible items based on a quantile value. In this model, each agent is endowed with a specific quantile, and the value of a given bundle is defined by the corresponding quantile of the individual values of the items within it. Our model captures the diverse ways in which agents may perceive a bundle, even when they agree on the values of individual items. It enables richer behavioral modeling that cannot be easily captured by additive valuation functions. We study the problem of maximizing utilitarian and egalitarian welfare within the quantile-based valuation setting. For each of the welfare functions, we analyze the complexity of the objectives. Interestingly, our results show that the complexity of both objectives varies significantly depending on whether the allocation is required to be balanced. We provide near-optimal approximation algorithms for utilitarian welfare, and for egalitarian welfare, we present exact algorithms whenever possible.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 1 minor

Summary. The paper proposes a quantile valuation model for aggregating preferences over indivisible items, where each agent has a fixed quantile parameter q and the value of a bundle is the q-quantile of the individual item values. It studies the problem of finding allocations that maximize utilitarian welfare (sum of agent values) and egalitarian welfare (minimum agent value). The analysis shows that the computational complexity of both problems depends on whether the allocation must be balanced (i.e., each agent receives the same number of items). Near-optimal approximation algorithms are given for utilitarian welfare, while exact algorithms are provided for egalitarian welfare in the cases where they exist.

Significance. If the algorithmic and complexity results hold, the work introduces a flexible non-additive valuation model that captures bundle perceptions not possible under additive valuations, which is a useful addition to the fair division literature. The observation that complexity hinges on the balanced-allocation constraint is a substantive structural finding, and the provision of both approximation and exact algorithms strengthens the contribution.

minor comments (1)
  1. [Abstract] Abstract: the phrase 'near-optimal approximation algorithms' is used without stating the ratio or the precise sense in which optimality is measured; this should be made explicit in the introduction or results overview.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their accurate summary of the paper, positive assessment of its significance, and recommendation for minor revision. No specific major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper introduces a novel quantile valuation model defined directly from per-item values and a chosen quantile parameter, then derives algorithmic results (complexity classifications, approximation algorithms for utilitarian welfare, exact algorithms for egalitarian welfare) for welfare maximization under this model. No equations, predictions, or central claims reduce by construction to fitted parameters from the same data, self-citations, or renamed inputs. The derivation chain is self-contained against the stated model definition, with no load-bearing self-citation chains or ansatzes smuggled from prior work.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, background axioms, or new postulated entities.

pith-pipeline@v0.9.0 · 5676 in / 1007 out tokens · 34257 ms · 2026-05-23T03:05:48.187965+00:00 · methodology

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Reference graph

Works this paper leans on

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