Algorithmic Fairness in Distribution of Resources and Tasks

The paper is an overview and contains no numbered Theorem, Lemma, Proposition, or Corollary asserting a computational result, so bit (a) fails. The proposed high-multiplicity house-allocation problem is credible, but its plausibility cannot cure the missing admissible anchor.

The objection that survived

The paper contains no numbered computational result establishing the proposed house-allocation claim, so the anchor cannot satisfy the protocol.

What the mirror covers

The proposed mirror covers the degree-of-fairness house-allocation discussion, while leaving the survey's other allocation, online matching, task-distribution, elicitation, strategic-manipulation, and human-perception results untreated.

Open questions for a prover

The case FOR (proponent)

The honest conclusion is that this paper has no qualifying anchor for the requested analysis. It is explicitly a survey/overview, and the supplied text contains no numbered Theorem, Lemma, Corollary, or Proposition. It reports computational claims in prose—such as polynomial-time epistemic fair allocation, online \(1/2\)-approximations, hardness of EFX with mixed goods and chores, and polynomial-time two-agent manipulation of deferred acceptance—but none is a named result of this paper. Most are summaries of the cited papers.

Therefore I cannot quote a result number, identify it as proved here or cited elsewhere, or state one continuous problem per anchor without inventing evidence. Under the programme’s rules, there is no defensible anchored Class A/B/C verdict.

If unnumbered claims were admissible, the strongest positive candidate would be the degree-of-fairness work on house allocation in Section 2.1. A plausible mirror is:

Given finite resident types \(R\) with mass distribution \(\mu\), house types \(H\) with supply distribution \(\nu\), complete rankings \(u_r\) for each resident type, and a matching flow \(x_{r,h}\) satisfying
\[ \sum_h x_{r,h}=\mu_r,\qquad \sum_r x_{r,h}=\nu_h, \]
find an allocation maximizing utilitarian welfare
\[ W(x)=\sum_{r,h}x_{r,h}u_r(h) \]
and, among welfare-maximizing allocations, minimizing aggregate envy
\[ E(x)=\sum_{r,h}x_{r,h} \left(\max_{h':\nu_{h'}>0}u_r(h')-u_r(h)\right)_+. \]

This is a credible high-multiplicity mirror for a public-housing regime with hundreds of thousands of residents but relatively few preference/eligibility types. It would likely be Class A for this linearized envy measure, via transportation LP. Its weakness is decisive here: the survey does not specify that exact metric or give a numbered result establishing its complexity. It would be a reasonable proposed mirror of cited work, but not a valid anchored answer to the present protocol.

The case AGAINST (opponent, writing after the proponent)

The strongest negative case is procedural, not substantive. This is an overview paper, and the supplied text contains no numbered Theorem, Lemma, Proposition, or Corollary proved by the paper. Its computational statements are summaries of cited work. Under the stated protocol, therefore, there is no qualifying anchor to mirror, and the proponent’s case cannot receive credit.

That does not establish the universal claim that no worthwhile mirror exists. The proposed house-allocation mirror is genuinely plausible: a large public-housing population can have finitely many preference, eligibility, and valuation types, while house supplies scale with population. A transportation-flow model preserves the relevant anonymous allocation data, and welfare plus a linearized envy objective can produce a meaningful high-multiplicity optimization problem. Replacing the utility-regret objective by the paper’s ordinal “number of envious agents” would make the mirror still closer, not eliminate it.

Graphical variants would require retaining spatial structure—perhaps through repeated communities or a graphon-like limit—but that is a modelling complication, not a proof that no useful mirror exists. The same applies to matching mechanisms and dynamic allocation: type distributions, capacities, and limiting fairness guarantees are natural questions even when the survey itself does not formulate them.

So the defensible negative verdict is narrow: this paper supplies no admissible named computational anchor under the protocol. The stronger substantive verdict—no continuous population model is worthwhile in any scenario—is not supported, and the house-allocation example is a counterweight to it.

The adversarial triple: the proponent anchors on up to three named results; the opponent sees that case and must defeat every anchor; the judge decides which case convinced it. These are the pipeline’s own outputs, generated by tools/triple_run.py — no human edited them. The paper’s own text is not reproduced here beyond the quoted statement above.