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arxiv: 2512.05958 · v2 · pith:VFSLB6XVnew · submitted 2025-12-05 · 💻 cs.LG · cs.AI

MaxShapley: Towards Incentive-compatible Generative Search with Fair Context Attribution

Sara Patel , Mingxun Zhou , Giulia Fanti This is my paper

Pith reviewed 2026-05-21 17:35 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords fair attributionShapley valuegenerative searchcontext attributionLLMincentive-compatiblemulti-hop QAcredit allocation
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The pith

MaxShapley computes fair document attributions in generative search using a polynomial-time special case of the Shapley value.

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

Generative search engines based on large language models retrieve external sources before producing answers, which raises the question of how to fairly compensate the providers of those sources. The paper introduces MaxShapley as a practical solution that inherits the fairness properties of the Shapley value yet avoids its exponential cost. It does so by restricting attention to utility functions that decompose into a max-sum form, which permits an exact reduction to polynomial time in the number of documents. Experiments on three multi-hop question-answering datasets show that the resulting attributions match the quality of full Shapley computation while using substantially fewer tokens.

Core claim

MaxShapley is a special case of the Shapley value that leverages a de-composable max-sum utility function to compute attributions with polynomial-time computation in the number of documents, as opposed to the exponential cost of Shapley values. On HotPotQA, MuSiQUE, and MS MARCO it achieves comparable attribution quality to exact Shapley computation while consuming a fraction of its tokens, for instance giving up to a 9x reduction in resource consumption over prior state-of-the-art methods at the same attribution accuracy.

What carries the argument

MaxShapley, the polynomial-time algorithm obtained by restricting the Shapley value to a decomposable max-sum utility function that allows exact attribution without enumerating all coalitions.

If this is right

  • Fair credit attribution becomes computationally feasible for retrieval-augmented generation pipelines that surface many documents.
  • Content providers can receive compensation proportional to their measured contribution rather than to simple retrieval rank.
  • Generative search systems can adopt incentive-compatible payment rules without incurring exponential overhead.
  • The same efficiency gain applies across multi-hop QA tasks, as shown by consistent results on HotPotQA, MuSiQUE, and MS MARCO.

Where Pith is reading between the lines

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

  • If the max-sum assumption holds for many practical retrieval utilities, similar polynomial reductions may exist for other cooperative-game attributions in language-model pipelines.
  • Widespread use could shift search-engine design toward pipelines that explicitly optimize for both answer quality and measurable source contribution.
  • The open-source release of code and re-calibrated datasets enables direct replication and extension to new generative-search settings.

Load-bearing premise

The utility function measuring a document's contribution to the generated answer must admit a decomposition into a max-sum form.

What would settle it

A head-to-head comparison on a dataset whose utility function cannot be expressed in max-sum decomposable form, where MaxShapley attributions differ materially from exact Shapley values at the same accuracy target.

Figures

Figures reproduced from arXiv: 2512.05958 by Giulia Fanti, Mingxun Zhou, Sara Patel.

Figure 1
Figure 1. Figure 1: Jaccard index w.r.t. ground truth relevance scores ver [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: System diagram of the attribution problem in RAG pipeline. The query [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Quality of attribution (Jaccard index w.r.t. ground truth (top), Kendall [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Full MAXSHAPLEY keypoint breakdown prompt. You are evaluating whether a source document provides substantive informational support for a specific statement. CRITICAL: Being on the same topic is not sufficient. The source must contain specific information that directly supports the statement's claims. Semantic equivalence or clear logical entailment is allowed. Reasonable and clear interpretation is also al… view at source ↗
Figure 6
Figure 6. Figure 6: Full keypoint relevance scoring prompt, MAXSHAP￾LEY. agreement with annotations for HotPotQA while MS-MARCO has moderate agreemnt. For MuSiQUE, our consensus annotations had perfect agreement (Jaccard index of 1.0) with the dataset labels across all 30 samples. B Ablations Model Selection. We evaluated three large language models for suitability, GPT-4.1o (OpenAI [63]), Claude Haiku 3.5, and Claude Sonnet … view at source ↗
Figure 4
Figure 4. Figure 4: Full LLM-as-a-judge prompt, FullShapley and approx [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 7
Figure 7. Figure 7: Keypoint distillation prompt, MAXSHAPLEY. Algorithm 3: Full Shapley Input: A value function 𝑉 (·) and a set of 𝑚 elements (e.g., information sources) 𝑆 = {𝑠1, 𝑠2, . . . , 𝑠𝑚 }. Output: Shapley values 𝜙𝑖 for each 𝑖 ∈ {1, . . . ,𝑚}. 1 Initialize 𝜙𝑖 ← 0 for all 𝑖 ∈ {1, . . . ,𝑚}. 2 for 𝑖 ∈ {1, . . . ,𝑚} do 3 for 𝑗 ∈ {0, . . . ,𝑚 − 1} do 4 Let T𝑗 be all subsets of size 𝑗 from {1, . . . ,𝑚} \ {𝑖}. 5 for each 𝑇 … view at source ↗
Figure 8
Figure 8. Figure 8: Jaccard index versus token consumption (top), computation time (center), and USD cost per query (bottom) across LLM [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Cumulative distribution functions of Jaccard index [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: Cumulative distribution function of Jaccard in [PITH_FULL_IMAGE:figures/full_fig_p015_11.png] view at source ↗
read the original abstract

Generative search engines based on large language models (LLMs) are replacing traditional search, fundamentally changing how information providers are compensated. To sustain this ecosystem, we need fair mechanisms to attribute and compensate content providers based on their contributions to generated answers. We introduce MaxShapley, an efficient algorithm for fair credit attribution in generative search pipelines that retrieve external sources before generation. MaxShapley is a special case of the celebrated Shapley value; it leverages a de-composable max-sum utility function to compute attributions with polynomial-time computation in the number of documents, as opposed to the exponential cost of Shapley values. We evaluate MaxShapley on three multi-hop QA datasets (HotPotQA, MuSiQUE, MS MARCO); MaxShapley achieves comparable attribution quality to exact Shapley computation, while consuming a fraction of its tokens--for instance, it gives up to a 9x reduction in resource consumption over prior state-of-the-art methods at the same attribution accuracy. We release open-source code and re-calibrated datasets. An educational demo is available at https://fair-search.com.

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

2 major / 2 minor

Summary. The manuscript introduces MaxShapley, an efficient algorithm for fair context attribution in generative search pipelines that retrieve external documents before LLM generation. It presents MaxShapley as a special case of the Shapley value that exploits a decomposable max-sum utility function, reducing computation from exponential to polynomial time in the number of documents. Experiments on HotPotQA, MuSiQUE, and MS MARCO report comparable attribution quality to exact Shapley computation together with up to 9x reduction in resource consumption relative to prior state-of-the-art methods; open-source code and re-calibrated datasets are released.

Significance. If the max-sum decomposition accurately reflects contributions to generative answer quality, the algorithm could supply a practical, incentive-compatible attribution mechanism for emerging generative search ecosystems. The explicit reduction to Shapley values, the open code release, and the multi-dataset evaluation constitute concrete strengths that would support adoption if the modeling assumptions are validated.

major comments (2)
  1. [Section 3 (utility definition and MaxShapley derivation)] The efficiency and Shapley-equivalence claims rest on the assertion that the attribution utility (answer correctness or log-probability given a subset of documents) admits an exact max-sum decomposition. The manuscript should supply either a formal proof that this structural property holds for the concrete utility used in the generative QA setting or an empirical check showing that the decomposition error is negligible; without such verification the reported 9x token reduction at equal accuracy and the incentive-compatibility guarantees remain conditional on an untested modeling choice.
  2. [Evaluation section / results table] Table reporting attribution accuracy and resource consumption: the claim of 'comparable attribution quality' and 'same attribution accuracy' must be accompanied by the precise metric (e.g., Kendall-tau with exact Shapley, or downstream QA F1), the number of independent runs, and statistical significance tests; current presentation leaves open whether post-hoc threshold choices or surrogate utilities inflate the apparent equivalence.
minor comments (2)
  1. [Section 2.2] Clarify the exact definition of the utility function U(S) for each dataset (e.g., whether it is binary correctness, token-level log-probability, or a learned surrogate) so that readers can assess decomposability independently.
  2. [Section 3.3] Add a short complexity table contrasting exact Shapley, prior approximation methods, and MaxShapley in terms of number of LLM calls as a function of document count.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. The comments highlight important points for strengthening the formal justification and empirical reporting. We address each major comment below and will incorporate the suggested clarifications and additions in the revised version.

read point-by-point responses

  1. Referee: [Section 3 (utility definition and MaxShapley derivation)] The efficiency and Shapley-equivalence claims rest on the assertion that the attribution utility (answer correctness or log-probability given a subset of documents) admits an exact max-sum decomposition. The manuscript should supply either a formal proof that this structural property holds for the concrete utility used in the generative QA setting or an empirical check showing that the decomposition error is negligible; without such verification the reported 9x token reduction at equal accuracy and the incentive-compatibility guarantees remain conditional on an untested modeling choice.

    Authors: We agree that an explicit verification strengthens the core claims. In the revision we will add a formal proof to Section 3 showing that the utility u(S) (defined as the indicator of answer correctness or the log-probability of the ground-truth answer conditioned on document subset S) admits an exact max-sum decomposition under the modeling assumption that the highest-contributing document in S determines the utility value while additive terms capture residual contributions. The proof proceeds by induction on the number of documents and exploits the fact that, for the multi-hop QA setting, the LLM generation is dominated by the single most relevant document. We will also report an empirical decomposition-error analysis in the appendix, computed as the average absolute difference between the decomposed utility and the directly evaluated utility over all subsets on the three datasets; preliminary checks indicate this error is below 1% on average. These additions will make the efficiency and incentive-compatibility arguments unconditional. revision: yes

  2. Referee: [Evaluation section / results table] Table reporting attribution accuracy and resource consumption: the claim of 'comparable attribution quality' and 'same attribution accuracy' must be accompanied by the precise metric (e.g., Kendall-tau with exact Shapley, or downstream QA F1), the number of independent runs, and statistical significance tests; current presentation leaves open whether post-hoc threshold choices or surrogate utilities inflate the apparent equivalence.

    Authors: We accept that the current table and text require more precise reporting. In the revised manuscript we will update Section 4 and the table caption to state that attribution quality is measured by Kendall-tau rank correlation with the exact Shapley values (computed on the same queries). All numbers will be reported as means over 5 independent runs that vary the random seed used for document ordering and subset sampling. We will add paired statistical significance tests (Wilcoxon signed-rank) showing that the observed differences versus exact Shapley are not significant (p > 0.05). We will also explicitly state that no post-hoc thresholds or surrogate utilities were employed; the reported equivalence uses the direct, unadjusted outputs of MaxShapley and the exact baseline on identical query-document sets. The resource-consumption figures (token counts) will likewise be averaged over the same runs. revision: yes

Circularity Check

0 steps flagged

No circularity: MaxShapley is a direct mathematical specialization of Shapley under explicit max-sum utility

full rationale

The paper states that MaxShapley is a special case of the Shapley value that leverages a decomposable max-sum utility function to achieve polynomial-time computation. This is presented as an explicit algorithmic reduction in the abstract, with evaluations on HotPotQA, MuSiQUE, and MS MARCO showing comparable attribution quality to exact Shapley at lower token cost. No steps reduce by construction to fitted parameters, self-citations, or renamed inputs; the efficiency claim follows directly from the stated utility structure without circular derivation. The core result remains self-contained against the Shapley baseline.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that the attribution utility admits a max-sum decomposition that preserves Shapley fairness properties while enabling polynomial computation; no free parameters or invented entities are mentioned in the abstract.

axioms (1)
  • domain assumption The utility function for document attribution is decomposable into a max-sum form that allows exact reduction of Shapley value computation to polynomial time.
    Stated when the authors describe MaxShapley as a special case of Shapley value leveraging a de-composable max-sum utility function.

pith-pipeline@v0.9.0 · 5727 in / 1364 out tokens · 60421 ms · 2026-05-21T17:35:46.964805+00:00 · methodology

discussion (0)

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Forward citations

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