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REVIEW 2 major objections 2 minor 13 references

Pluralistic Leaderboards

T0 review · 2 major / 2 minor · reviewed 2026-06-28 · grok-4.3

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Pith's one-line read A mechanism for LLM leaderboards achieves local stability to heterogeneous preferences with O(k) pairwise comparisons per user.

desk verdict The paper adapts local stability from social choice to LLM leaderboards and gives an O(k)-query mechanism that meets it, while showing BT can fail on LMArena data. read the letter →

arxiv 2606.02547 v1 pith:E2AL5ZW6 submitted 2026-06-01 cs.GT

Nika Haghtalab , Ariel D. Procaccia , Han Shao , Serena Lutong Wang , Kunhe Yang This is my paper · ORCID
classification cs.GT
keywords pluralisticleaderboardslocalstabilityBradley-TerrymodelLLMevaluationpairwisecomparisonssocialchoicetheoryheterogeneouspreferencesrankingaggregation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Standard Bradley-Terry aggregation fits a single latent score to all pairwise comparisons and produces one global ranking. This collapses distinct user preferences into one ordering that can systematically misrepresent groups favoring different model behaviors. The paper adapts local stability from social choice theory, requiring that no model outside the top-k set is preferred over that set by more than an O(1/k) fraction of users. It gives a mechanism that meets this condition while collecting only roughly O(k) comparisons from each user. On LMArena data the standard approach can violate the stability condition, while the new mechanism maintains it.

What carries the argument

Local stability, defined as the requirement that no model outside the reported top-k is preferred over the top-k set by more than an O(1/k) fraction of users, and the query-efficient aggregation procedure that enforces it.

What would settle it

A preference profile or LMArena subsample in which the mechanism's reported top-k set is collectively preferred over by more than an O(1/k) fraction of users.

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Extended reading notes

Core claim

The paper claims that an alternative leaderboard mechanism, built from social choice techniques, satisfies local stability—no model outside the top-k is collectively preferred to the top-k by more than O(1/k) of users—while eliciting only tilde O(k) pairwise comparisons per user, and that this holds on real LMArena comparison data where Bradley-Terry aggregation violates the condition.

Load-bearing premise

Local stability is the appropriate stability notion for LLM leaderboards and that LMArena pairwise data sufficiently represents the relevant heterogeneous user populations.

Editorial extensions

If this is right

  • The mechanism meets the local stability guarantee for any chosen prefix length k.
  • Only tilde O(k) comparisons per user are needed to produce the stable ranking.
  • Bradley-Terry aggregation can and does violate local stability on existing LLM comparison data.
  • The new procedure supplies measurably stronger stability than single-score aggregation.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Leaderboards could report stable sets rather than total orders, allowing different user cohorts to see different top models without extra data collection.
  • The same local-stability approach might transfer to ranking other AI systems or consumer products that serve heterogeneous populations.
  • If platforms adopted the method, evaluation costs could drop while still protecting against large-group misrepresentation.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 2 minor

Summary. The paper proposes pluralistic leaderboards for LLMs that achieve local stability (no outside model preferred to the top-k by more than O(1/k) fraction of users) for heterogeneous preferences, drawing on social choice theory. The mechanism elicits only ilde{O}(k) pairwise comparisons per user while satisfying the stability property, in contrast to standard Bradley-Terry aggregation which the authors show can violate local stability on LMArena data.

Significance. If the local-stability guarantee and the empirical contrast hold under the stated modeling assumptions, the work supplies an efficient, axiomatically grounded alternative to single-score leaderboards that respects preference heterogeneity. The ilde{O}(k) sample bound and the parameter-free character inherited from social choice are concrete strengths that could influence evaluation practice.

major comments (2)
  1. [Experimental evaluation / data-processing pipeline] The claim that standard Bradley-Terry aggregation violates local stability on LMArena data (abstract and experimental section) requires an auxiliary model to estimate the 'O(1/k) fraction of users' from anonymous pairwise votes that lack per-user longitudinal structure. The precise aggregation, clustering, or thresholding step used to operationalize collective preference must be stated explicitly and subjected to sensitivity checks; without this, the reported violation risks being an artifact of the auxiliary modeling choice rather than evidence against BT.
  2. [Theoretical analysis / mechanism definition] The local-stability guarantee and the ilde{O}(k) comparison bound (theoretical section) are load-bearing for the central contribution. The manuscript should verify that the mechanism satisfies the exact definition of local stability given in the paper (no outside model collectively preferred by >O(1/k) users) without hidden homogeneity assumptions, and that the bound remains valid under the heterogeneous population model used for the LMArena experiments.
minor comments (2)
  1. [Introduction] Add a short, self-contained paragraph in the introduction that recalls the precise definition of local stability before invoking it in the abstract claim.
  2. [Preliminaries] Clarify notation for the prefix size k and the hidden constants in the ilde{O}(k) bound when first introduced.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive feedback on the experimental pipeline and theoretical guarantees. We address each major comment below.

read point-by-point responses

  1. Referee: [Experimental evaluation / data-processing pipeline] The claim that standard Bradley-Terry aggregation violates local stability on LMArena data (abstract and experimental section) requires an auxiliary model to estimate the 'O(1/k) fraction of users' from anonymous pairwise votes that lack per-user longitudinal structure. The precise aggregation, clustering, or thresholding step used to operationalize collective preference must be stated explicitly and subjected to sensitivity checks; without this, the reported violation risks being an artifact of the auxiliary modeling choice rather than evidence against BT.

    Authors: We agree that the auxiliary modeling steps used to estimate the fraction of users from anonymous LMArena votes require explicit documentation. In the revised manuscript we will describe the precise aggregation, clustering, and thresholding procedures, and we will add sensitivity analyses over a range of parameter choices to show that the reported violation of local stability by Bradley-Terry aggregation is robust. revision: yes

  2. Referee: [Theoretical analysis / mechanism definition] The local-stability guarantee and the ilde{O}(k) comparison bound (theoretical section) are load-bearing for the central contribution. The manuscript should verify that the mechanism satisfies the exact definition of local stability given in the paper (no outside model collectively preferred by >O(1/k) users) without hidden homogeneity assumptions, and that the bound remains valid under the heterogeneous population model used for the LMArena experiments.

    Authors: The mechanism is taken from social-choice results that hold for arbitrary heterogeneous preference profiles and contain no homogeneity assumptions. We will add a short verification subsection confirming that the mechanism meets the paper's exact local-stability definition and that the ilde{O}(k) bound continues to hold when the underlying population is the heterogeneous model used in the LMArena experiments. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; derivation from external social choice literature

full rationale

The paper adapts local stability from social choice theory and designs a mechanism building on techniques from that literature, then tests the Bradley-Terry violation claim on independent LMArena data. No equations reduce results to fitted parameters defined by the same inputs, no self-definitional steps, and no load-bearing self-citations or uniqueness theorems imported from the authors' prior work are quoted or evident. The central theoretical guarantee and empirical demonstration remain self-contained against external benchmarks.

Assumptions & free parameters 0 free parameters · 1 assumptions · 0 invented entities

The central claim rests on adopting local stability as the target property and assuming pairwise comparisons suffice to identify preference clusters; no free parameters or new entities are introduced in the abstract.

assumptions (1)
  • domain assumption Local stability is a suitable stability criterion for leaderboards under heterogeneous preferences
    The paper selects this notion from social choice theory as the definition of a good pluralistic leaderboard.

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Cite this review

Pith. "Pith review of Pluralistic Leaderboards." pith.science (2026). https://pith.science/paper/E2AL5ZW6

@misc{pith2026260602547,
  author       = {Pith},
  title        = {Pith review of: Pluralistic Leaderboards},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/E2AL5ZW6}},
  note         = {Machine review of arXiv:2606.02547}
}
abstract

Recent leaderboard-based evaluations of large language models aggregate user feedback by fitting a Bradley--Terry model to pairwise comparisons, producing a single global ranking based on a latent quality score. While appealing for its simplicity, this approach is incompatible with heterogeneous preferences: when LLMs are used across diverse tasks and use cases, users who favor fundamentally different model behaviors can be systematically misrepresented when collapsed into a single quality score. To address this issue, we study \emph{pluralistic leaderboards} that aim to remain \emph{stable} with respect to heterogeneous user populations. Drawing on ideas from social choice theory, we adapt the notion of \emph{local stability}, which requires that no model outside the top-$k$ positions is collectively preferred to the top-$k$ set by more than $O(1/k)$ fraction of users. Building on techniques from the social choice literature, we design an alternative leaderboard mechanism that satisfies local stability while eliciting only $\widetilde{O}(k)$ pairwise comparisons per user, where $k$ is the size of the prefix for which stability is guaranteed. Using data from LMArena, we show that standard Bradley--Terry aggregation can violate local stability in practice, whereas our method provides substantially stronger stability guarantees.

Figures

Figures reproduced from arXiv: 2606.02547 by the authors.

Figure 1
Figure 1. Comparison on mixtures of Mallows of the stability of committees produced by Algorithm 1 and the two described baseline methods. For each k, a mixture of Mallows model is created with k central rankings sampled uniformly at random, and a committee of size k is produced by each method. Values of γˆ ≤ 1 indicate that the committee produced was stable. The plotted points and error regions show the mean and standard err… view at source ↗
Figure 2
Figure 2. Comparison on LMArena-based simulation of the stability of Bradley-Terry rankings [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Histogram of pairwise comparisons per user for a single run of Algorithm 1 for committee [PITH_FULL_IMAGE:figures/full_fig_p024_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Histogram of pairwise comparisons per user for a single run of Algorithm 3 on LMArena [PITH_FULL_IMAGE:figures/full_fig_p024_4.png]
Figure 5
Figure 5. Figure 5: Histogram of pairwise comparisons per user for a single run of Algorithm 3 on LMArena [PITH_FULL_IMAGE:figures/full_fig_p025_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

13 extracted references · 1 canonical work pages

  1. [1]

    Voting procedures

    1, 2, 5 Michael Dummett. Voting procedures. 1984. 6, A Edith Elkind, Piotr Faliszewski, Piotr Skowron, and Arkadii Slinko. Properties of multiwinner voting rules.Social Choice and Welfare, 48(3):599–632, 2017. 4 S. Fish, P. G¨ olz, D. C. Parkes, A. D. Procaccia, G. Rusak, I. Shapira, and M. W¨ uthrich. Generative social choice. InProceedings of the 25th A...

    1984

  2. [2]

    Prompt-to-leaderboard: Prompt-adaptive LLM evaluations

    1 13 Evan Frick, Connor Chen, Joseph Tennyson, Tianle Li, Wei-Lin Chiang, Anastasios Nikolas Angelopoulos, and Ion Stoica. Prompt-to-leaderboard: Prompt-adaptive LLM evaluations. In Proceedings of the 42nd International Conference on Machine Learning (ICML), 2025. 1 L. Ge, D. Halpern, E. Micha, A. D. Procaccia, I. Shapira, Y. Vorobeychik, and J. Wu. Axiom...

    work page arXiv 2025

  3. [3]

    The distributions{D c}c∈[m′] arek-indistinguishable, and

  4. [4]

    We extend each Dc to a distribution eDc ∈ ∆(Sym(C)) by appending the remaining candidates {m′ + 1,

    In each distribution Dc, candidate c is the unique candidate in A whose plurality score exceeds 1 m′ : pluDc(c) := Pr i∼D [c≻ i A\ {c}]> 1 m′ ; whereasplu Dc(a)< 1 m′ ,∀a∈A\ {c}. We extend each Dc to a distribution eDc ∈ ∆(Sym(C)) by appending the remaining candidates {m′ + 1, . . . , m} to the bottom of every ranking in a fixed order. Formally, if σi ∼ D...

    2020

  5. [5]

    Set mixture weights to 1 k, and set all dispersions to the same givenϕ

    Sample k permutations uniformly at random and set these as centers π1, ..., πk. Set mixture weights to 1 k, and set all dispersions to the same givenϕ

  6. [6]

    Run Algorithm 1 with default parameters to produce a committee of size k. Figure 3 gives a breakdown of the samples drawn for an example run, which sampled 18 , 540 users at a maximum of 98 pairwise comparisons per user, and a median of 38 pairwise comparisons per user

  7. [7]

    Compute the Bradley-Terry ranking over a sample of 10, 000 users and all pairwise comparisons for each user, and produce a committee of sizekconsisting of the top-kranked candidates

  8. [8]

    Mallows centers

    Produce a committee consisting of {π1(1), ..., πk(1)} (labeled “Mallows centers” in Figure 1)

Show all 13 references
  1. [9]

    D.3 Additional details for experiments on ranking stability with LMArena simulation (Section 5.2) To produce the plots in Figure 2, we run the following procedure 5 times:

    Draw a sample ofn= 10,000 users, and compute ˆγfor all committees. D.3 Additional details for experiments on ranking stability with LMArena simulation (Section 5.2) To produce the plots in Figure 2, we run the following procedure 5 times:

  2. [10]

    Run Algorithm 2 with default parameters over the data distribution to produce a ranking. Figure 4 gives a breakdown of the samples drawn for an example run, which sampled 39 , 080 users at a maximum of 95 pairwise comparisons per user, and a median of 24 pairwise comparisons per user

  3. [11]

    Run Algorithm 3 with default parameters over the data distribution to produce a ranking. Figure 5 gives a breakdown of the samples drawn for an example run, which sampled 74 , 150 users at a maximum of 45 pairwise comparisons per user, and a median of 5 pairwise comparisons pe...

    2000

  4. [12]

    This is equivalent to ranking by Borda count over all sampled users, and is also equivalent to ranking by Elo-score over all possible pairwise comparisons from all sampled users

    Compute the Bradley-Terry ranking over a sample of 100, 000 users and all pairwise comparisons for each user. This is equivalent to ranking by Borda count over all sampled users, and is also equivalent to ranking by Elo-score over all possible pairwise comparisons from all sam...

  5. [13]

    Compute the stability approximation factors ˆγfor all top- k prefix committees of all rankings using a draw ofn= 100,000 users. D.4 Specific model rankings on LMArena simulation Here we give more details the specific Bradley-Terry rankings per category from the LMArena data th...

    2025

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Reviewed June 28, 2026 · model on record in the stance chip above.