{"id":"c10e0ce5-8edd-483a-98f3-adbd303d262a","arxiv_id":"2502.07166","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"high","formal_verification":"none","parameter_count":5,"one_line_summary":"SBO estimates an unknown social influence graph from paired public and private votes, then debiases cheap public votes to find the aggregation-maximizing consensus with few expensive private queries.","lead":"This paper introduces Social Bayesian Optimization (SBO), an algorithm for group decisions that combines cheap public votes, which may be distorted by social influence, with a few expensive private votes that reveal true preferences. The authors claim SBO learns the social influence graph fast enough to stop using private votes early while still converging to the consensus that would be reached without influence.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The private-vote sample-complexity proof in Appendix E.6.2 yields O(T^{4q}), not the O(T^q) stated in Tables 1 and 2; with the paper's q=1/2, the lower-cost guarantee is not established.","rationale":"The reader's verdict is REJECT, with high correctness risk. The reader's weakest_assumption focuses on identifiability of the linear graph from noisy pairwise votes, but the reader's rationale also lists the private-vote sample-complexity mismatch with q = 1/2. I agree that the private-vote complexity contradiction is the most direct threat to the central claim, because the claim 'social graph estimation converges faster... allowing us to reduce reliance on costly private votes' is literally the assertion that |Qu_T|/T -> 0 for the algorithm as run. The proof in Appendix E.6.2, if correct, gives |Qu_T| = O(T^{4q} ...), requiring q <= 1/4, yet the paper fixes q = 1/2. The Tables 1 and 2 quote a T^q rate that does not come from the derivation. This is not a matter of disagreement with a research community or a stylistic choice; it is an internal inconsistency in the formal guarantee. A second supporting issue is the graph-identification theorem: Appendix E.8 has the strong-convexity constant m in the numerator after 'MER >= (m/2)||Ahat-A||^2', whereas solving the inequality puts m in the denominator; this affects the claimed O(|Qu_t|^{-1/2}) graph rate and its constants. The impossibility theorem proof also uses dictatorial matrices with zero entries, violating the model's strict positivity constraint Aij > 0, so that separate theorem is not proven as stated. These multiple formal gaps independently support the REJECT verdict. I do not see independent evidence that would rescue the central guarantee: the experiments are simulations with synthetic vote generators and utility models, not human-subject data, and no formal verification or released reproducible code is provided. The correct response is therefore to keep the reader's REJECT verdict rather than downgrading to CONDITIONAL, because the main proof chain is currently broken at the point where the central cost claim is established.","tokens_in":51033,"tokens_out":7169,"duration_ms":68022,"concrete_test":"Independently re-derive Eqs. (106)-(110) of Appendix E.6.2 without simplification: substitute the definition of βu_T into the inequality |Qu_T| <= T^q sqrt(βu_T γuu_T |Qu_T|), solve for |Qu_T|, and evaluate with q = 1/2. If the resulting exponent is 4q = 2 rather than the q = 1/2 appearing in Tables 1 and 2, then the private-vote complexity row is unsupported and the claimed lim |Qu_T|/T = 0 does not follow. A complementary check is to simulate Algorithm 1 on the two-agent example of Appendix H.1 for T = 1000 with q = 1/2 and count |Qu_T|/T.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's headline claim is that SBO reaches a social-influence-free consensus at lower cost, formalized as |Qu_T|/T -> 0 for the number of expensive private votes. The only derivation of this quantity is in Appendix E.6.2, Eqs. (106)-(110). Starting from the stopping rule, the proof obtains |Qu_T| <= T^q Σ_{t in Qu_T} 1/t^q <= T^q Σ wu_t, then Theorem E.3 and the definition of βu_T give |Qu_T| <= O(T^q |Qu_T|^{3/4} (γuu_T log T N/δ)^{1/4}). Solving this inequality yields |Qu_T| = O(T^{4q} (γuu_T)^2 log T N/δ). The proof explicitly concludes that sublinearity requires q <= 1/4. However, Theorem 3.5 / Table 1 and Table 2 report |Qu_T| = O(T^q (γvv_T)^2 log T N/δ), and Section 3.4 and the experiments set q = 1/2. With q = 1/2, the proven T^{4q} factor is T^2, which is not sublinear and gives no private-vote savings. Furthermore, Theorem 3.6's pointwise utility bound O(|Qu_T|^{-1/4}) is looser than the q = 1/2 stopping threshold 1/t^{1/2}, so nothing in the proof guarantees that private queries stop at a vanishing frequency. Since the central claim is exactly that the algorithm provably reduces reliance on costly private votes, this algebraic mismatch is load-bearing.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes Social Bayesian Optimization (SBO), a dual-voting algorithm for collective decision-making under social influence. It models social influence as an unknown row-stochastic graph convolution v = Au, combines cheap public votes with expensive private votes, and claims (i) an impossibility theorem for groupthink-proof aggregation, (ii) a no-regret bound on cumulative regret, and (iii) sublinear sample complexity of private votes. The theoretical results are supported by several appendices and evaluated on synthetic and real-world tasks.","tokens_in":51451,"tokens_out":6208,"duration_ms":55371,"significance":"The problem of reaching a consensus free of social influence is timely and practically relevant, and the dual public/private voting mechanism is an interesting formulation. If the theoretical claims were correct, the paper would make a useful contribution to preferential Bayesian optimization and social-choice-inspired algorithm design. The authors also provide a wide experimental evaluation across four real-world tasks. However, the central theoretical guarantees are not established as written: the private-vote sample-complexity proof contradicts the paper's own tables, the impossibility proof uses matrices outside the admissible model, and the graph-identification proof contains an algebraic error. These issues are load-bearing for the main claims.","major_comments":[{"comment":"The proof of the private-vote sample complexity in Appendix E.6.2 derives |Qu_T| = O(T^{4q} (γuu'_T)^2 log T N/δ), and explicitly concludes that sublinearity requires q ≤ 1/4. However, Table 1 and Table 2 report |Qu_T| = O(T^q (γvv'_T)^2 log T N/δ), and Section 3.4 and the experiments set q = 1/2. With q = 1/2, the derived bound is O(T^2), which is not sublinear and gives no private-vote savings. This directly contradicts the central claim that SBO reduces reliance on costly private votes while maintaining no-regret.","section":"Appendix E.6.2, Eqs. (106)-(110), Table 1, Table 2"},{"comment":"The impossibility proof considers the set G_dictatorial = {G_i | A_jk = I{i=k}} whose adjacency matrices have zero off-diagonal entries. This violates the strict positivity requirement A_ij > 0 in Eq. (3) for the social-influence model. The proof therefore establishes impossibility for a class of graphs outside the model, not for the model asserted in the paper. The theorem may be repairable by a limiting argument with ε-perturbations, but as written the proof is not sound.","section":"Appendix C.2, proof of Theorem 3.3"},{"comment":"The derivation of the graph-identification rate contains an algebra error. From MER ≥ (m/2)||Â - A||^2 and MER ≤ O(n^2/|Qu_t|), the correct conclusion is ||Â - A||^2 ≤ O(n^2/(m|Qu_t|)), not O(m n^2/|Qu_t|). The paper's subsequent choice m ≈ 1/n^2 yields, with the correct formula, ||Â - A|| = O(n^2/√|Qu_t|) rather than the claimed O(1/√|Qu_t|). The claimed faster graph-learning rate and the stated q = 1/2 optimality are therefore not established.","section":"Appendix E.8.3, Eqs. (131)-(140)"},{"comment":"Condition (c) assumes A is identifiable from votes, and Lemma B.5 proves identifiability from full-rank exact utility pairs (u(xτ, :), v(xτ, :)). The algorithm, however, collects noisy Bernoulli comparisons at adaptively chosen pairs (x_t, x_{t-1}); it is not shown that such data identify A, nor that the adaptive query process guarantees the full-rank condition. The identifiability assumption is load-bearing for both the graph-estimation theorem and the debiasing step, and the paper does not bridge this gap.","section":"Section 3.4, condition (c); Lemma B.5"},{"comment":"The regret bound in Theorem 3.5 relies on Assumptions E.7 and E.8, which assert pointwise inequalities of the optimistic estimate and a Lipschitz property of sorting-induced weight differences. These assumptions are stated as postulates rather than derived from the model; the justification for E.7 via monotonicity does not imply the needed pointwise dominance at both x_t and x_{t-1}. Since Lemma E.11 and the main regret bound depend on these assumptions, the no-regret claim is conditional on assumptions that remain unverified.","section":"Appendix E.5.2, Assumptions E.7 and E.8"}],"minor_comments":[{"comment":"The word 'findigns' should be 'findings'.","section":"Abstract"},{"comment":"'Bradly-Terry' is a typo; the standard name is Bradley-Terry.","section":"Assumption 2.2"},{"comment":"'Tiknohov' should be 'Tikhonov'.","section":"Table 5"},{"comment":"The figure captions are missing the legend for some curves; consider adding a consistent legend across Figures 4-8.","section":"Section 5 and Figure 4"},{"comment":"The social-influence matrix for Thermal comfort repeats in EnergyTrading; if this is intentional, state it explicitly to avoid confusion.","section":"Appendix H.2.1"}],"recommendation":"major_revision","confidential_remarks":"The manuscript has several internal inconsistencies that a careful reader will notice quickly; the authors should be asked to reconcile the private-vote complexity bound, correct the algebra in the graph-identification proof, and justify the identifiability and acquisition assumptions. The paper is not yet ready for acceptance, but the core idea is salvageable with a substantial revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper introduces a genuinely new problem—consensus-building under social influence via dual public/private votes with an unknown influence graph—and the SBO algorithm is clearly described and sensibly motivated. The writing is good, and the experiments, while only synthetic, cover several plausible real-world tasks. That is real value.\n\nThe theoretical core, however, does not hold as written. Two load-bearing algebraic mistakes invert the main claims. First, the private-vote sample complexity derivation in Appendix E.6.2 yields |Qu_T| = O(T^{4q} ...), not the O(T^q) reported in Theorem 3.5 and Table 1. The appendix even states that sublinearity requires q ≤ 1/4, while the main text claims 0 < q < 1 and the experiments set q = 1/2. With q = 1/2, the proven bound is T^2, which gives no private-vote savings. This directly contradicts the paper's headline promise that SBO provably relies less on costly private votes.\n\nSecond, the graph identification bound in Appendix E.8.3 has the strong-convexity constant m on the wrong side. From MER ≥ (m/2)||Â - A||^2 and MER ≤ O(n^2/|Qu|), you get ||Â - A||^2 ≤ O(n^2/(m |Qu|)), not O(m n^2/|Qu|). With their chosen m ≈ 1/n^2, the correct bound grows with n^2 instead of vanishing at the claimed rate. The asymptotic graph-identification argument collapses. There is also a smaller problem: the impossibility theorem's proof uses dictatorial graphs with zero entries, which violate the strict positivity of Eq. (3). That one is probably patchable by taking a limit, but it is not valid as written.\n\nThe exponential-family likelihood and graph prior are standard, and the citations look appropriate. The problem is not circularity; the flaws are concrete mathematical errors. Because these errors sit at the heart of the paper's guarantees, I would not cite it as a reliable result right now. I would, however, send it to referees rather than desk-reject: the problem formulation is novel enough that a careful revision could be publishable, and reviewers can point to exactly what needs fixing.","headline":"Novel problem setup and clear algorithm, but the central cost-saving guarantee is undone by two algebra errors in the appendix; reject as written, worth a careful revision.","tokens_in":51962,"tokens_out":3900,"would_cite":false,"duration_ms":36399,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Social Bayesian Optimization can reach a social-influence-free consensus mostly from cheap public votes by learning the social graph faster than the utilities themselves.","keywords":["social Bayesian optimization","consensus building","social influence","dual voting","graph convolution","preference learning","no-regret learning","groupthink"],"falsifier":"Run SBO on synthetic agents whose true influence is nonlinear, for example $v(x,i) = \\sigma(\\sum_j A_{ij}u(x,j))$, while keeping utilities in the same RKHS family; if the private-vote fraction $|Q^u_T|/T$ fails to vanish or the cumulative regret stops converging under the same identifiability condition, the linear-convolution premise is falsified.","tokens_in":50801,"feed_emoji":"🗳️","tokens_out":9646,"duration_ms":87550,"temperature":0.7,"pith_summary":"The paper claims that group consensus can be found without paying for private votes most of the time, despite public votes being distorted by social influence. It first proves an impossibility theorem: with noisy feedback alone, no aggregation rule can be guaranteed to preserve the social-influence-free consensus unless everyone already agrees on the best option. To get around that, it introduces Social Bayesian Optimization, which uses a cheap public vote and an expensive private vote for the same pairwise comparison, models the influence as an unknown graph convolution $v = Au$, and estimates both the graph and the utilities from the two vote streams. The main guarantee is that when the influence graph is identifiable, the cumulative regret $R_T/T$ and the fraction of private votes $|Q^u_T|/T$ both go to zero as $T\\to\\infty$, because the graph estimate converges at a faster rate than the utility estimates. If the guarantee holds, a facilitator can mostly run show-of-hands votes and still converge to the consensus of the true aggregated preferences.","feed_headline":"Dual voting reaches group consensus while cutting private votes to zero","feed_subtitle":"Cheap public votes are debiased with a learned social graph, so costly one-on-one interviews stop being needed.","key_machinery":"The load-bearing identity is the graph convolution $$v(\\cdot,:)^{\\top} = A u(\\cdot,:)^{\\top},$$ with $A$ a row-stochastic, strictly positive adjacency matrix; the algorithm treats private utilities $u$ and public utilities $v$ as linked by this unknown $A$. The rest of the machinery is optimistic MAP: confidence sets of utility functions whose log posterior lies near the MAP estimate, an acquisition function that maximizes the upper confidence bound of social-utility improvement, and a stopping criterion $w_t^u(x_t,x_{t-1})$ that stops querying private votes once the graph is sufficiently well estimated.","core_discovery":"The central claim is that the influence-free consensus $x^\\star$ is reachable without sustained private voting. Under the dual voting design, public votes follow the corrupted utility $v$, private votes follow the truthful utility $u$, and the link is the linear convolution $v(\\cdot,:)^{\\top} = A u(\\cdot,:)^{\\top}$ with an unknown row-stochastic adjacency matrix $A$. The paper proves that if $A$ is identifiable from the votes, SBO has no-regret cumulative regret and its private-vote complexity satisfies $|Q^u_T|/T\\to0$, because the graph identification error decays like $|Q^u_t|^{-1/2}$, faster than the pointwise utility error $|Q^u_t|^{-1/4}$. This is the precise sense in which cheap public votes can replace expensive private votes after an initial learning phase.","pith_inferences":["The model's symmetry in $u$ and $v$ leaves implicit a reverse application: if public discussion corrects individual mistakes rather than corrupting them, the same graph convolution could turn cheap public votes into the signal and private votes into a calibration check.","A natural stress test beyond the paper is to replace the linear graph convolution with a nonlinear or time-varying influence mechanism and observe whether the faster graph-learning rate and vanishing private-vote fraction still hold.","The identification-rate gap between $|Q^u_t|^{-1/2}$ and $|Q^u_t|^{-1/4}$ suggests the economic value of the method comes from recovering a low-dimensional linear structure, so the practical benefits should shrink as the influence process becomes more complex."],"forward_implications":["With an identifiable influence graph, SBO is no-regret: the average error between its consensus estimate and the true social optimum vanishes as $T\\to\\infty$.","The number of expensive private votes grows sublinearly, so a facilitator can eventually stop one-on-one interviews and rely on public votes debiased by the learned graph.","If the graph is known and invertible, only public votes are needed, giving $|Q^u_T|=0$, but estimation noise is amplified by up to $\\|A^{-1}\\|\\le n$.","If the graph is not identifiable, the guarantee reverts to private-votes-only behavior with linear private-vote complexity, so identifiability is exactly what buys the cost saving.","The decay parameter $q$ trades convergence speed against the number of private votes, and the experiments set $q=1/2$ as a practical balance."],"supporting_citations":[{"why":"Supplies the Bernoulli pairwise-comparison likelihood that both public and private votes are assumed to follow.","marker":"Bradley and Terry [1952]"},{"why":"Supplies the likelihood-ratio confidence sets and regret-bound machinery that SBO's optimistic MAP analysis builds on.","marker":"Xu et al. [2024a]"},{"why":"Supplies the optimistic GP-UCB acquisition template and no-regret style that Algorithm 1 follows.","marker":"Srinivas et al. [2010]"},{"why":"Supplies the generalized Gini social-welfare aggregation function that interpolates utilitarian and egalitarian consensus rules.","marker":"Sim et al. [2021]"},{"why":"Supplies the minimum-excess-risk convergence rate used to show that graph identification error decays faster than utility estimation error.","marker":"Xu and Raginsky [2022]"},{"why":"Supplies the information-gain lemma used to turn summed confidence widths into the cumulative regret bound.","marker":"Chowdhury and Gopalan [2017]"},{"why":"Supplies the maximum information gain bounds used for the kernel-specific regret rates in Table 2.","marker":"Kandasamy et al. [2015]"}],"fun_headline_variants":["Debiased public votes replace costly private polling for group consensus","Social graph learning makes cheap votes as good as private ones","Bayesian optimizer cuts private votes by learning social influence","Group consensus via dual voting: private votes go to zero","Influence-free consensus from noisy public votes alone"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The debiasing step collapses if social influence is not exactly a fixed linear mixture of the agents' true utilities, written $v = Au$, that is recoverable from the noisy public and private vote pairs the algorithm collects; nonlinear, time-varying, or unidentifiable influence would break the graph-learning speedup.","fun_headline_variants_meta":{"raw":{"variants":["Debiased public votes replace costly private polling for group consensus","Social graph learning makes cheap votes as good as private ones","Bayesian optimizer cuts private votes by learning social influence","Group consensus via dual voting: private votes go to zero","Influence-free consensus from noisy public votes alone"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000621,"raw_usage":{"total_tokens":2875,"prompt_tokens":940,"completion_tokens":1935,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":556,"completion_tokens_details":{"reasoning_tokens":1856}},"tokens_in":556,"tokens_out":1935,"duration_ms":12614,"temperature":1.0,"reasoning_tokens":1856,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T13:35:35.359869+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run SBO on synthetic agents whose true influence is nonlinear, for example $v(x,i) = \\sigma(\\sum_j A_{ij}u(x,j))$, while keeping utilities in the same RKHS family; if the private-vote fraction $|Q^u_T|/T$ fails to vanish or the cumulative regret stops converging under the same identifiability condition, the linear-convolution premise is falsified.","supporting_citations":[],"review_version":1}