{"id":"8aa44396-8ad4-48a5-a257-ad547d9f23e7","arxiv_id":"2508.17489","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A dynamic paragraph-voting model for collaborative documents is shown to have a fundamental trade-off between social welfare and stability, and simulations with LLM agents map Pareto-optimal aggregation rules.","lead":"This paper proposes a voting mechanism for groups to co-write a document one paragraph at a time, with agents proposing and voting on paragraphs. It proves that no rule can simultaneously maximize voter satisfaction and guarantee the document stops changing, then uses simulations to map rules that trade one goal against the other.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The claimed stability–welfare balance is measured with a finite-horizon update-frequency proxy, not the formal Definition 8 stability; exponential smooth rules never lock, so 'rapid convergence' is not established.","rationale":"The reader's CONDITIONAL verdict is appropriate, but the weakest assumption is not the additive satisfaction model. The additive utility assumption is a modeling choice, explicitly scoped to the paper's formal definitions, and the impossibility theorem is conditional on it in the usual way. The load-bearing gap is internal: the theoretical stability property (Definition 8) and the experimental stability metric (Definition 13) are different, and the paper's headline positive claim depends on the experimental metric. For exponential smooth rules, the score of a newly proposed paragraph is always 1 because Fexp_alpha(1,t)=1; hence a new proposal after any supposed stabilization point changes the output. This is not merely a missing error bar or a need for more seeds; it is a definitional mismatch that affects what the simulations can demonstrate. The theoretical results themselves appear correct: the RM characterization follows from the additive decomposition of satisfaction, and Observation 1 can be justified by flipping the current approvers (or disapprovers) on a paragraph, so Corollary 1 stands. The stable versatile non-static CCR in Appendix C shows the design space is nonempty, but that rule is not the smooth family used in the Pareto experiments. A long-horizon lock-in test, together with the adversarial fresh-proposal perturbation, would settle whether the 'rapid convergence' claim survives. If it does not, the paper should be reframed as studying finite-horizon update frequency, not formal stability; this is a conditional acceptance issue rather than a rejection of the theoretical core.","tokens_in":18207,"tokens_out":21428,"duration_ms":253423,"concrete_test":"Take a reported smooth configuration, e.g., SCSF[APS, |E|, t, Fexp_alpha=0.1] with threshold 0.5. Run event lists to 10,000 events under the same scheduler and compute the update rate in the last window of 1,000 events. Separately test Definition 8 directly: for a candidate stable prefix E', append a fresh proposal (a, p*, +1) for a paragraph p* not in P(E'), then enough downvote events to lower APS(p*) below the threshold; record whether the output changes. If the last-window update rate is bounded away from 0, or the fresh-proposal step changes the output, the configuration is not stable in the formal sense. The Pareto analysis should then be re-run using a true lock-in criterion instead of stability[updates], and 'rapid convergence' must be qualified.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The impossibility result (Theorem 1, Observation 1, Corollary 1) is sound, but the paper's positive claim—that CCRs, especially smooth rules, balance welfare and stability—is not connected to the formal stability notion used in the impossibility. In experiments, 'stability' is measured by stability[updates] = (|E| - U(R,E)) / |E| (Definition 13), i.e., the fraction of event steps with no output change over a fixed finite horizon. Definition 8, by contrast, requires a finite extension E' after which no further extension can change the output. These are different properties. For the exponential smooth family SCSF[Cs,param,t,Fexp_alpha] with Fexp_alpha(x,t) = x * e^{-t*alpha*(1-x)} (Section 4.5), a paragraph proposed after any alleged freezing point has x=1 and therefore score Fexp_alpha(1,t)=1. Under the threshold x=1/2 used throughout, that paragraph is immediately included. Thus no finite E' can make a smooth rule insensitive to a later proposal event plus subsequent downvotes; the output can always be changed. Consequently, every smooth rule in the reported Pareto analysis fails Definition 8 stability. The simulation plots show update frequency under one scheduler, not convergence. The abstract's 'rapid convergence to a high social welfare collaborative text' is therefore unsupported by the reported metric, and ranking rules by this proxy may differ from ranking them by true lock-in.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces a formal model of collaborative document writing in which agents propose paragraphs and vote on existing ones, and an aggregation rule maps the event list to a set of included paragraphs. The central theoretical results are: (i) a rule maximizes the paper's additive satisfaction-based social welfare objective if and only if it is a relative majority (RM) rule (Theorem 1); (ii) no RM rule satisfies the paper's eventual lock-in notion of stability (Observation 1); hence no rule is simultaneously SWM and stable (Corollary 1); and (iii) no versatile static consensus-conditioned rule (CCR) is stable (Theorem 2). The paper then proposes harsh and smooth dynamic CCRs and reports agent-based simulations, including LLM-driven agents, in which rules are compared on a normalized stability proxy (the fraction of event steps with no document update) and normalized community satisfaction. The simulations are used to claim that smooth rules achieve a good balance between the two goals and that the process rapidly converges to a high-welfare text.","tokens_in":18560,"tokens_out":9319,"duration_ms":95589,"significance":"The theoretical part is clean and correct as far as it goes. The characterization of SWM rules, the impossibility corollary, and the proof that versatile static CCRs are unstable are nontrivial and well suited to a social-choice audience. Appendix C's concrete example of a versatile, stable non-static CCR is a nice complement to Theorem 2, and Appendix D verifies the monotonicity and amendability properties of exponential smoothing functions by elementary calculus. The simulation infrastructure is described in considerable detail, including the LLM prompts, which is a strength. However, the advertised positive message—that smooth rules balance stability and welfare—is not supported by the evidence presented. The simulation metric is a finite-horizon update frequency, not the formal stability notion used in the impossibility theorems, and smooth rules in fact never lock in. With five repetitions and no error bars, the empirical claims are also not statistically grounded.","major_comments":[{"comment":"The stability metric used in all simulations, stability[updates] = (|E| − U(R,E))/|E|, is not a proxy for Definition 8 stability. For any exponential smooth rule SCSF[Cs,param,t,Fexp_alpha], a newly proposed paragraph p has score 1 under APS and RAPS at the moment of proposal (the proposer is the only voter, so p+_r > 0 and p−_r = 0), and therefore Fexp_alpha(1,t) = 1. With the threshold x = 1/2 used throughout, the paragraph is immediately included, and subsequent downvotes can remove it. Consequently, for every such rule and every finite extension E′, there is a further extension that changes the output; no smooth rule satisfies Definition 8. Thus the Pareto frontiers in Figures 3 and 4 and the abstract's 'rapid convergence' statement do not provide evidence about the formal stability objective that appears in Corollary 1. The authors should either explicitly define and analyze a weaker 'bounded update frequency' notion, or modify the rule family so that the formal lock-in property is actually achieved.","section":"§4.5 and §5.1 (Definition 13 vs Definition 8)"},{"comment":"The positive conclusions of the simulation study rest on five repetitions per configuration with no error bars, confidence intervals, or significance tests. For instance, the claim in §5.3 that the bimodal population 'exhibits a wider Pareto front' and the claim in §5.4 that longer event lists 'offer broader satisfaction-oriented configurations' are presented without any measure of variance or a statistical comparison of rules. No code or data archive is referenced, so the experiments are not reproducible. Since these simulations are the sole evidence for the paper's central claim that smooth rules achieve a good balance, this is a load-bearing weakness.","section":"§5.2–5.4"}],"minor_comments":[{"comment":"The necessity direction assumes that R and an RM rule differ on exactly one paragraph p; if R is not an RM rule, the instance may have multiple differing paragraphs. The proof can be repaired by constructing an RM rule that agrees with R on all other paragraphs via tie-breaking, but the text should state this construction explicitly.","section":"Appendix A.1 (proof of Theorem 1)"},{"comment":"The notation 'SCSF[Cs,param,t,Fα] := Fα(Cs(p,E),tparam) → [0,1]' conflates a function with its value; it should read 'SCSF[Cs,param,t,Fα](p,E) = Fα(Cs(p,E), param(E))', and the symbol 'tparam' is never formally defined (in Example 4 it is written as t|E|).","section":"Definition 17"},{"comment":"Agent satisfaction is undefined when Na = 0 because of division by Na; the paper should specify the convention for agents who have voted on no paragraphs (e.g., they contribute zero to community satisfaction).","section":"Definition 3"},{"comment":"The text states that the threshold x = 1/2 is used throughout, but Example 5 in §5.4 evaluates CCR[APS,0.7]; the authors should reconcile this inconsistency.","section":"§5.1"},{"comment":"The derivatives of Fexp_alpha with respect to t and α are nonpositive, not strictly negative, at boundary values such as x = 0, x = 1, or α = 0; the text should say 'nonpositive' rather than 'negative'.","section":"Appendix D.2"},{"comment":"The versatile stable rule in Appendix C locks the document after a designated abstention event on a special paragraph p*, which is a very weak notion of stability; the paper should discuss why such a rule is not a desirable resolution of the impossibility result.","section":"Appendix C"},{"comment":"The statement 'our simulation framework has proven to be effective' is too strong given the absence of error bars and the small number of repetitions; 'appears to be effective' would be more appropriate.","section":"§6"}],"recommendation":"major_revision","confidential_remarks":"The formal impossibility results are sound but fairly narrow, and the empirical section currently oversells the smooth rules by using an update-frequency proxy in place of the formal stability definition. The paper could become suitable for publication after a substantial revision that either proves a formal stability guarantee for a modified rule family or explicitly reframes all positive claims in terms of update frequency and adds proper statistical support. I would not support acceptance in its current form."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nHere's the short version: the theoretical core of this paper is solid, but the abstract oversells the simulations. The impossibility result—no aggregation rule over this dynamic paragraph-voting model can be both social-welfare-maximizing and stable—is a clean, correct piece of computational social choice. The characterization of SWM rules as relative majority rules (Theorem 1) and the proof that no versatile static CCR is stable (Theorem 2) are the real contributions. The dynamic model itself, with proposals and votes on an unordered paragraph set, is a reasonable stylization of collaborative constitution drafting.\n\nCredit where it's due. The proofs in Appendix A are complete; the exponential smoothing properties in Appendix D are verified by straightforward calculus. The CCR family, especially the harsh/smooth distinction, gives a structured way to explore the welfare-stability trade-off. The appendix describes the experimental setup in detail, including prompts and a census-based agent population.\n\nNow the soft spots, in proportion. The stress-test note is on target. The 'stability' measured in the simulations is not Definition 8 stability. They report the fraction of event steps with no output change over a fixed horizon (Definition 13), but formal stability requires a finite extension after which no further extension can change the output. Smooth exponential rules never satisfy that: a later proposal event for a new paragraph has x=1, the smoothing function gives it score 1, and under threshold 1/2 it enters the document immediately. So 'rapid convergence' in the abstract is unsupported. This does not kill the theory paper, but it does mean the empirical section cannot support the claim that smooth rules balance stability and welfare.\n\nThe simulation evidence is also thinner than it should be: five repetitions, no error bars, no code or data archive. The satisfaction measure is narrow—additive over paragraphs, binary votes, no ordering—so the theorems and the simulations both operate in a stylized world. The paper acknowledges this in the outlook.\n\nThe stress-test note is worth checking on one point: it asserts that every smooth rule in the reported Pareto analysis fails Definition 8 stability. That seems right for the exponential family, but the paper also includes other smoothing functions; if any of them eventually lock, the claim would need qualification. Still, the central point stands: the positive results are about a proxy, not the formal property.\n\nBottom line: this is a decent theory paper with an overstated empirical section. If I were the editor, I'd send it to a referee. The referee should ask the authors to either align the simulation metric with Definition 8, provide code/data, or soften the convergence claims. I'd cite Theorem 1 myself.","headline":"A sound impossibility theorem plus a family of rules that are promising in simulations, but the simulation 'stability' metric does not measure the paper's own formal stability, so the convergence claims are overstated.","tokens_in":19004,"tokens_out":3278,"would_cite":true,"duration_ms":30775,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["91B12","91B14"],"pacs":[],"model":"deepseek-v4-flash","headline":"In a dynamic model of collaborative text, no aggregation rule can both maximize social welfare and guarantee that the document eventually stops changing.","keywords":["collaborative document writing","dynamic voting","social welfare","stability","consensus-conditioned rules","relative majority","agent-based simulation","large language models"],"falsifier":"Concrete check: in an instance with two agents and one paragraph, let the event sequence be $(a_1,p,+1), (a_2,p,+1), (a_1,p,-1), (a_2,p,-1)$. The relative majority rule includes $p$ after event 2 and excludes it after event 4, reproducing the instability of Observation 1; a rule claimed to be both stable and welfare-maximizing must instead return a constant document on this sequence while also beating the relative majority outcome in satisfaction. Alternatively, in the LLM simulation, record the document-update count under CCR[RAPS,0.5] with 40 agents and 500 events: Observation 1 predicts updates keep occurring whenever the final vote balance crosses the threshold.","tokens_in":18010,"feed_emoji":"🗳️","tokens_out":6582,"duration_ms":70823,"temperature":0.7,"pith_summary":"The paper tries to establish a fundamental trade-off at the heart of any system where a community co-writes a document by proposing paragraphs and voting on each other's suggestions. It proves that no aggregation rule can simultaneously maximize the community's additive satisfaction with the final text and guarantee that the text eventually stops changing. What can be achieved instead, the paper argues, is a family of consensus-conditioned rules whose strictness grows over time, so a designer can pick a point on the stability-versus-welfare frontier. Using agent-based simulations, including agents modeled by large language models, it shows these tunable rules converge quickly to documents with high satisfaction.","feed_headline":"No voting rule can maximize welfare and stay stable","feed_subtitle":"Theorem plus simulations: tunable consensus rules offer a practical trade-off.","key_machinery":"The load-bearing objects are the relative majority rule and the Consensus-Conditioned Rule (CCR) framework. A relative majority rule weighs each agent's approval or disapproval by $1/N_a$, the inverse of the number of paragraphs that agent voted on, and includes a paragraph exactly when the weighted approvals exceed the weighted disapprovals; Theorem 1 establishes that this class is exactly the set of social-welfare maximizers. A CCR assigns each paragraph a consensus score via a scoring function $CSF(p,T)$ and includes paragraphs whose score clears a threshold $x$. The dynamic subfamily used to escape the impossibility uses a smoothing function, here exponential, $F^{\\mathrm{exp}}_\\alpha(x,t) = x\\,e^{-t\\alpha(1-x)}$, so that as events accumulate the effective score of a paragraph decays unless it has strong support; this is what lets the rule asymptotically stabilize while remaining amendable.","core_discovery":"On the paper's own terms, the central discovery is an impossibility: under the satisfaction model where each agent's welfare is the fraction of paragraphs they voted on that match their last vote, a rule maximizes social welfare if and only if it is a relative majority rule—include a paragraph when the activity-weighted approvals exceed the activity-weighted disapprovals (Theorem 1). But every such rule is unstable: a paragraph already in the document can be flipped by enough additional opposing votes, so no extension of the event list can guarantee the output never changes again (Observation 1). Together these yield the paper's headline theorem, Corollary 1: no rule is both social-welfare-maximizing and stable. The paper then introduces Consensus-Conditioned Rules, which score paragraphs and include those above a threshold, and shows through simulations that smooth versions—where the required score rises gradually via exponential decay—offer a tunable Pareto trade-off between satisfaction and stability.","pith_inferences":["Beyond the paper: the impossibility depends on additive, paragraph-separable satisfaction; if real writers care about how paragraphs interact or about document order, a rule that is both stable and welfare-maximizing over those richer preferences may exist, and Theorem 1 would not transfer.","Beyond the paper: the paper's stability notion is existential—there exists some continuation that stabilizes. A stricter notion requiring stabilization under every fair scheduler would be even harder to satisfy; testing smooth rules under adversarial scheduling would reveal how much of the reported convergence is scheduler luck.","Beyond the paper: the exponential smoothing rule gives late-arriving voters less influence, so a testable implication is that postponing votes can lock in an early document; measuring the degree of first-mover advantage in the LLM simulations would quantify this cost.","Beyond the paper: the same CCR machinery could be applied to ordered documents by adding a score for paragraph position, turning the current unordered-set model into a testbed for constitution drafting with structural constraints."],"forward_implications":["Every practical collaborative-writing mechanism must sacrifice either welfare optimality or the guarantee of eventual stability; the choice is a design parameter, not an implementation bug.","The relative majority rule, with per-agent normalization by voting activity, is the only welfare-optimal rule family, so any attempt to improve stability by changing the aggregation rule necessarily moves away from welfare optimality.","Smooth consensus-conditioned rules, such as exponential smoothing on event count, provide a monotone dial between the two goals: higher $\\alpha$ stabilizes faster, lower $\\alpha$ preserves more satisfaction.","Harsh rules that freeze the document after a fixed number of events are stable but vulnerable to adversarial event flooding, so they fit settings like budgeting deadlines rather than ongoing constitution drafting.","In simulations, larger and more diverse communities push the Pareto frontier outward: more agents yield higher achievable satisfaction but make stability harder."],"supporting_citations":[{"why":"Supplies the static model of aggregation with incomplete votes that the paper extends to a dynamic setting.","marker":"[15]"},{"why":"Grounds the CCR design space in committee scoring rules through an axiomatic classification and hierarchy.","marker":"[8]"},{"why":"Introduces generative social choice, the method combining surveys and LLM-driven statement generation that the simulations build on.","marker":"[12]"},{"why":"Provides the agent-based LLM modeling approach used to simulate collective decision-making.","marker":"[24]"},{"why":"Supplies the demographic census data from which simulated agent profiles are sampled.","marker":"[22]"},{"why":"Frames constitution stability and amendment under supermajority rules, the background for the stability desideratum.","marker":"[2]"}],"fun_headline_variants":["No voting rule maximizes welfare and stays stable","Welfare-maximizing voting rules are inherently unstable","Consensus-conditioned rules enable welfare-stability trade-off","Voting paradox: max welfare or stability, not both"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole impossibility rests on measuring satisfaction as the fraction of paragraphs each agent voted on that end up matching that agent's last vote; if real preferences depend on how paragraphs fit together, on document order, or on how much the agent cares, the trade-off theorem does not apply.","fun_headline_variants_meta":{"raw":{"variants":["No voting rule maximizes welfare and stays stable","Welfare-maximizing voting rules are inherently unstable","Consensus-conditioned rules enable welfare-stability trade-off","Voting paradox: max welfare or stability, not both"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000282,"raw_usage":{"total_tokens":1613,"prompt_tokens":836,"completion_tokens":777,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":452,"completion_tokens_details":{"reasoning_tokens":714}},"tokens_in":452,"tokens_out":777,"duration_ms":8566,"temperature":1.0,"reasoning_tokens":714,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T17:04:19.818663+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Concrete check: in an instance with two agents and one paragraph, let the event sequence be $(a_1,p,+1), (a_2,p,+1), (a_1,p,-1), (a_2,p,-1)$. The relative majority rule includes $p$ after event 2 and excludes it after event 4, reproducing the instability of Observation 1; a rule claimed to be both stable and welfare-maximizing must instead return a constant document on this sequence while also beating the relative majority outcome in satisfaction. Alternatively, in the LLM simulation, record the document-update count under CCR[RAPS,0.5] with 40 agents and 500 events: Observation 1 predicts updates keep occurring whenever the final vote balance crosses the threshold.","supporting_citations":[{"cited_title":"Halpern, G","cited_arxiv_id":null,"evidence_quote":"Supplies the static model of aggregation with incomplete votes that the paper extends to a dynamic setting."},{"cited_title":"Faliszewski, P","cited_arxiv_id":null,"evidence_quote":"Grounds the CCR design space in committee scoring rules through an axiomatic classification and hierarchy."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces generative social choice, the method combining surveys and LLM-driven statement generation that the simulations build on."},{"cited_title":"Population by age, sex and edu- cational attainment: Israel","cited_arxiv_id":null,"evidence_quote":"Supplies the demographic census data from which simulated agent profiles are sampled."},{"cited_title":"Abramowitz, E","cited_arxiv_id":null,"evidence_quote":"Frames constitution stability and amendment under supermajority rules, the background for the stability desideratum."}],"review_version":2}