Generative Social Choice: The Next Generation

Ariel D. Procaccia; Niclas Boehmer; Sara Fish

REVIEW 2 major objections 5 minor 32 references

Generative Social Choice: The Next Generation

T0 review · 2 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A democratic process can generate a proportional slate of opinion statements from imperfect LLM queries, and the fairness loss is exactly quantifiable and essentially unavoidable.

desk verdict Solid theory connecting query accuracy to cost-BJR, but the deployed system's accuracy parameters are never measured; the impossibility results alone justify a serious referee. read the letter →

arxiv 2505.22939 v1 pith:HAYUJLB6 submitted 2025-05-28 cs.GT cs.AIcs.LG

Niclas Boehmer , Sara Fish , Ariel D. Procaccia This is my paper

classification cs.GTcs.AIcs.LG MSC 91B1491B12

keywords generativesocialchoiceproportionalrepresentationbalancedjustifiedapproximatequerieslargelanguagemodelsparticipatorybudgetingcostBJRdemocraticdeliberation

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

This paper asks whether a democratic process that uses a large language model to produce a short slate of opinion statements can still give proportional representation when the two underlying queries are imperfect. The answer is yes, at a quantifiable price: with a discriminative query that estimates a person's utility up to additive error $\beta$ and a generative query that is off by a support factor $\gamma$, a utility slack $\delta$, and a cost factor $\mu$, a specific algorithm guarantees $(2\beta+\delta,1/(\gamma\mu))$-costBJR under a total budget on slate length. The paper also proves this price is nearly unavoidable: no algorithm can guarantee $(2\beta+\delta-\epsilon,1)$-costBJR even with exact generative queries, and the $1/\gamma$ factor cannot be improved except by a term vanishing in the slate size. The same machinery powers PROSE, a practical system that uses GPT-4o to build representative slates from unstructured user reviews and deliberation comments. If these results are right, the cost of AI imperfection in such democratic processes is exactly characterized and cannot be removed by clever algorithm design.

What carries the argument

The load-bearing object is the pair of approximate query types together with the loop structure of Algorithm 1. A discriminative query $Disc(i,\alpha)$ returns $u_i(\alpha)$ with additive error $\beta$, while a generative query $Gen(S,\ell,x)$ returns a statement whose support at relaxed utility $\ell-\delta$ is at least a $\gamma$ fraction of the best statement of cost at most $\mu x$, bounding misestimation of utility, supporters, and cost. Complex-DemocraticProcess takes $C=[B]$ and $f(\ell)=[\ell,r]$, so at each utility level it queries across all costs and all higher levels, selects the generated statement with the most predicted approvers, and removes exactly its fair share of agents. The proof takes the first agent of a hypothetical violating coalition that gets removed and shows its assigned utility must contradict the violation, while the impossibility theorems construct adversarial query answers that hide every good statement from the algorithm.

What would settle it

Measure the four accuracy parameters on a deployed system: collect true utility judgments such as the Polis up-vote and down-vote pairs, and check whether GPT-4o's discriminative estimates stay within $\beta$ of true values and whether generated statements satisfy the support ratio in Equation (1) for the advertised $(\gamma,\delta,\mu)$. If violations occur on a non-negligible fraction of queries, the theorem's premise fails. On the theoretical side, running any algorithm on the $n=2B$, $B\ge 8$ instance constructed in Theorem 3.3 and achieving $(2\beta+\delta-\epsilon,1)$-costBJR would refute the impossibility claim.

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Extended reading notes

Core claim

On its own terms, the paper's central result is that approximate proportionality guarantees survive approximate queries. For a budget $B$ over statement costs, a coalition $S$ deserves a statement $\alpha$ if $|S| \ge d\cdot\lceil c(\alpha)n/B\rceil$, and a slate satisfies $(b,d)$-costBJR when each agent can be matched to a statement in a balanced way so that no such coalition agrees on $\alpha$ at threshold $\theta$ while all its members are matched to statements scoring below $\theta-b$. Theorems 3.2 and 3.4 state that Complex-DemocraticProcess, which iterates over utility levels and candidate costs and removes represented agents, achieves $(2\beta+\delta,1/(\gamma\mu))$-costBJR from $\beta$-accurate discriminative and $(\gamma,\delta,\mu)$-accurate generative queries, and that no algorithm can do substantially better: the additive utility-error contribution $2\beta+\delta$ is sharp up to $\epsilon$, and the multiplicative supporter and cost error cannot be improved except for a term vanishing in the slate size. Thus, in the worst case, AI imperfection has an exact, unavoidable price in this setting.

Load-bearing premise

The guarantees hold only if the LLM's errors fit the bounded model: every utility estimate is within $\beta$, and every generated statement is within a $\gamma$ factor of the best statement at relaxed utility $\delta$ and cost factor $\mu$; if real errors exceed these bounds in even one query, the theorem's conclusion does not apply.

Editorial extensions

If this is right

Slate creation from unstructured text can carry formal proportionality guarantees even when the LLM answers are wrong in bounded ways.
The additive query error $\beta$ appears twice in the final fairness loss, so improving utility-prediction accuracy yields a double dividend; the multiplicative errors enter as $1/(\gamma\mu)$.
Because the algorithm is agnostic to query implementation, any future model that satisfies the accuracy bounds inherits the same guarantee without changing the process.
A budget on total slate length replaces the need to fix the number of statements in advance; the process splits the budget among groups proportionally.
The impossibility results show that no alternative algorithm can remove the error cost, so the bound is a property of the information model, not of this particular algorithm.

Reading between the lines

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

If real LLM errors are heavy-tailed rather than bounded by $\beta$, $\gamma$, $\delta$, and $\mu$, the theorem's guarantee does not apply; a practical calibration step would estimate these parameters on a validation set before deployment.
Applied to participatory budgeting, the same algorithm would select projects as statements with monetary costs, provided the generative query can propose feasible new projects; the paper notes this is beyond current LLMs but is a natural next target.
The low correlation between PROSE's discriminative query and the chain-of-thought evaluator suggests that reported utility gains depend heavily on the choice of preference model; a neutral reading is that evaluation and optimization should use different models.
A testable extension would run the algorithm on synthetic instances with known true utilities, compare observed violations against the $(2\beta+\delta,1/(\gamma\mu))$ envelope, and check whether the gap shrinks as the slate grows.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Colleague, the main thing to know: this is a genuine extension of Fish et al. 2024, not a repackaging. The paper adds costs and budgets to generative social choice, defines cost-BJR with approximation parameters (b,d), and proves that a specific iterative algorithm (Complex-DemocraticProcess) achieves (2β+δ, 1/(γμ))-costBJR under β-accurate discriminative and (γ,δ,μ)-accurate generative queries. It also proves two impossibility results showing the dependence on β,δ and on γ,μ is essentially tight. That part is real. I checked the proofs in the appendix: they are careful, and the oracle-style arguments in Theorems 3.3 and 3.4 look right. The synthetic environment is a reasonable complement, and the finding that all processes beat the worst-case guarantee is plausible.

The empirical part is where I get cautious. PROSE is sensible engineering, and the authors are honest that GPT-4o comes with no formal guarantees. But they never measure β, γ, δ, μ for the actual GPT-4o implementation, so the headline guarantee is not connected to the system they evaluate. Worse, the implementation deviates from Theorem 3.2's preconditions: the cost list C is a hand-picked subset of [B] (App. D.3), the approval levels are a fixed list, and the generative query is an embedding-clustering heuristic that may not satisfy Eq. (1) in general. That means the theorem, as stated, does not apply to PROSE as deployed. The authors note that extra statements can only help the algorithm, but that does not fix a generative query that might return a statement with support far below the γ-fraction of optimum.

On evaluation: using a separate chain-of-thought GPT-4o as the utility oracle is a reasonable proxy given the datasets, and they do validate both discriminative queries against real Polis up/downvotes (84% correct ordering, with low correlation between the two implementations). That is more than most LLM papers do. Still, 'user satisfaction' is actually 'LLM-proxy satisfaction' and the paper should say so clearly. The cBJR violation measure is computed against the same proxy, so it inherits that caveat.

Overall: the theory is solid and worth serious refereeing. The experimental section should be reframed as a case study of the framework with an LLM proxy, not as a demonstration of the formal guarantee. If the authors add an empirical estimate of the accuracy parameters (e.g., by comparing against human judgments on a subset), the connection becomes much stronger. Regardless, the impossibility results alone justify publication.

Referee Report

2 major / 5 minor

Summary. This paper extends the generative social choice framework of Fish et al. by adding statement costs and a total budget to the slate-selection problem and by replacing exact queries with an approximate-query model. The authors define (b,d)-costBJR, prove that their Complex-DemocraticProcess with C=[B] and f(ℓ)=[ℓ,r] achieves (2β+δ,1/(γµ))-costBJR for β-accurate discriminative and (γ,δ,µ)-accurate generative queries, and provide impossibility results showing that this dependence is close to optimal. They validate the algorithms in a synthetic environment and introduce PROSE, a GPT-4o-based implementation, which they evaluate on drug-review and Polis datasets against four baselines. The theoretical part is self-contained, with full proofs in the appendix and code provided; the experimental part claims statistically significant improvements in mean and 25th-percentile utilities and fewer cBJR violations.

Significance. The main theoretical result is a clean, parameterized degradation theorem with matching lower bounds, and the proof structure is careful; the synthetic validation is a useful complement because it instantiates the error model directly rather than relying on an LLM. The paper also ships code and full proofs, which materially strengthens the contribution. That said, the significance for practice is currently overstated: the PROSE deployment neither verifies Eq. (1) nor instantiates the exact algorithm of Theorem 3.2, and the evaluation's 'true' utilities are another GPT-4o estimator. The theoretical contribution itself is valuable and publishable; the gap is in the bridge from theorems to the deployed system.

major comments (2)

[§3.2, Eq. (1), App. D.3] Theorem 3.2's guarantee is conditional on the generative query being (γ,δ,µ)-accurate in the sense of Eq. (1), and on the algorithm running with C=[B] and f(ℓ)=[ℓ,r]. PROSE uses a truncated cost list (e.g., C=[80,70,...,2] for the drug instances), a different approval-level schedule that includes fractional values such as 5.5, and a minimum statement length, so it is not Complex-DemocraticProcess. Moreover, the paper never measures or bounds β,γ,δ,µ for the GPT-4o implementations; the Limitations paragraph concedes that GPT-4o 'comes without guarantees on the query answers,' but that concession is not operationalized. As a result, the framing that 'the cost of AI imperfection is exactly quantifiable' is not established for PROSE, and the abstract's promise of guarantees under approximately optimal queries is only a theorem about an idealized query model, not about the deployed system.
[§4.2.3, App. D.4, D.5] The experimental evaluation treats the chain-of-thought GPT-4o scores as 'true, underlying utilities' and computes both user-satisfaction comparisons and cBJR violation rates against them. Since PROSE's own discriminative query is also a GPT-4o approximation of the same unknown utilities, the reported improvements could reflect a favorable interaction between two model-based estimators rather than genuine representativeness. The low Pearson correlation (0.13) reported in App. D.5 shows that the two estimators are not identical, but it does not validate the CoT scores as ground truth; the Bowling Green up/downvote check validates the queries on voting behavior, not on the statements and agents evaluated in Table 1. The paper should either obtain human judgments on the generated slates for at least a subset of agent-statement pairs, or explicitly reframe the experiments as a model-in-the-loop evaluation and soften the 'user satisfaction' conclusion.

minor comments (5)

[Theorem 3.4] The theorem statement contains a typo: 'W it the slate returned' should read 'W is the slate returned'; the proof's footnote gives a more precise B/c version, and the main-text statement should be reconciled with that formulation.
[Eq. (1)] When the denominator max is zero, the fraction in Eq. (1) is undefined; the paper should specify a convention for this case, since the proof of Theorem 3.4 already relies on such a convention.
[§4.2.3] The zero-shot baselines receive an optimal maximum-weight balanced assignment while PROSE's internal mapping is used; although the authors acknowledge this asymmetry, they should also report results with PROSE's mapping recomputed by the same optimal assignment, since they state this changes utilities by around 15%.
[App. D.3] The implementation depends on several free choices (specificity coefficient, approval-level list, cost list, minimum statement lengths, generators, and embedding choice); the claim that PROSE 'does not require dataset-specific tuning' only means the same choices were used across datasets, and the sensitivity of the results to these choices is not explored.
[Table 1] The pairwise p-values are reported without multiple-comparison correction; with four baselines and four instances there are 16 tests, so some of the 'statistically significant' differences may not survive a correction procedure.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the theoretical guarantees are derived from explicit query-accuracy axioms, and the empirical evaluation uses an independent chain-of-thought scorer rather than the algorithm's own scoring function.

full rationale

The paper's derivation chain is self-contained relative to its stated model. Theorem 3.2 is a conditional statement: if discriminative queries are β-accurate and generative queries are (γ, δ, µ)-accurate as defined in Eq. (1), then Complex-DemocraticProcess provably satisfies (2β+δ, 1/(γµ))-costBJR. The proof derives this bound from the accuracy inequalities themselves, not from any quantity being fitted to the axiom or to the empirical results. The impossibility results (Theorems 3.3 and 3.4) are proved by constructing adversarial instances whose generative and discriminative queries satisfy the accuracy definitions; they do not import a uniqueness theorem or rely on the authors' prior work to rule out alternatives. The main self-citations, to Fish et al. [2024], supply the framework and the BJR notion, but the costed axiom, the approximate-query model, the algorithm, and the proofs are new contributions rather than restatements of those citations. Empirically, PROSE is not evaluated with its own discriminative query: the paper deliberately employs a separate chain-of-thought discriminative implementation and treats those CoT utilities as the ground truth for evaluation, additionally validating both implementations against real Polis up/downvote data in Appendix D.5. This addresses the main circularity risk in the experimental design. The genuine weaknesses of the paper are applicability gaps, not circularity: the accuracy parameters β, γ, δ, µ are never measured for GPT-4o, and the deployed PROSE configuration uses a reduced cost list and discrete approval levels, so Theorem 3.2's conditions are not literally satisfied by the implementation. Those are correctness or external-validity limitations, not cases where a prediction is equivalent to its input by construction.

Assumptions & free parameters 6 free parameters · 4 assumptions · 2 invented entities

The central theoretical claim rests on a clean axiomatic model: a cardinal utility space, exact or approximate query oracles, and the cost-BJR axiom. The theorems are proven relative to these assumptions. The practical system adds several fitted heuristics: the specificity coefficient, the lists of cost values and approval levels, minimum statement lengths, and generator choices. These are not load-bearing for the theory (the paper says any query implementation works), but they are load-bearing for the empirical performance claims. The model also assumes the universe is closed under unions and that a statement exists for each integer cost, which are stated simplifications that may not hold in real text.

free parameters (6)

specificity coefficient = 1
A hyperparameter in the discriminative query utility formula: agreement - specificity_coefficient*(6-specificity)/5. It is set to 1 in experiments without a principled justification.
approval levels list ℓ = [5.5, 5, 4.5, 4, 3.5, 3, 2, 1, 0]
The choice of these specific approval levels for PROSE is a configuration decided by the authors, not derived from theory.
cost list C (drugs) = [80, 70, 60, 50, 40, 36, 32, 28, 24, 20, 16, 12, 10, 8, 6, 4, 2]
A selected subset of cost values, justified only by 'cost efficiency' and 'strong performance of the Fast algorithm', not by theory.
cost list C (bowling green) = [80, 60, 40, 36, 32, 28, 24, 20, 16, 12, 8, 4]
Different subset of cost values for the Bowling Green dataset, manually chosen.
minimum statement lengths = 10 words (drugs), 8 words (Bowling Green)
Imposed to ensure meaningful statements; a heuristic without theoretical justification.
clustering / generator choices = four generators, two embeddings, two runs each
Practical choices for the generative query implementation that are not derived from the theory, though the theory is agnostic to them.

assumptions (4)

domain assumption Utility functions are cardinal and map to [r], and agents' utilities for statements are additive in the statement content.
The model assumes ui: U -> [r] and additivity is used implicitly in Appendix A for the cBJR-EJR connection; this is a standard but substantive modeling assumption.
domain assumption The universe U is closed under union of statements, so any two statements can be concatenated into a statement costing the sum of their costs and affording utility at least the sum.
Invoked in Lemma A.2; the authors call it 'quite natural' in the natural language context, but it is a domain assumption that may fail for statements that conflict.
ad hoc to paper For each cost x in [B], there exists at least one statement in U with that exact cost.
Stated in a footnote in Section 2 'for simplicity'; it is needed to make the algorithmic argument that a statement will always be generated at the lowest utility level.
standard math The generative query returns a statement of cost at most the queried cost x in the approximate version.
This is part of the definition of (γ,δ,μ)-accuracy, an assumption about the oracle's behavior.

invented entities (2)

The two-query model with (β,γ,δ,μ)-approximate queries
purpose: Abstractly characterizes errors in LLM-based discriminative and generative queries.
This is a new formalism, not a physical entity; its usefulness is measured by whether real LLMs satisfy the bounds, which the paper does not verify.
(b,d)-costBJR axiom
purpose: Formalizes approximate proportional representation under statement costs.
A new normative axiom; it is justified by analogy with existing axioms, but its practical meaningfulness is unproven empirically.

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Cite this review

Pith. "Pith review of Generative Social Choice: The Next Generation." pith.science (2026). https://pith.science/paper/HAYUJLB6

@misc{pith2026250522939,
  author       = {Pith},
  title        = {Pith review of: Generative Social Choice: The Next Generation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HAYUJLB6}},
  note         = {Machine review of arXiv:2505.22939}
}

read the original abstract

A key task in certain democratic processes is to produce a concise slate of statements that proportionally represents the full spectrum of user opinions. This task is similar to committee elections, but unlike traditional settings, the candidate set comprises all possible statements of varying lengths, and so it can only be accessed through specific queries. Combining social choice and large language models, prior work has approached this challenge through a framework of generative social choice. We extend the framework in two fundamental ways, providing theoretical guarantees even in the face of approximately optimal queries and a budget limit on the overall length of the slate. Using GPT-4o to implement queries, we showcase our approach on datasets related to city improvement measures and drug reviews, demonstrating its effectiveness in generating representative slates from unstructured user opinions.

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Reviewed August 7, 2026 · model on record in the stance chip above.

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D. M. Alavi, M. W\"ahlisch, C. Irwin, and A. Konya. Using artificial intelligence for peacebuilding. Journal of Peacebuilding & Development, 17 0 (2): 0 239--243, 2022

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Out of one, many: Using language models to simulate human samples

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