Title: Does Representation Guarantee Welfare?
Venue: NeurIPS 2025
Accepted: yes
Keywords: sortition

citizens’ assemblies

governance
Abstract: A panel satisfies *descriptive representation* when its composition reflects the population. We examine the role of descriptive representation in collective decision making through an optimization lens, asking whether representative panels make decisions that maximize social welfare for the underlying population. Our main results suggest that, in general, representation with respect to *intersections* of two or more features guarantees higher social welfare than that achieved by the status quo of proportionally representing individual features. Moreover, an analysis of real data suggests that representation with respect to pairs of features is feasible in practice. These results have significant implications for the design of *citizens' assemblies*, which are gaining prominence in AI governance.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper studies the role of descriptive representation in collective decision making. They show that requiring representation for pairs of demographic features (2-representation) significantly improves worse-case welfare guarantees beyond today's single-feature quotas. They demonstrate through empirical analysis that 2-representation is generally feasible in practice.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n1. Theoretical results are interesting and concrete. They prove that 1-representation is perfect for utilitarian social welfare but can be arbitrarily bad for $p < 1$. They then derive explicit $\\epsilon$-accuracy bounds for both 1- and 2-representation via a moment problem reduction.\n2. Practical feasibility of finding 2-representative panels is shown through empirical analysis.\n\nWeaknesses:\n\n1. In addition to the feasibility of finding 2-representative panels, I'm also curious about the welfare of 2-representative panels compared with 1-representative panels on real-world datasets. Would be good if the authors could show this.\n2. Modeling assumptions are strong. For example, utilities are additive across features. I understand that this is necessary for theoretical analysis, but just not sure how much practitioners can still get out of this paper with these assumptions.\n3. The related works section should be more about how this work stands among the works on computational social choice, instead of trying to persuade the reviewers that NeurIPS is a suitable venue foe this paper.\n\nQUESTIONS:\nAs discussed in weaknesses, some questions and suggestions include:\n\n1. How are the welfare of 2-representative panels compared with the 1-representative panels in empirical analysis? Would be good if the authors could show that.\n2. Can the modeling assumptions be weaken?\n3. Would be good to add discussions on more related works so that we can have a better sense of how this work stands among relevant works in this area.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 2, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-10"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper studies how well the welfare of representative citizen assemblies translates to the welfare of the underlying population. In particular, the paper focuses on 1- and 2-representative panels, which mirror the population with respect to the proportion of individuals possessing one or two protected attributes, such as, for example, being male and a parent.\n\nThe welfare notion considered is p-welfare, the power mean welfare: when p = 1 it captures utilitarian welfare; when p = 0 it captures Nash social welfare; and for negative p it becomes increasingly egalitarian. The question studied is how good an additive approximation the panel’s p-welfare–optimal outcome is to the p-welfare of the underlying population.\n\nFor p ≤ 1 and 1-representative assemblies, the authors prove tight bounds on the additive approximation gap ε. For 2-representative committees, they show upper bounds as well as a lower bound in the case when some alternative provides zero utility to some type. On real-world data, the authors demonstrate the feasibility of selecting 2-representative citizen assemblies.\n\nSTRENGTHS AND WEAKNESSES:\nThis paper is very well written and well motivated. It tackles a practically driven theoretical problem, and as a result must contend with quite involved mathematics that don’t yield neat closed-form solutions. In that light, Figure 1 is especially valuable for visualizing and understanding the resulting bounds.\n\nMoreover, the theoretical findings are backed up by experiments demonstrating that 2-representative citizen panels often exist in practice. Taken together, this evidence suggests we should consider moving beyond single-member representation in real-world applications.\n\nThat said, the paper could be clearer in its exposition of ε-accuracy and in guiding the reader through how to interpret the additive approximations (see my questions on this point). It would also benefit from a more in-depth discussion of the challenges involved in proving a lower bound for 2-representative panels when \nu_min >0.\n\n____\nMinor comments:\n\nPage 4 Line 177: doesn't -> does not\n\nPage 6 Line 236: or alternative -> for an alternative\n\nPage 7 Line 276: doesn't -> does not\n\nQUESTIONS:\nCould you elaborate on epsilon‐accuracy - for example, why you focus on additive approximations rather than multiplicative ones? \n\nIt would also be helpful if you could discuss lower bounds on the worst‐case epsilon‐accuracy when u_min > 0. Additionally, could you expand on your utility assumption, namely that individuals’ utilities for alternatives derive from the attributes those alternatives possess? \n\nFinally, in line 123 you state “This is essentially equivalent to the notion of representation considered in prior work on panel selection.” Could you clarify to what extent these two notions are equivalent, and where they might differ?\n\nLIMITATIONS:\nIt’s questionable whether people’s preferences for various options can truly be captured by demographic attributes like gender or age. While it’s reasonable to assume that individuals with similar characteristics with form clusters of some sort, this approach inevitably misrepresents a substantial portion of the group - particularly when we rely on the limited set of attributes commonly used in practice.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-30"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nFor citizen assemblies a panel of individuals is selected from the population in a way that proportionally reflects the population’s composition across multiple features, such as age, gender, and ethnicity. However, even when an individuals preferences are only determined by their features, an optimal decision for a (1-)representative panel must not be optimal for the population. In this paper, the authors explore how close the social welfare of a representative panel aligns with the social welfare of the entire population. They show that the welfare aligns significantly better when every combination of two features is proportionally represented in the panel, where welfare is measured using the p norm of individual utilities with $p < 1$. Depending on the size and diversity of the volunteer pool, it may not be possible to select such a panel. To address this, the authors include an experimental section in which they assess the feasibility using data from four past citizen assemblies.\n\nSTRENGTHS AND WEAKNESSES:\nThe paper is well-written and addresses a relevant question in the context of selecting citizen assemblies. The long introduction effectively motivates the research and clearly presents the main questions and results. However, some parts are difficult to follow without prior knowledge of the model, which is introduced in the subsequent section. \n\nThe related work section feels rushed and lacks a structured overview of relevant literature. A proper discussion of existing approaches and how this work relates to them is necessary in my opinion.\n\nThe main theoretical results seem significant, their proofs are deferred to the appendix. The paper does provide an outline of the proof for one of the key results (Theorem 9). However, an important concept—the 'moment problem'—is never properly introduced or explained, despite its apparent centrality to the argument.\n\nIn the experimental section, the authors check whether a 2-proportional panel of desired size can be found for four real-world instances. While this provides some insight, the small number of instances limits the ability to draw broader conclusions about feasibility. This limitation may be due to the inavailability of data, though this is not explicitly addressed in the paper.\n\nQUESTIONS:\n* In line 123, you state that that your definition of 1-representation is \"essentially equivalent\" to notions defined in the literature. Could you clarify what the differences are?\n\n* In the theoretical part of the paper, you assume panels to be perfectly m-proportional. In the experimental section, this requirement is relaxed to proportionality rounded up or down. How would this relaxation affect the theoretical guarantees?\n\n* What was the rationale behind the selection of the four specific citizen assemblies used in the experimental evaluation?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-07-01"}

comments: SUMMARY:
The paper studies citizens’ assemblies. Its goal is to determine whether descriptively representative panels make welfare-optimal decisions for the broader population.

The authors use the notion of m-representatives and show that 1-representatives are accurate for the arithmetic mean, but not necessarily for other means. They show that for 2-representatives, the worst-case accuracy is better than in the 1-representative case.

Finally, the paper presents an empirical analysis, showing the relationship between the representation level and panel size in practice.

STRENGTHS AND WEAKNESSES:
My overall evaluation of this paper is very positive.

+Assemblies are one of the most interesting recent topics within computational social choice.

+The paper is extremely clearly written and well-positioned within the literature.

+The concept of *m*-representation is intuitive and elegant, and the paper provides bounds on the accuracy of such representation.

+The paper includes an empirical analysis, showing, among other things, that it is indeed possible to select 2-representative panels in real-world instances.

Side notes:

-Minor issue regarding the plots: the text size is too small to read comfortably.

-I'm not sure the title accurately reflects the paper's content. It is catchy but not very descriptive.

QUESTIONS:
Why is there an assumption of the uniformity among voters? (That is, all individuals with the same values for the features used in the model (e.g., age and gender) are assumed to have the same utility for any given alternative.)

LIMITATIONS:
Yes.
TITLE: Official Review
CLARITY: 4
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-07-01

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper explores descriptive representation in the context citizens' assembly, focusing on the worst-case guarantees of 2-representative panels (i.e., representative of the underlying population over intersections of features). The paper quantitatively shows that 2-representative panels can more accurately estimate $p$-mean social welfare, and presents theoretical and experimental results.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\n+ The paper provides a strong motivation for studying 1- and 2-representative panels with clear practical implications. The paper could be strengthened by discussing limitations of current methods (a real-world situation like Example 7?) and plans for trying out 2-representative assemblies in practice.\n+ The authors give tight bounds for the worst-case guarantee of 1-representative panels (as a function of $p$ and the minimum utility $u_{\\mathrm{min}}$).\n+ Overall the paper is well written and the presentation is clear.\n\nWeaknesses\n- The paper could be strengthened by highlighting its technical contributions, e.g., which results are the most challenging to prove, and how the authors overcome the challenges. Is the upper bound in Theorem 9 tight, and is there any concrete evidence that the optimization program in Theorem 9 does not admit a closed-form solution?\n- The authors could consider exploring a weighted version of descriptive representation (where each person on the panel is assigned a nonnegative weight), which may help address the issue that $q_i k$ is not an integer. The authors may want to look into characteristic functions, Fourier transforms, and their connections to low-degree moments. The reviewer wonders if the notions in the paper have any connections to proportional fairness (i.e., no subpopulation wants to leave and form a proportional smaller panel).\n- The experimental setup is clearly described, but the paper could better justify the design choices. It feels a bit unnatural to use the maximum possible panel size as a measure of how easy it is to satisfy the representative constraints (i.e. it is harder to round the estimates to the true value when the true value is large). Would it make sense to study a multiplicative notion (e.g., the desired and actual number of people are within a factor of $1 \\pm 0.1$)? And following this line of thought, does randomly sampling $O(k \\log d / \\epsilon^2)$ times from the population gives a $1 \\pm \\epsilon$ multiplicative tolerance for $k$-representativeness (which seems to follow from standard application of Chernoff bound and the union bound).\n\nTypos\n- Line 87: \"foundational results ... has\".\n- Page 7: the printed version of Figure 1 is hard to read.\n- Line 309: missing a period.\n\nQUESTIONS:\nThe authors are encouraged but not required to answer the questions mentioned in “Strengths & Weaknesses” above.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-13"}