Query-Based Committee Selection

Abstract: Purpose: Multiwinner voting rules typically require full knowledge of voter preferences, which becomes impractical in large-scale or attention-limited settings. This paper investigates how accurately a winning committee can be approximated when voter preferences are elicited using a limited budget of structured queries. Methods: We introduce a query-based framework for multiwinner elections in which voter preferences are elicited through refinement queries over subsets of candidates under a limited budget. We analyse several cost functions that model the cognitive effort needed to answer such queries, propose axiomatic properties for evaluating them, and experimentally evaluate simple query-based committee selection rules across multiple election models. Results: Experimental results show that strategies based on recursively splitting candidate sets provide the best trade-off between elicitation cost and committee accuracy. Across several statistical models, these strategies approximate the outcome of k-Borda elections significantly more efficiently than alternative query types. Conclusion: The results demonstrate that well-designed query strategies can substantially reduce the amount of preference information required while still producing high-quality committee outcomes, suggesting that query-based elicitation is a promising approach for scalable multiwinner decision-making.

• The paper demonstrates that binary-split queries can recover near-optimal multiwinner committees while drastically reducing elicitation costs.
• The study formulates expressive cost functions and compares query strategies like next/last, split, and next+last through rigorous experiments across diverse election models.
• The work offers practical insights for large-scale decision systems, such as decentralized governance, by efficiently balancing query budget and committee accuracy.

Query-Based Committee Selection in Multiwinner Elections: A Structured Elicitation Framework

Problem Setting and Motivation

Traditional multiwinner voting rules presuppose full access to the complete ordinal preferences of all agents, an assumption infeasible in large-scale or cognitively constrained collective decision scenarios. Examples include decentralized blockchain governance systems, where eliciting detailed rankings from every participant is impractical due to voter fatigue, scale, and inattention. The study addresses the fundamental question: To what extent can high-fidelity committee selection be approximated when the information elicited from voters is constrained by a budget on the number and kind of queries posed to each?

The formulation adopts a general query-based elicitation paradigm, wherein only partial preference data is collected via structured queries. The main challenge lies in modeling and optimizing the trade-off between elicitation cost (interpreted as the aggregate cognitive effort invoked by queries) and the resulting committee quality.

Formal Framework and Cost Function Design

Refinement Queries

The core mechanism is the refinement query, parameterized by a subset of candidates and a partition vector, capturing a wide spectrum of elicitation methods, from approval partitioning to truncated lists. The query response is a weak order on the subset, consistent with the agent’s latent strict ranking, divided into indifference classes of prescribed sizes. This expressive query language subsumes many formats previously examined only for the approval setting, and is thus suitable for general ordinal rules.

Cost Modeling

The framework introduces several formal axioms for cost functions, intended to encode natural properties such as monotonicity with query granularity, scaling with the number of candidates, and sensitivity to bucket (partition) variance. The authors analyze several candidate functions:

• Linear candidate count
• Discounted (via last bucket size) candidate count
• Bucket count-weighted cost
• A novel cost function incorporating variance in partition sizes: $|C'| \cdot |B| \cdot (1 - \text{Var}(B))$
• Computational cost modeled as $|C'| \log |B|$ (relevant for automated agents)

Crucially, only the variance-based cost satisfies all formalized axioms, including variance monotonicity, which asserts that queries requiring more fine-grained distinctions (e.g., splitting into buckets of equal size) carry greater cognitive cost than lopsided partitions.

Query Strategies and Committee Selection Rules

The proposed end-to-end rule comprises two phases: (1) adaptive or non-adaptive query selection, subject to the elicitation budget and cost function, and (2) committee construction using a partial scoring extension. Several basic, non-adaptive families are experimentally evaluated:

• Next/Last Queries: Elicit the voter's top or bottom candidate(s) within subsets.
• Split Queries: Iteratively partition candidate sets into halves, recursively refining information in a binary search-like fashion.
• Next+Last: Combination of top and bottom queries.

Two budget allocation regimes are explored: evenly splitting query budgets per voter ("Equally") and an FCFS policy where voters are interrogated to completion before moving on.

In committee construction (Phase 2), partial ballots are scored via a positional vector extension: each indifference class in the partial order receives the average score corresponding to possible positions. A $k$-Borda rule is used as the canonical multiwinner method.

Experimental Evaluation

Three main experimental designs are undertaken:

• Impartial Culture (IC): Voter orders are sampled uniformly at random.
• Euclidean Culture: Voters and candidates are embedded in $\mathbb{R}^2$, preferences induced by distances.
• Mapof Statistical Models: Diverse election structures, including Mallows, Polya-Eggenberger urn, identity, uniformity, stratification, and antagonism settings.

The primary accuracy metric is Hamming distance between the committee elected by the query-based rule and the full-information $k$-Borda committee.

Numerical Results

The key finding is that Split strategies (binary partitioning of candidate sets) consistently outperform alternative query types in terms of balancing budget expenditure and committee accuracy. For both human-oriented and computational cost functions, Split strategies achieve full committee recovery with budgets an order of magnitude lower than next/last-based approaches. Even allocation of query budget slightly outperforms FCFS, except in elections with very high consensus (identity elections), where exhaustive querying of a representative agent can be marginally more efficient.

Moreover, performance deteriorates most sharply in "hard" election types—uniform and antagonistic cultures—where voter preferences are highly dispersed. Here, even optimal strategies require substantially more elicitation or must settle for coarser committees due to increased sensitivity to partial information.

Theoretical and Practical Implications

The axiomatic cost function analysis provides a principled template for modeling cognitive or computational burden in eliciting richer partial rankings, advancing the formal study of partial preference queries beyond the binary/approval context.

Experimentally, the work establishes that, for a wide range of election structures, binary-split queries (analogous to recursive "divide and conquer") are the most cost-efficient for approximating positional scoring committee rules such as $k$-Borda. This validates and formally extends "logarithmic" elicitation protocols common in active learning and ranking aggregation.

For large-scale applications such as decentralized digital governance, the findings indicate that significant reductions in elicitation load are possible without material loss of representativeness: committees are recoverable to high fidelity under tight attention or bandwidth constraints.

Future Directions

Possible avenues include:

• Design of adaptive or dynamic querying policies that exploit observed partial profiles or societal priors
• Extending the approach to other multiwinner rule families (e.g., Chamberlin–Courant, Monroe, PAV) and considering settings with weighted agents or correlated noise models
• Empirical human-subject studies to further calibrate the cost models to actual cognitive burden and optimize interface design
• Investigation of query rules capable of robust performance even in maximally antagonistic or uniform preference structures

Conclusion

This work delivers a comprehensive analytic and empirical framework for query-based committee selection under ordinal rules. The incorporation of expressive, axiomatically justified cost functions and the empirical evaluation over a range of social choice cultures demonstrate that carefully chosen query strategies, particularly recursive binary splits, can yield near-optimal committees with drastically reduced elicitation effort. These advances lay groundwork for practical and theoretically sound multiwinner decision systems in both digital and traditional large-scale collectives.

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Reference:

"Query-Based Committee Selection" (2603.29729)