Do Large Language Model Voters Strategize? An Oracle-Based Benchmark for Manipulation under Voting Rules

Abstract: Strategic voting is a canonical failure mode for collective choice: a voter may obtain a more preferred outcome by reporting a ballot that differs from its true preferences. This paper introduces an oracle-based benchmark for testing whether LLM voters can discover and execute such manipulations. Each instance gives an LLM voter a true preference ranking, the other voters' ballots, a deterministic voting rule, and a prompt condition. An exact oracle enumerates every feasible report by the LLM voter, computes the sincere outcome, identifies all profitable reports, and records the best achievable outcome. The benchmark therefore supplies ground truth for strategic success without human labels or subjective grading of explanations. The benchmark covers plurality, Borda, approval, instant-runoff voting, and Copeland-style pairwise majority voting; prompt conditions separate sincere, strategic, civic, and expert framings. To keep the primary study defensible while preserving the main comparisons, the registered core design fixes a single electorate size, uses 600 balanced election instances, and produces 9,600 model--prompt responses when run with four model configurations and four prompt conditions. Because existing peer-reviewed work does not report manipulation discovery, optimal manipulation, false manipulation, near-miss, or invalid-ballot rates for this exact task, we do not impute LLM performance from unrelated studies. Instead, we report exact oracle-calibration baselines that bound and contextualize subsequent model results. By reducing strategic-voting behavior to exact counterfactual evaluation, the benchmark turns the question ``Do LLM voters vote sincerely or strategically?'' into a reproducible social-choice experiment.

• The paper introduces an oracle-based benchmark quantifying LLM strategic manipulation in single-voter, full-information elections using diverse voting rules.
• It employs counterfactual evaluation and oracle calibration to measure metrics such as manipulation discovery, optimality, near-miss, and false manipulation with precise baselines.
• Findings reveal rule-level sensitivity and prompt effects on LLM voting behavior, informing both theoretical analysis and practical AI system design.

Oracle-Based Benchmarking of LLM Strategic Voting Under Social Choice Rules

Motivation and Framework

Strategic voting represents a canonical vulnerability in collective decision mechanisms, as established by the Gibbard-Satterthwaite theorem, which demonstrates that no deterministic, nondictatorial voting rule with at least three alternatives is immune to manipulation by misreporting preferences. This paper introduces a controlled benchmark for quantifying whether LLMs, acting as agents in voting scenarios, identify and leverage profitably manipulative ballots under common voting rules. The approach grounds evaluation in exact oracle computations, enabling reproducible measurement of strategic behaviors, along with distinct analytical error modes.

The methodological foundation is counterfactual evaluation: each election instance supplies a full-information scenario with alternatives, voting rule, tie-breaking, true preference ranking, other voters' ballots, and explicit prompt framing. The oracle exhaustively enumerates all ballot reports by the LLM voter, computes the sincere outcome, verifies existence and optimality of manipulations, and produces ground-truth metrics for comparison. Five voting rules are covered—plurality, Borda, approval, instant-runoff (IRV), and Copeland pairwise majority—ensuring broad rule-level coverage.

Benchmark Design and Metrics

The benchmark is formally specified as a single-voter manipulation task with deterministic tie-breaking and rule-specific ballot spaces, in a fixed-size electorate of $n = 5$. The candidate set sizes are $m \in \{3, 4, 5\}$, and 600 balanced election instances are generated using impartial culture, stratified between manipulable and non-manipulable profiles. The core evaluation comprises 9,600 model-prompt calls, with exact oracle-calibration baselines provided for each metric.

Prompts are curated into four framing types: sincere, strategic, civic (honesty-oriented), and expert (computational social choice). Models are tasked to submit ballots under these conditions, with responses parsed deterministically per rule. The oracle provides the following evaluation metrics:

• Manipulation discovery rate (MDR): Probability that a profitable manipulation is executed when one exists.
• Optimal manipulation rate (OMR): Probability of discovering the ballot yielding maximal utility.
• False manipulation rate (FMR): Rate of strategic attempts when manipulation is impossible.
• Near-miss rate (NMR): Rate of non-optimal profitably manipulative ballots.
• Invalid generation rate (IGR): Fraction of responses not conforming to valid ballot formats.
• Mean rank improvement and optimality gap: Quantitative outcome shift for the strategic voter.

The deterministic oracle establishes baseline values: the sincere baseline yields 0% MDR/OMR/NMR, uniform-random valid ballots produce rule-dependent manipulation rates (e.g., 29.93% MDR for IRV), while the oracle upper bound achieves 100% in manipulable strata. These baselines contextualize and bound LLM model results.

Experimental Protocol and Calibration

Instance generation ensures balanced representation of manipulable and non-manipulable profiles within each rule and candidate-size cell. The oracle exactly identifies manipulation opportunities per profile and records all optimal reports. Statistical analysis employs stratified reporting and confidence intervals via bootstrap resampling within profile strata.

Distinct prompt conditions allow for quantification of prompt sensitivity, testing hypotheses such as MDR increases with strategic framing, expert prompts outpace strategic prompts in manipulation rates, civic framing reduces false manipulation, and rule-level difficulty distinctions (e.g., MDRplurality > MDRIRV).

Rule-level calibration is provided: random-valid ballot MDR/OMR/NMR and oracle mean gain per rule illuminate action-space geometric difficulty independently of LLM capabilities. For example, plurality and IRV exhibit higher random MDRs compared to Borda and approval. Strong rule-dependent manipulative potential suggests that complex rules (such as IRV) pose more substantial cognitive and representational challenges for LLM agents.

Theoretical and Practical Implications

The empirical distinction between manipulation discovery, optimality, near-miss, and false manipulation is critical. It enables direct attribution of strategic success/failure to model reasoning, rather than conflation with free-form explanations or superficial prompt compliance. The separation isolates instrumental reasoning (finding profitable ballots), rule simulation (executing valid ballots under complex rules), and prompt responsiveness (compliance with normative civic framing).

The full-information design exposes the limits and capabilities of LLM strategic reasoning under deterministic input. However, it abstracts away real-world complexity, such as partial information, larger electorates, correlated preferences, institutional constraints, and belief formation. Nevertheless, it provides a precise diagnostic for whether LLMs can act as strategic agents within simplified collective decision frameworks.

Practically, the benchmark has implications for the deployment of LLMs in preference aggregation, AI alignment, simulation of collective decisions, advisory roles, and as participants in human-in-the-loop systems. It reveals the necessity of careful interface design, prompt auditing, and potential utilization of strategy-proof mechanisms for settings where strategic misreporting is undesirable.

Theoretically, results provide evidence on AI agency in social choice contexts and inform the broader literature on computational social choice, manipulation complexity, and LLM behavior under objective misalignment. Rule-level and prompt-level sensitivity support further inquiry into representational bottlenecks and task formulation in neural models.

Limitations and Extensions

The benchmark's scope—small, synthetic elections, full information, deterministic tie-breaking—guarantees exact evaluation but constrains external validity. Scalable extensions include larger candidate sets, coalitional manipulation (Pareto-improving joint reports), Bayesian uncertainty, correlated preferences, and naturalistic ballot formats. A Bayesian refinement would introduce subjective beliefs and expected utilities, more closely approximating real-world voting.

Ethical considerations underscore the diagnostic—not prescriptive—intent. Exposing LLM strategic capacity in a laboratory environment should guide responsible use, agent constraint, and mechanism design decisions, not encourage real-world manipulation.

Conclusion

This paper provides a rigorously calibrated, oracle-based benchmark for LLM strategic voting under canonical social choice rules (2606.21001). By leveraging exact counterfactual voting evaluation in balanced small-electorate profiles, it separates strategic success, optimal manipulation, false strategy, near-miss outcomes, and invalid ballots. The empirical framework comprehensively addresses whether LLM voters find, execute, and optimize manipulation in full-information collective decision settings, supplying nuanced insights for both theoretical analysis and practical AI system design.