More Isn't Always Better: Balancing Decision Accuracy and Conformity Pressures in Multi-AI Advice

When the same question is asked of multiple AI advisers, as in self-consistency and LLM-as-a-judge panels, Condorcet's jury theorem predicts that adding independent, competent advisers makes the majority more reliable. The theorem, however, has a latent dimension when viewed from the user's vantage: adding advisers also makes disagreement more visible. A binomial model reveals that this ``visible dissent'' becomes nearly inevitable as the number of advisers grows, and that reliability and disagreement approach certainty at rates that cross at an adviser accuracy of 4/5 (0.8); below it, visible dissent eventually becomes more likely than a correct majority. Even ideal panels of independent and competent advisers can be correct in aggregate but appear divided; such disagreement does not by itself indicate aggregation failure. The way advisers split also provides a common basis for predictive multiplicity, reconciliation load, and reliance miscalibration. These results separate aggregation from disclosure and turn the latter into testable questions about how disagreement should be presented and interpreted.

Multi-agent debate improves LLM reasoning, yet agreement is not evidence of correctness. When agents converge on a wrong answer through social reinforcement, consensus stopping commits that error to automated action with no recourse. We introduce Conformal Social Choice, a post-hoc layer that converts debate outputs into calibrated act-versus-escalate decisions. Verbalized probability distributions from heterogeneous agents are aggregated via a linear opinion pool and calibrated with split conformal prediction, yielding fixed-round marginal coverage: at any pre-specified round, the correct answer is included with probability ${\geq}\,1{-}α$, without assumptions on individual model calibration. A hierarchical action policy maps singletons to autonomous action and larger sets to human escalation. Across eight MMLU-Pro domains and two additional benchmarks, fixed-round coverage stays close to target. The key finding is not that debate becomes more accurate, but that the conformal layer makes its failures actionable: at the final round, 81.9% of wrong-consensus cases are flagged by non-singleton sets at $α{=}0.05$. Separately, among cases that reach a singleton before the final round, accuracy reaches 90.0--96.8% on MMLU-Pro (up to 22.1pp above consensus stopping): a selection effect, not a reasoning improvement. Simple probability- and entropy-threshold rules attain comparable interception; conformal's distinct value is a finite-sample fixed-round coverage guarantee together with explicit candidate sets for escalation. Adaptive first-singleton stopping is evaluated empirically and not covered by this guarantee.

As humans increasingly rely on multiround conversational AI for high stakes decisions, principled frameworks are needed to ensure such interactions reliably improve decision quality. We adopt a human centric view governed by two principles: counterfactual harm, ensuring the AI does not undermine human strengths, and complementarity, ensuring it adds value where the human is prone to err. We formalize these concepts via user defined rules, allowing users to specify exactly what harm and complementarity mean for their specific task. We then introduce an online, distribution free algorithm with finite sample guarantees that enforces the user-specified constraints over the collaboration dynamics. We evaluate our framework across two interactive settings: LLM simulated collaboration on a medical diagnostic task and a human crowdsourcing study on a pictorial reasoning task. We show that our online procedure maintains prescribed counterfactual harm and complementarity violation rates even under nonstationary interaction dynamics. Moreover, tightening or loosening these constraints produces predictable shifts in downstream human accuracy, confirming that the two principles serve as practical levers for steering multi-round collaboration toward better decision quality without the need to model or constrain human behavior.