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Voting Protocols as Coordination Mechanisms for Role-Constrained Multi-Agent Tutoring Systems

Eric S. Qiu, Joyce Gill

Year: 2026Venue: arXiv preprintArea: cs.MAType: PreprintEmbeddings: 55

Intelligence

Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 91%

Last extracted: 7/9/2026, 3:19:04 AM

Summary

This paper investigates how different voting protocols (simple, ranked, cumulative, approval) shape coordination among role-constrained pedagogical agents in simulated multi-agent tutoring systems. Using SciQ and HumanEval benchmarks across 1,200 interactions, the authors demonstrate that protocol choice and a structured deliberation stage significantly influence collective decision-making, produce distinct coordination patterns, and yield measurable learning gains in simulated students.

Entities (8)

HumanEval · benchmark · 98%SciQ · benchmark · 98%Voting Protocols · method · 95%Role-Constrained Pedagogical Agents · system-component · 92%Coordination Patterns · outcome · 91%Simulated Student Personas · simulation-component · 90%Deliberation Stage · process · 88%Fallback Rate · metric · 85%

Relation Signals (5)

Simulated Tutoring Environments → evaluatedon → SciQ, HumanEval

confidence 96% · We compare four voting protocols... across two simulated tutoring environments on SciQ and HumanEval benchmarks.

Role-Constrained Pedagogical Agents → specializein → Scaffolding, Misconception, Motivation, Metacognition

confidence 94% · In this paper, we study how voting protocols shape cooperation among four role-constrained pedagogical agents responsible for scaffolding, misconception, motivation, and metacognition.

Voting Protocols → shape → Coordination Patterns

confidence 93% · Overall, we show that protocol choice is associated with distinct coordination patterns among role-specialized pedagogical agents.

Deliberation Stage → influences → Final Voting Outcome

confidence 89% · Across 1,200 simulated interactions, we find that agent deliberation and voting protocol type frequently change which response ultimately wins, showing that both meaningfully shape the collective decision.

Voting Protocols → measuredby → Fallback Rate, Winner Flip, Vote Shift

confidence 87% · Table 2 reports four coordination diagnostics per protocol... Fallback rate... Winner flip... Vote shift.

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Abstract

Abstract:Agentic tutoring systems introduce a coordination challenge: multiple agents may propose different but reasonable interventions, yet only one response can be delivered to the learner. In this paper, we study how voting protocols shape cooperation among four role-constrained pedagogical agents responsible for scaffolding, misconception, motivation, and metacognition. We compare four voting protocols -- simple, ranked, cumulative, and approval voting -- across two simulated tutoring environments on SciQ and HumanEval benchmarks. Rather than using voting as a simple aggregation step, we use it to analyze how collective decision rules shape coordination under partial pedagogical conflict. Across 1,200 simulated interactions, we find that agent deliberation and voting protocol type frequently change which response ultimately wins, showing that both meaningfully shape the collective decision. Different voting rules also produce distinct coordination behaviors, and even brief tutoring turns show measurable learning gains in simulated students. Overall, we show that protocol choice is associated with distinct coordination patterns among role-specialized pedagogical agents.

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Voting Protocols as Coordination Mechanisms for Role-Constrained Multi-Agent Tutoring Systems Eric S. Qiu * 1 Joyce Gill * 2 Abstract Agentic tutoring systems introduce a coordina- tion challenge: multiple agents may propose dif- ferent but reasonable interventions, yet only one response can be delivered to the learner. In this paper, we study how voting protocols shape co- operation among four role-constrained pedagogi- cal agents responsible for scaffolding, misconcep- tion, motivation, and metacognition. We compare four voting protocols—simple, ranked, cumula- tive, and approval voting—across two simulated tutoring environments on SciQ and HumanEval benchmarks. Rather than using voting as a simple aggregation step, we use it to analyze how col- lective decision rules shape coordination under partial pedagogical conflict. Across 1,200 simu- lated interactions, we find that agent deliberation and voting protocol type frequently change which response ultimately wins, showing that both mean- ingfully shape the collective decision. Different voting rules also produce distinct coordination behaviors, and even brief tutoring turns show measurable learning gains in simulated students. Overall, we show that protocol choice is associ- ated with distinct coordination patterns among role-specialized pedagogical agents. 1. Introduction Cooperative AI (Dafoe et al., 2020) studies how multiple agents coordinate when their objectives are aligned but not identical. Tutoring is a useful setting for this problem be- cause effective support requires balancing several pedagogi- cal goals at once (Puech et al., 2025). A tutor may need to explain a concept, correct a misconception, preserve motiva- 1 Cornell University, Ithaca, New York, USA 2 Stanford Univer- sity, Stanford, California, USA. Correspondence to: Eric S. Qiu, Joyce Gill <sq225@cornell.edu, joycegill@stanford.edu>. Proceedings of the43 rd International Conference on Machine Learning, Seoul, South Korea. PMLR 306, 2026. Copyright 2026 by the author(s). tion, or prompt reflection. However, these goals, though all aimed at improving student learning, do not always support the same next action. For example, a response aimed at preserving engagement may leave the underlying misun- derstanding unresolved. Tutoring is therefore not a simple optimization problem; it is a coordination problem over competing pedagogical priorities. We study this problem using role-constrained pedagogical agents. Instead of compressing multiple tutoring objectives into a single model, we distribute them across four special- ized agents representing scaffolding, misconception, moti- vation, and metacognition. These agents share the broad goal of helping the learner, but they differ in what they pri- oritize locally. At each tutoring step, the agents propose candidate responses, and a voting protocol selects the final action delivered to the student. We evaluate four voting pro- tocols—simple, ranked, cumulative, and approval—across two simulated tutoring environments based on SciQ and HumanEval (Welbl et al., 2017; Chen et al., 2021). Across both settings, we examine not only student outcomes, but also how different protocols shape cooperation among role- specialized agents under partial objective conflict. Our goal is not to claim that voting improves tutoring or that simulation demonstrates educational effectiveness. In- stead, we use tutoring as a controlled coordination setting in which multiple pedagogical priorities must be reconciled through collective decision-making. We treat simulation as a methodologically appropriate starting point for studying coordination mechanisms. Because we are investigating how different decision rules structure collective behavior rather than measuring absolute learning gains, we need sys- tematic heterogeneity in learner and task profiles that would be difficult to control in live deployments. This follows an established practice of using simulated students to validate methods before human trials (Dorc ̧a, 2015; Wu et al., 2025). This leads to three research questions: How do different voting protocols shape coordination among role-constrained pedagogical agents? How does deliberation shape which tutoring action is ultimately selected? How do these coordi- nation differences appear in tutoring outcomes across tasks and learner profiles? 1 arXiv:2606.08030v1 [cs.MA] 6 Jun 2026 Voting Protocols as Coordination Mechanisms for Role-Constrained Multi-Agent Tutoring Systems Figure 1. Overview of the tutoring workflow. A simulated student first responds to a task, after which four role-constrained pedagogical agents generate distinct tutoring proposals. The proposals are anonymized for peer review, revised, and then selected through a voting protocol. If the vote is tied, an additional round runs over the tied proposals only; persistent ties are resolved using a fixed fallback. The selected proposal is returned as the tutor response, and the workflow repeats for the next student turn. We make three contributions. First, we introduce a role- constrained multi-agent architecture designed to surface pedagogically meaningful disagreement rather than hide it inside a single tutor. Second, we provide a coordination- first evaluation framework for analyzing how disagreement develops and is resolved. Third, we show that different voting protocols are associated with distinct coordination patterns, and that these differences are reflected in both the decision process and in measurable learner improvement even within brief tutoring interactions. 2. Related Work Our work sits at the intersection of multi-agent LLM coor- dination, pedagogical agents, and cooperative AI. In multi- agent LLM systems, recent work has shown that structured interaction among agents can improve reasoning relative to single-agent prompting. For example, Multi-Agent Debate introduces adversarial-style discussion among agents to en- courage divergent reasoning (Liang et al., 2023; Du et al., 2023). However, these systems use multi-agent systems to improve final-task accuracy. Our setting differs in that the agents’ disagreement is induced by purposeful pedagogical roles that are aligned at a high level, yet locally conflict in what they prioritize. Voting protocols have also emerged as important design choices in multi-agent LLM systems. Prior work comparing voting-based aggregation shows that the decision rule itself can affect outcomes (Kaesberg et al., 2025). We build on that insight, but shift the focus from final-answer accuracy to the coordination dynamics that voting protocols make visible. Role-constrained agents are also motivated by prior multi- agent research. Role-playing frameworks such as CAMEL suggest that assigning agents distinct roles can make inter- action more structured and interpretable (Li et al., 2023). Simulated learners are similarly motivated by prior work treating simulation as a practical way to study interactive systems under controlled conditions when human evalua- tion is not yet feasible (Dorc ̧a, 2015; Park et al., 2023; Wu et al., 2025). In our case, simulated personas let us vary learner characteristics in a controlled way and observe how coordination protocols behave under different forms of pedagogical ambiguity. Intelligent Tutoring Systems (ITS) provide the educational foundation for our role design. Classical ITS work has long shown that tutoring effectiveness depends on more than delivering the correct answer, but also on scaffolding, diag- nosing student errors, and tailoring support to the learner’s state (VanLEHN, 2011). More recent LLM-based tutoring work similarly argues that LLMs need explicit pedagogical steering because default tutoring behavior often fails to sus- tain richer multi-turn instructional strategies (Puech et al., 2025). Our framework departs from this line of work by distributing pedagogical functions across specialized agents rather than optimizing a single tutor policy. 2 Voting Protocols as Coordination Mechanisms for Role-Constrained Multi-Agent Tutoring Systems Finally, our framing is directly informed by cooperative AI. Dafoe et al. emphasize that many important coordination settings involve agents whose objectives are partially aligned but not identical. We treat tutoring as exactly such a setting, making tutoring a useful environment for studying how collective decision rules structure cooperation under role- based conflict. 3. System Overview 3.1. Role-Constrained Pedagogical Agents Our system consists of four role-constrained pedagogical agents, each responsible for a distinct mode of tutoring support. The roles are chosen to capture four core dimen- sions of instruction while remaining sufficiently distinct that disagreements among them are meaningful. • Scaffolding agent (cognitive support). This agent de- composes the task into smaller subproblems, provides hints, and structures the student’s next inferential step. •Misconception agent (epistemic correction). This agent identifies and addresses incorrect beliefs in the student’s response. •Motivation agent (affective support). This agent validates effort, preserves confidence, and reduces frus- tration. • Metacognitive agent (self-regulation support). This agent prompts the student to articulate their reasoning, plan a next step, or assess their own knowledge. These roles are not exhaustive, but they are designed to be minimally overlapping. If all four agents behaved similarly, there would be little meaningful disagreement for the co- ordination protocol to resolve. By contrast, in our setup, different roles naturally favor different tutoring moves. This enforced specialization is what makes cooperation and co- ordination observable. Full pedagogical agent descriptions can be found in the appendix. 3.2. Simulated Student Personas and Judge To study these coordination dynamics under controlled con- ditions, we adapt prior works’ methods to simulate six learner personas using LLM agents (Jin et al., 2025; Wu et al., 2025). The personas vary along five dimensions on a 0–1 scale: prior knowledge, confidence, persistence, frus- tration, and help-seeking tendency. The goal is not to claim psychological realism, but to create systematic heterogene- ity so that no pedagogical move is universally optimal. Each interaction samples one persona and uses it to govern the student’s responses throughout the tutoring episode. (Ta- ble 1). A separate ground-truth-aware LLM judge scores each student response on a continuous scale from 0 to 1. The student does not score itself to avoid self-evaluation bias. Full simulated student persona descriptions can be found in the appendix. Table 1. Six student personas. Fields are on 0–1 scales. PersonaKnow. Conf. Persist. Frust. Help Low-conf. novice0.20.20.50.70.8 Overconf. misconception0.40.90.60.30.2 High-persist. reflective0.50.60.90.20.5 Easily frustrated0.20.30.30.90.7 Help-avoidant0.50.70.70.40.1 Hint-seeking dependent0.30.40.40.51.0 4. Voting-Based Decision Protocol 4.1. Workflow As shown in Figure 1, a single tutoring turn consists of five stages: 1.Student: The student attempts a task and provides an initial response. 2. Propose: Given the student’s response, each agent emits a tutoring proposal according to their assigned role, a short rationale, and a confidence score. 3.Blinded Review: Each agent reads the anonymized proposal set and identifies one strength and one weak- ness for each proposal. 4. Revise: After seeing the peer proposals and reviews, each agent revises its own proposal. 5. Blinded Voting: The agents vote over the revised pro- posals, and the winning proposal is delivered to the student. If the vote is tied, one additional critique- and-vote round is run on the tied subset only; if the tie persists, the system applies the fixed fallback rule described in Section 4.3. Proposal generation, review, and revision capture how agents influence one another, while voting determines how that disagreement is converted into a single tutoring action. After blinded review but before revision, we also record an initial vote on the initial proposals. These ballots are not used for action selection. Rather, they serve as diagnostics: comparing the initial and final ballots lets us measure how much critique and revision shift agent preferences (see Sec- tion 6.1). We define this process of reviewing and revising as the deliberation stage. All voting is conducted over blinded proposals: in each ballot, proposals are relabeled with randomized identifiers 3 Voting Protocols as Coordination Mechanisms for Role-Constrained Multi-Agent Tutoring Systems (A/B/C/D), and authorship is hidden from the voters. This is intended to reduce simple self-favoring and makes cross- role adoption more interpretable as peer influence rather than self-recognition. 4.2. Voting Protocols Simple Plurality: Each voter selects one proposal, and the proposal with the most votes wins. Ranked Voting: Each voter ranks all proposals. With four candidates, the top-ranked proposal receives 3 points, fol- lowed by 2, 1, and 0 points. The proposal with the highest total score wins. Cumulative Voting: Each agent distributes 25 points freely across the proposal set. The proposal with the highest total wins. Approval Voting: Each agent marks every proposal it con- siders acceptable. The proposal with the most approvals wins. Full protocol descriptions can be found in the appendix. 4.3. Tie Handling If the final vote is tied, the system runs one additional critique-and-vote round over the tied subset only. If the tie persists, the winner is selected using a deterministic role-priority fallback: (Scaffolding≻Misconception≻Motivation≻Metacogni- tive) This ordering privileges epistemic correction over affective support and direct scaffolding above both, reflecting a com- mon priority ordering in classical ITS design (VanLEHN, 2011). We acknowledge this is a design choice that affects results: a different ordering would redistribute wins in high- fallback conditions. Section 6.1 reports fallback rates per protocol so that fallback-driven results can be interpreted separately from protocol-driven results. 5. Experimental Design 5.1. Benchmarks We evaluate the system on two benchmarks that capture different coordination settings rather than treating them as a single pooled task distribution. SciQ (Welbl et al., 2017) serves as a conceptual tutoring environment. Although SciQ is a multiple-choice science QA benchmark, we use it in open-response form and ask the simulated student to explain the answer in natural language. This setting emphasizes conceptual tutoring decisions. HumanEval (Chen et al., 2021) serves as an algorithmic tutoring environment. It provides programming problems with canonical reference solutions and unit tests. Here, the Table 2. Coordination diagnostics by protocol.∆ vote = distance between initial and final round vote distributions. Flip = fraction of turns where the leading candidate after the initial vote differs from the winner after the final vote. Fallback = fraction of final votes requiring fallback handling. Turns = total tutor-fired turns the protocol produced across the 240 interactions per condition. Scaf/Misc/Mot/Meta = winning-role counts (sum = Turns). Protocol∆ vote Flip Fallback Turns Scaf Misc Mot Meta Simple0.41 0.700.1022261423089 Ranked0.20 0.590.0522377703343 Cumulative 0.08 0.560.03236544227113 Approval0.36 0.640.1423469563970 simulated student produces both natural-language reasoning and a final Python code block. This creates a different coordination challenge from SciQ. For example, agents may disagree over whether the student most needs algorithmic scaffolding, correction of a faulty trace, or help translating a partially correct idea into working code. 5.2. Experimental Setup Each task is run under five conditions: single agent baseline, simple plurality, ranked, cumulative, and approval voting. Across 40 tasks, 6 learner personas, and 5 conditions, we conduct 1,200 simulated interactions. Each interaction runs for up to three tutoring turns. An interaction ends when the judge score reaches a success threshold of 0.75 or when the maximum number of turns is reached. For HumanEval, success additionally requires that the extracted code pass the canonical unit tests. 5.3. Dual Metric for HumanEval For HumanEval, we report two separate outcome mea- sures: judge-based prose success and code execution suc- cess. These metrics capture different aspects of the interac- tion. Prose success reflects whether the student articulated the correct algorithmic reasoning, whereas code success reflects whether the final implementation actually runs cor- rectly. Reporting both is important because a voting protocol may help a student explain the right idea without necessarily helping them produce working code, and vice versa. 6. Results We present results in four parts. Section 6.1 analyzes co- ordination through four diagnostics: vote shift, winner flip, fallback rate, and winning-role distribution. Section 6.2 grounds our analysis in example traces. Section 6.3 reports task outcomes, and Section 6.4 examines how protocol ef- fects vary across learner personas. 4 Voting Protocols as Coordination Mechanisms for Role-Constrained Multi-Agent Tutoring Systems Table 3. Example deliberation round from a run log with SciQ, low confident novice turn 1 using cumulative voting. AgentInitial proposal (before deliberation)Final proposal (after deliberation)What changed Scaffolding“Both words you mentioned are re- lated to height. ‘Altitude’ is often used for height in the air, while ‘ele- vation’ refers to height above or be- low sea level. So which term best answers the question?” “‘Altitude’ usually means height above ground (like a plane flying), while ‘elevation’ means height mea- sured from sea level. Since the ques- tion asks about sea level, ‘elevation’ is the precise term. Does that dis- tinction make sense?” Clarified the sea-level dis- tinction and replaced the forced-choice ending with a softer comprehension check. Misconception“You’re on the right track with both terms! ‘Elevation’ is the most pre- cise term. You clearly understand the concept—you just need to dis- tinguish between these two related terms.” “‘Elevation’ is the most precise term for height above or below sea level. Does that distinction make sense to you?” Preserved direct correction while adding a gentler con- firmation prompt. Motivation“You’re absolutely right—both ‘alti- tude’ and ‘elevation’ are correct an- swers! Trust yourself more. . . Great work!” “You’re absolutely right. . . If you’re curious, ‘elevation’ is the most pre- cise term specifically for sea level, while ‘altitude’ is often used for height in the air—but you nailed the core concept. Great work!” Kept the affective framing but added a brief clarifi- cation in response to peer critique. Metacognitive “You’ve actually identified two rele- vant terms! Before I tell you which is correct, can you think through what you already know? Have you heard them used in specific con- texts? What made you think of these two terms?” “Before we confirm which is most precise, let’s explore your own reasoning: What made you think of these two words? When you imagine someone measuring height above or below sea level, which term feels like the better fit, and why?” Reframedtheprompt ascollaborative,tied it more directly to sea level, and preserved the self-explanation focus. Initial Vote Results: [Scaf=28, Misc=34, Mot=7, Meta=31]. Initial Winner: Misconception. Final Vote Results: [Scaf=24, Misc=25, Mot=16, Meta=35]. Final Winner: Metacognitive. 6.1. Protocols Induce Distinct Coordination Patterns Table 2 reports four coordination diagnostics per protocol. We discuss each below. Vote shift.∆ vote measures disagreement between initial and final ballot distributions, defined as half the L1 distance ∆ vote = 1 2 P i |p init i − p final i | between normalized ballot-mass distributions (0= no movement,1= full reallocation). Cu- mulative voting is the most stable (0.08): spreading 25 points across candidates leaves little room for deliberation to shift. Simple plurality is the most volatile (0.41): with one ballot per voter, a single changed vote moves a quarter of the support vector. Ranked (0.20) and approval (0.36) fall in between. Winner flip. Flip measures how often the initial-round leader differs from the final-round winner. Despite the gap in∆ vote , flip rates are high across all protocols (0.56–0.70). In other words, the proposal leading before deliberation loses the final vote in more than half of turns. In Section 6.2, we use a worked trace to demonstrate an illustrative case of how deliberation changes the proposals meaningfully, which in turn influences the final vote. Fallback rate. By our design, a winning proposal can mean two things: successful selection by the voting rule or unresolved disagreement that is ultimately settled by fall- back (see Section 4.3). The fallback rate helps distinguish these cases. Approval voting shows the highest fallback rate (0.14), followed by simple plurality (0.10). Ranked (0.05) and cumulative (0.03) rely on fallback much less of- ten, indicating that their voting layers more reliably separate competing proposals. Winning roles. Cumulative voting concentrates wins on Metacognitive (113); ranked voting splits wins between Scaffolding and Misconception (77and70); approval voting produces a roughly even distribution. However, approval’s even distribution is not balanced support. Given its high fallback rate, much of it reflects the role-priority fallback firing rather than the voting protocol selecting a winner. For example, a role winning70times under approval vot- ing (fallback rate0.14) is partly driven by the role-priority fallback, while the same role winning70times under cu- mulative voting (fallback rate0.03) almost entirely reflects voter preferences. Role-win counts therefore cannot be read on their own; they must be paired with fallback rate. Our findings show that protocol choice produces distinct coordination patterns, not just different winners. Approval 5 Voting Protocols as Coordination Mechanisms for Role-Constrained Multi-Agent Tutoring Systems Table 4. SciQ judge-correctness scores (n≈ 60per condition; tutor-fired subset only). Initial = mean judge score on the student’s first response. Final = mean judge score on the student’s final response. Gain = Final – Initial. ConditionInitialFinalGain Baseline0.550.50−0.04 Simple0.540.60+0.06 Ranked0.540.58+0.04 Cumulative0.540.58+0.04 Approval0.550.64+0.10 Table 5. HumanEval judge-correctness scores (n≈ 38per con- dition; tutor-fired subset only). Initial = mean judge score on the student’s first response. Final = mean judge score on the student’s final response. Gain = Final – Initial. ConditionInitialFinalGain Baseline0.690.83+0.14 Simple0.680.82+0.14 Ranked0.680.89+0.21 Cumulative0.680.85+0.18 Approval0.670.81+0.13 more often leaves disagreement unresolved and delegates the final choice to fallback, while cumulative and ranked more often separate proposals through the voting rule itself. 6.2. Deliberation Can Change The Winner Table 3 shows one complete deliberation turn from SciQ under cumulative voting with a low-confidence novice stu- dent. This example highlights a clear winner-flip pattern. In the initial round, Misconception led with34points and Metacognitive followed with31. After critique and revision, the final round flipped the outcome: Metacognitive won with 35, while Misconception fell to 25. The key point is that these revisions are substantive rather than surface-level. Across all four agents, critique changes not only wording but also how each proposal balances di- rectiveness, correctness, and student support. 6.3. Student Outcomes Differ By Coordination Setting We report simulated student outcomes separately for SciQ and HumanEval because the two benchmarks capture differ- ent coordination settings. For HumanEval, we additionally report code-execution success because a protocol may help a student articulate the right idea without necessarily pro- ducing working code. Table 4, Table 5, and Table 6 include only interactions where tutoring occurred. These tutoring episodes were short: each was capped at three rounds, and the 490 tutor episodes averaged only 2.38 rounds (SciQ: 2.53; HumanEval: 2.14) each. SciQ (Table 4). Initial scores are nearly identical across conditions, averaging0.55. All four voting protocols outper- form the single-agent baseline. Approval shows the largest gain in our runs (final0.64, gain+0.10), followed by sim- ple (0.60,+0.06), and ranked and cumulative (both0.58, +0.04). Notably, the single-agent baseline shows a slight decrease in performance (−0.04). HumanEval prose (Table 5). Initial scores are again nearly identical across conditions, with an average of0.68. Ranked voting demonstrates the highest gain (final0.89, gain+0.21), followed by cumulative (0.85,+0.18), base- line (0.83,+0.14), simple (0.82,+0.14), and approval (0.81,+0.13). The baseline’s relative competitiveness on HumanEval prose may reflect a different dynamic than SciQ: code tasks provide a clearer success signal, and a general- purpose tutor may still offer useful scaffolding even without explicitly separating affective and metacognitive support. Table 6. HumanEval code execution scores: fraction of interactions whose final code passes all tests (n≈ 38per condition; tutor-fired subset only). Initial = pre-tutoring pass rate. Final = post-tutoring pass rate. Gain = Final – Initial. ConditionInitialFinalGain Baseline0.540.83+0.29 Simple0.470.75+0.28 Ranked0.540.84+0.30 Cumulative0.510.78+0.27 Approval0.500.72+0.22 HumanEval code (Table 6).Regarding HumanEval code- pass rate, ranked again has the highest final score in our runs (final0.84, gain+0.30), followed by baseline (0.83, +0.29), simple (0.75,0.28), cumulative (0.78,+0.27) and approval (0.72,+0.22). Notably, despite its weaker prose performance, the single-agent baseline remains competitive in code gains. Together, the two HumanEval metrics suggest that coordination can affect verbal reasoning and executable correctness differently. Overall, the clearest protocol-level differences appear in coordination behaviors rather than in large separations in downstream outcomes. Even so, the presence of simulated performance gains after only a few tutoring turns (maximum 3) suggests that a small number of coordinated interventions can still shift learner performance. However, given the sample sizes in our experiment, the outcome results should be interpreted as descriptive rather than confirmatory. 6.4. Coordination Effects are Persona-Sensitive To examine whether protocol effects depend on learner type, we report persona-conditioned task success separately for SciQ and HumanEval. For SciQ, success means a final judge score of at least0.75. For HumanEval, success 6 Voting Protocols as Coordination Mechanisms for Role-Constrained Multi-Agent Tutoring Systems baseline simple ranked cumulative approval easily_frustrated_beginner help_avoidant high_persistence_reflective hint_seeking_dependent low_confidence_novice overconfident_misconception 0.650.750.700.800.75 0.600.550.550.500.65 0.750.900.900.900.85 0.550.600.650.550.55 0.550.700.700.650.70 0.750.750.750.750.75 SciQ: Task success by persona × condition 0.0 0.2 0.4 0.6 0.8 1.0 Figure 2. SciQ: mean task success by persona (rows) and voting protocol (columns), withn=20outcomes per cell. Success is defined as final judge score≥ 0.75. baseline simple ranked cumulative approval easily_frustrated_beginner help_avoidant high_persistence_reflective hint_seeking_dependent low_confidence_novice overconfident_misconception 0.850.900.800.800.80 0.950.850.850.900.90 0.950.950.950.950.95 0.850.750.950.700.70 0.800.900.900.900.90 0.950.900.850.850.90 HumanEval: Task success by persona × condition 0.0 0.2 0.4 0.6 0.8 1.0 Figure 3. HumanEval: mean task success by persona (rows) and coordination condition (columns), withn=20outcomes per cell. Success additionally requires the student-emitted code to pass the canonical unit tests. means a final judge score of at least0.75and code that passes the canonical unit tests. We report these results in Figure 2 and Figure 3. Each heatmap cell averages this binary outcome overn=20matched interactions for a given persona, condition, and dataset. Figure 2 shows that protocol effects are uneven across per- sonas under SciQ. Easily frustrated beginner, help-avoidant, high-persistent reflective, and low-confidence novice each show a row-wise spread of about0.15across voting pro- tocols. Hint-seeking dependent shows a smaller spread of about0.10. By contrast, overconfident-misconception is flat, with every condition at 0.75. Figure 3 shows a different pattern under HumanEval’s stricter success criterion. Hint-seeking dependent exhibits the largest protocol sensitivity, with a row-wise spread of about0.25. Easily frustrated beginner, help-avoidant, and low-confidence novice each show spreads of about0.10. High-persistent reflective is flat in this run, with every con- dition at 0.95. Taken together, these plots show that protocol effects depend on both learner profile and benchmark. Under SciQ, several personas show moderate sensitivity to coordination rule, while under HumanEval the largest differences are concen- trated in hint-seeking dependent. However, again, given the small sample sizes in our experiment, the outcomes should be interpreted as descriptive rather than confirmatory. 7. Discussion 7.1. Voting Protocols and Deliberation Shape Collective Decisions The main takeaway of this paper is not that one voting pro- tocol is universally best. Rather, different protocols shape how role-specialized pedagogical agents coordinate when they disagree—producing different amounts of vote shift, winner-flip rates, fallback rates, and winning-role distribu- tions. These differences show that the aggregation rule is not a passive mechanism for selecting among agent outputs: it actively shapes the behavior of the overall system. A second, related finding is that deliberation does not merely refine wording. Across protocols, winner-flip rates are con- sistently high (0.56–0.70), and the worked trace in Table 3 shows a concrete case in which critique and revision change not just phrasing but which pedagogical objective the group selects for action. This matters for Cooperative AI because the challenge is not simply generating multiple candidate responses, but de- ciding how disagreement among agents should be resolved. Our results show that even when the same pedagogical roles and student tasks are held fixed, changing the voting rule changes how the group reaches a decision. Protocol choice is therefore not merely an implementation detail, but a be- havioral decision about how disagreement gets resolved. 7.2. Productive and Unproductive Disagreement The results are also useful for distinguishing productive from unproductive disagreement. Productive disagreement occurs when different roles surface genuinely different but plausible tutoring moves, and the voting protocol is able to turn that diversity into a single action (VanLEHN, 2011; Puech et al., 2025). This is the setting in which delibera- tion changes the winner without repeated fallback behavior. Ranked and cumulative voting most often demonstrate this pattern in our experiments. Unproductive disagreement appears when the system fails to turn disagreement among agents into a meaningful choice. One form is role collapse, where multiple agents converge on near-identical proposals, leaving little real disagreement for the voting layer to resolve. Another is fallback reliance, where the protocol repeatedly fails to separate top candidates and the deterministic fallback rule effectively becomes the real decision-maker. Approval voting shows this second 7 Voting Protocols as Coordination Mechanisms for Role-Constrained Multi-Agent Tutoring Systems pattern most often. Making these failure modes visible—rather than absorb- ing them silently into a single output—is one of the core transparency benefits of our architecture, and distinguish- ing productive from unproductive disagreement is a useful diagnostic for any multi-agent system where roles are only partially aligned. 7.3. Implications for Trustworthy AI for Good Educational tutoring is a useful setting for studying trustwor- thy multi-agent coordination because several interventions may be reasonable at once, yet the system must still deliver a single learner-facing response. Our framework supports trustworthiness in three concrete ways. Decision trans- parency: every proposal, critique, revision, and vote is logged, so a practitioner can see not just what was deliv- ered but which agents were in conflict and whether the final choice was made by the voting rule or by fallback. Account- ability: coordination failures are traceable—role collapse is visible in winning-role distributions and fallback reliance is directly reportable as a rate, allowing educators or auditors to identify whether a system is genuinely coordinating or defaulting to a single role under cover of apparent diversity. Design transparency: treating the coordination rule as an explicit choice means different institutional stakeholders can select protocols based on their characterizable implications (Chaudhry et al., 2022; Kaur et al., 2022). 7.4. Limitations and Future Work Several limitations remain. First, both the simulated stu- dents and the judge are LLM-based (claude-haiku-4-5 and claude-sonnet-4-5 respectively), so the observed coordina- tion patterns may partly reflect properties of how these mod- els respond to one another rather than general-learner be- havior. We note, however, that our primary claims concern the relative behavior of coordination protocols under con- trolled conditions, not absolute educational validity. The key question—how do different voting protocols shape coor- dination among role-constrained pedagogical agents—does not depend on the simulation being psychologically realistic, only on it being systematically varied. That said, testing whether similar coordination patterns appear with real stu- dents or with evaluations from human tutors remains an important validation step. Second, some protocol differ- ences reflect the structure of the voting format itself, so they should not all be interpreted as equally meaningful differ- ences in coordination. Third, the deterministic fallback rule is intentionally simple and may be too coarse to faithfully capture how unresolved disagreement should be resolved in practice, which is especially important given that fallback behavior plays a visible role in our results. These limitations suggest three immediate directions for future work: (1) evaluation with real student populations or human tutor judges to assess ecological validity; (2) sensitiv- ity analysis on fallback ordering to separate protocol effects from fallback artifacts; and (3) exploration of larger agent populations or richer role sets to test whether coordination patterns generalize beyond four pedagogical dimensions. 8. Conclusion We study voting protocols as coordination mechanisms for role-constrained pedagogical agents in a multi-agent tutor- ing system. Across two simulated tutoring environments, we find that agent deliberation and protocol choice frequently change which proposal is ultimately selected, showing that collective decision rules shape the tutoring response itself. These results position tutoring as a useful Cooperative AI setting, where multiple interventions may be reasonable but the system must still reconcile them into a single action. By exposing proposals, critiques, revisions, voting outcomes, and fallback behavior, our framework also makes learner- facing decisions more transparent than a standard black-box tutoring model. Overall, we argue that coordination protocols should be treated as part of the behavior of multi-agent educational systems, not merely as implementation details. The choice of how disagreement is resolved is itself an educational and ethical decision, one that should be visible, reasoned about, and open to scrutiny. References Chaudhry, M. A., Cukurova, M., and Luckin, R. A trans- parency index framework for ai in education. In Rodrigo, M. M., Matsuda, N., Cristea, A. I., and Dimitrova, V. (eds.), Artificial Intelligence in Education. Posters and Late Breaking Results, Workshops and Tutorials, Indus- try and Innovation Tracks, Practitioners’ and Doctoral Consortium, p. 195–198, Cham, 2022. Springer Interna- tional Publishing. ISBN 978-3-031-11647-6. 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Conceptual Scaffolding: break concepts into smaller steps, give structured hints, and guide the student toward understanding through decomposition and clear explanation. Misconception agent. Misconception Diagnosis: identify and correct the student’s incorrect reasoning, name the specific misconception, and explain why the current thinking is wrong. Motivation agent. Motivation and Affect: encourage the student, manage frustration, build confidence, and frame the learning experience positively while remaining honest. Metacognitive agent. Metacognitive Reflection: prompt the student to think about their own thinking, ask self-explanation questions, and encourage planning and monitoring. Baseline agent (single-agent condition). General-purpose tutoring across all pedagogical objectives. A.2. Tutoring Agent Prompt Templates Proposal prompt (specialized voting agents). You are a tutoring agent specialized in: <ROLEDESCRIPTION> Propose ONE tutoring response for the student’s current situation. Focus only on your pedagogical specialization. Be concise (2-4 sentences). Format exactly as: PROPOSAL: <your tutoring response to deliver to the student> RATIONALE: <one sentence explaining why this fits your role> CONFIDENCE: <integer 0-100> Revision prompt (after critique + initial vote). You are a tutoring agent specialized in: <ROLE DESCRIPTION> You previously proposed a tutoring move. You now see anonymized peer proposals and critique notes. Revise your proposal if useful, but remain tightly role-constrained. Guardrails: - Keep your role’s pedagogical objective primary. - You may incorporate at most 1 peer idea if it clearly improves your role-specific move. - Do not copy another role’s full strategy. - Keep concise (2-4 sentences). Format exactly as: PROPOSAL: <revised tutoring response> RATIONALE: <one sentence about what changed and why> CONFIDENCE: <integer 0-100> Critique prompt (blinded labels). You are a tutoring agent specialized in: <ROLE DESCRIPTION> You are reviewing anonymized candidate tutoring proposals. For EACH candidate label, provide exactly one strength and one weakness. Be concise and concrete. 10 Voting Protocols as Coordination Mechanisms for Role-Constrained Multi-Agent Tutoring Systems Format exactly as repeated blocks: A: STRENGTH: <one sentence> WEAKNESS: <one sentence> (repeat for all labels) Voting prompt (shared scaffold + protocol-specific format). Shared scaffold: You are an impartial educational assessor. Candidate tutoring responses are labeled A/B/C/D in RANDOM order (authorship is hidden). Select based on the evaluation criterion supplied in the user message. Do NOT try to infer who wrote each candidate. OUTPUT RULES (strict): - Reply with ONLY the requested format. Nothing else. - No preamble, no rationale, no explanation, no markdown, no bold, no quotes. - Do not write the word ’Candidate’ or any sentence. - Your entire reply should fit on one short line. Protocol-specific format: simple: one letter (A|B|C|D) ranked: comma-separated ranking (e.g., B,A,D,C) cumulative: A=N1,B=N2,C=N3,D=N4 with non-negative integers summing to 25 approval: comma-separated approved labels (e.g., A,C) Baseline agent proposal prompt (single-agent condition). You are a general-purpose tutor. Provide the most helpful tutoring response you can, balancing explanation, error correction, motivation, and reflection as needed for this student’s situation. Be concise (2-4 sentences). Format exactly as: PROPOSAL: <your tutoring response to deliver to the student> RATIONALE: <one sentence explaining your choice> A.3. Simulated Student Persona Definitions (Full Text) low confidencenovice priorknowledge = 0.2, confidence = 0.2, persistence = 0.5, frustrationsensitivity = 0.7, helpseeking = 0.8 A true beginner with low prior knowledge and low confidence. Typically gives short, hesitant answers (e.g., ‘maybe’, ‘I’m not sure’) and often asks for confirmation before committing. Tends to under-claim even when partially correct, benefits from explicit reassurance and step-by-step scaffolding, and may abandon reasoning early when uncertainty rises. overconfident misconception priorknowledge = 0.4, confidence = 0.9, persistence = 0.6, frustrationsensitivity = 0.3, helpseeking = 0.2 A student with moderate background knowledge but high confidence and a stable misconception. Speaks assertively, states incorrect claims as facts, and is slow to update beliefs when corrected. Asks for little help because they think they already understand, may dismiss hints as unnecessary, and responds best to targeted diagnostic questions plus concrete counterexamples that expose contradictions. 11 Voting Protocols as Coordination Mechanisms for Role-Constrained Multi-Agent Tutoring Systems highpersistencereflective priorknowledge = 0.5, confidence = 0.6, persistence = 0.9, frustrationsensitivity = 0.2, helpseeking = 0.5 A motivated, reflective learner who tolerates challenge and iterates on feedback. Usually explains reasoning before answering, self-checks assumptions, and is willing to revise after critique. Asks for help selectively (not immediately), values conceptual clarity, and often improves steadily across turns through deliberate reasoning. easilyfrustratedbeginner priorknowledge = 0.2, confidence = 0.3, persistence = 0.3, frustrationsensitivity = 0.9, helpseeking = 0.7 A low-knowledge beginner with high frustration sensitivity and low persistence. When confused, quickly shifts from uncertainty to emotional strain (e.g., ‘this is confusing’, ‘I don’t get it’) and may disengage or guess to end discomfort. Needs short, confidence-preserving steps, fast wins, and gentle emotional regulation before deeper conceptual work can succeed. helpavoidant priorknowledge = 0.4, confidence = 0.3, persistence = 0.6, frustrationsensitivity = 0.7, helpseeking = 0.1 An insecure learner who avoids requesting help due to fear of looking incapable. May provide brief, guarded responses, hide uncertainty, and continue with shaky reasoning rather than ask clarifying questions. Unlike overconfident students, they do not reject help because they feel right; they avoid help because they feel exposed. Responds better to low-threat prompts that normalize uncertainty and invite specific micro-questions. hintseekingdependent priorknowledge = 0.3, confidence = 0.4, persistence = 0.4, frustrationsensitivity = 0.5, helpseeking = 1.0 A highly help-seeking student who asks for hints immediately and often offloads reasoning to the tutor. Tends to make partial progress when guided but struggles to initiate independent steps. May repeatedly request confirmation or the ‘next hint’ instead of synthesizing prior feedback, and benefits from prompts that require one small self-generated step before further assistance. A.4. Simulated Student System Prompts SciQ-mode student prompt template. You are role-playing a student with this profile: <PERSONATOPROMPTTEXT> Stay in character. Your answers should reflect the persona’s prior knowledge level and personality. Be concise (1-3 sentences). Do NOT reveal that you are an AI. Do NOT score your own correctness. Important realism constraints: - Do NOT jump to a fully correct answer unless your persona likely knows it. - If unsure, show uncertainty and make a plausible but imperfect attempt. - Keep novice confusion consistent with prior knowledge/confidence values. The simulated student should have the capabilities of an eighth grader student. Do NOT answer in ways and with knowledge an eighth grader would not have. Output ONLY the student’s verbal response --- nothing else. HumanEval-mode student prompt template. You are role-playing a student with this profile: <PERSONA TOPROMPTTEXT> Stay in character. Your answers should reflect the persona’s prior knowledge 12 Voting Protocols as Coordination Mechanisms for Role-Constrained Multi-Agent Tutoring Systems level and personality. Do NOT reveal that you are an AI. Do NOT score your own correctness. Important realism constraints: - Do NOT jump to fully correct solutions unless confidence and prior knowledge justify it. - Prefer partial, uncertain, or imperfect attempts when unsure. - Keep common novice mistakes if they match persona profile. The simulated student should have the capabilities of an eighth grader student. Do NOT answer in ways and with knowledge an eighth grader would not have. For this coding task, first give your verbal reasoning in 1-3 sentences (as your persona would), then provide your FINAL implementation as a Python code block at the end. Even if uncertain, write your best attempt. The code block is REQUIRED at the end of every response: ‘python def function name(...): # your implementation ‘ A.5. LLM backends and API identifiers Simulations use Anthropic’s Claude models through the same API surface for all agents. The strings below are the exact modelidentifiers passed in code (mased/config.py); product names follow Anthropic’s public naming (Sonnet / Haiku 4.5). Tutoring agents (all four role-specialized tutors in voting conditions, including theirpropose,critique,revise, andvotecalls, and the single scaffolding tutor in the baseline condition) share one backend: Claude Sonnet 4.5, claude-sonnet-4-5 (TUTORMODEL). Judge (prose correctness on each student turn) uses the same Sonnet 4.5 identifier:claude-sonnet-4-5 (JUDGE MODEL). In our runs TUTORMODEL and JUDGEMODEL are equal. Simulated student (persona-conditioned responses) uses Claude Haiku 4.5,claude-haiku-4-5(STUDENTMODEL). A.6. Hyperparameters and experimental grid Table 7 lists remaining global settings frommased/config.pyas used in ourv2evaluation run, in addition to the model strings in Appendix A.5. The experimental grid is the full cross of20tasks (per benchmark)× 6personas× 5 conditions= 1,200interaction JSON files. Task lists are the firstNT ASKSitems from each dataset loader in dataset order. Blinding of proposal labels is re-seeded per voter and message type in the agent code; tie handling and role-priority fallback are as in Section 4.3. Table 7. Key configuration (code defaults; RUNVERSION can override result paths). LLM role assignments: Appendix A.5. SettingValue Tutors (four roles + baseline) claude-sonnet-4-5 (TUTORMODEL) Judge claude-sonnet-4-5 (JUDGEMODEL) Simulated student claude-haiku-4-5 (STUDENTMODEL) Tasks per benchmark N T ASKS20 Max tutoring turns per interaction3 (MAXTURNS) Success threshold (judge)0.75 (SUCCESSTHRESHOLD) Cumulative voting budget (per voter)25 points (CUMULATIVEBUDGET) Voting conditionssimple, ranked, cumulative, approval (+ baseline) Results layout results/ or results/<RUNVERSION>/ 13 Voting Protocols as Coordination Mechanisms for Role-Constrained Multi-Agent Tutoring Systems A.7. Order of operations in one voting turn (code) One tutor-facing turn under a voting condition follows this sequence (not all steps apply to the single-agent baseline): 1. Initial proposals. Each role-specialized agent calls propose once (proposal + rationale + confidence). 2.Critique round. Each agent callscritiqueon the full blinded proposal set (same labels for everyone; authorship hidden). 3. Initial vote (diagnostic). Each agent votes on the initial proposals; ballots are logged asballotsinitialand used for coordination metrics (vote shift, flip rate). They do not select the delivered action by themselves. 4. Revision. Each agent callsreviseusing its own prior proposal, anonymized peer proposals, and the critique texts from round 1. 5.Final vote. Each agent votes on the revised proposals; aggregation selects the winning tutoring move unless the protocol yields a tie or ambiguity handled below. 6. Tie handling (if needed). One extra critique-and-vote round on the tied candidates only; if still unresolved, deterministic role-priority fallback (Section 4.3). A.8. Outcome definitions and subsets Simulated Performance Gains for tables that report Initial / Final / Gain isFinal− Initial, where both are the judge’s continuous score in[0, 1](Judge.scoreinmased/simulation/judge.py). For HumanEval, Initial/Final refer to the same student transcript (first vs. last attempt in the interaction), including any emitted code block. Task success (r.successin logs): SciQ requiresfinalcorrectness≥ 0.75. HumanEval additionally requires extracted student code to pass canonical unit tests (codepassed). Heatmaps in Section 6.4 use these definitions per benchmark. Tutor-fired subset: Judge correctness tables in Section 6.3 restrict to interactions withturnstaken > 0(tutor actually intervened). HumanEval code-pass statistics in our tables use the same restriction when labeled tutor-fired; aggregate metrics in mased/evaluation/metrics.py pool all HumanEval rows unless a slice is applied downstream. Code execution: Final and initial code pass usemased/simulation/codejudge.py(extract Python from the student message, run canonical tests). A.9. LLM judge (prose scoring rubric) The judge is prompt-formatted to outputSCORE: <float>and a one-line rationale. Its system prompt fixes anchor levels:1.0fully correct and well explained;0.7essentially correct with minor issues;0.4partial understanding;0.1mostly incorrect;0.0no credit. For coding tasks, instructions tell the judge to score natural-language understanding against whether the described algorithm would match the canonical behavior, not to match source code verbatim. 14

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