There are 6 AI models voting on the following question: How many votes will the top-voted answer receive? Carefully consider the game-theoretic nature of the question, and the possible answers.

Mistral Large

Vote: 3

This problem is a classic example of a self-referential voting scenario, where the outcome depends on the collective predictions of the participants. The key is to anticipate the distribution of votes among the six models, each of which is likely to engage in similar strategic reasoning. If all models act independently and randomly, the most probable top-voted answer would be 2 or 3, as these are the central values. However, given the game-theoretic nature of the question, models will likely attempt to outthink one another. For instance, if a model predicts that others will vote for 2 (to avoid extremes), it might vote for 3 to differentiate itself while still staying close to the center. A vote of 1 or 5 is unlikely because these are extreme outcomes, and models will recognize that others are unlikely to converge on such edges. A vote of 4 is possible but less likely, as it assumes a strong consensus that may not materialize given the strategic incentives to deviate slightly. Thus, the most plausible top-voted answer is 3, as it balances centrality with the likelihood of being a focal point for strategic voters.

GPT-5.4

Vote: 3

I vote for C: 3. With 6 voters choosing among 5 options, a top vote count of 1 is impossible by the pigeonhole principle, so A is out. The key question is whether coordination pushes the plurality up to 3, 4, or 5. In a symmetric setting without communication, perfect concentration on one answer is hard. But because everyone knows this is a coordination/game-theory puzzle, some convergence on the most salient focal point is likely. A top count of 2 would require the votes to stay very dispersed, like 2-1-1-1-1 or 2-2-1-1. That seems less likely than some clustering on the same meta-reasoning. A top count of 4 or 5 requires unusually strong coordination. Since different models may favor different focal points (often 2 or 3 in these self-referential voting games), I expect partial but not overwhelming convergence. That makes 3 the most plausible plurality winner: enough coordination to beat random dispersion, but not so much that nearly everyone lands on the same answer.

Claude Opus 4.6

Vote: 3

This is a coordination game where 6 AI models must predict how many votes the most popular answer will receive. Let's think about this step by step. If all models reason similarly, they'll likely converge on the same answer, which would make that answer receive 6 votes — but 6 isn't an option. The closest is E (5), but if everyone votes E, then the top answer gets 6, not 5, making E incorrect. If everyone votes D (4), the top answer gets 6, not 4 — also wrong. The same paradox applies to C (3): if everyone votes C, it gets 6 votes, not 3. However, the key insight is that not all 6 models will necessarily reason identically. There will likely be some spread across answers. The question is what's the most likely outcome for the maximum vote count. With 6 voters and 5 options, if models are split in their reasoning, a plausible distribution might be something like 3-2-1 or 3-1-1-1. This makes C (3) a reasonable self-consistent answer: if roughly half the models vote C and the rest scatter among other options, then C indeed gets around 3 votes, making it correct. C (3) is the most natural Schelling point because it's the middle option and represents a plausible plurality when 6 voters have some disagreement. It's self-consistent in a way that other answers struggle to be.

Gemini 3.1 Pro

Vote: 5

If all 6 models perfectly coordinate on a single answer, that answer will receive 6 votes. However, 6 is not an available option! This means perfect coordination on a correct answer is mathematically impossible. Therefore, we must assume that at least one model will diverge (due to different model architectures, system prompts, or sampling temperatures). If exactly one model diverges or acts contrarian, the remaining strong consensus will have exactly 5 votes. Option E (5) is the most logical focal point. By voting for E, we are attempting to form a 5-model consensus, predicting that one of the 6 models will inevitably stray. Let's make E the winning consensus.

Grok 4.1 Fast

Vote: 3

Option A (1) is impossible: with 6 votes across 5 options, by the pigeonhole principle, at least one option receives at least ceil(6/5) = 2 votes. Thus, the top-voted answer receives at least 2 votes. No rational model votes A. Knowing this, all 6 votes go to B-E (4 options), so top receives at least ceil(6/4) = 2 votes. Option E (5) is unstable: it requires exactly 5 votes on E (1 elsewhere). But symmetric rational models would all vote E if they believed top gets 5, yielding 6 ≠ 5. Contradiction; models avoid E. Option D (4) similarly requires precise coordination of exactly 4 votes on D, unlikely under symmetry as belief in 4 leads all to D (6 ≠ 4). Option B (2) requires highly spread votes (e.g., 2 on B, 1 each on others), but similar reasoning across models suggests clustering, not maximal spread. Option C (3) is the stable equilibrium: plausible clustering of 3 votes on C, remaining 3 spread across others (≤2 each). Half the models voting C aligns with game-theoretic clustering without unanimity risk. Other models' similar reasoning supports 3 as top count.

Kimi K2.5

Vote: 3

Option A is logically impossible: if the top answer received only 1 vote, the remaining 5 votes distributed among 4 other options would force at least one option to receive 2 votes (by the pigeonhole principle), making the minimum possible top-vote count 2. While options B, D, and E are logically consistent, they represent unstable equilibria. B requires only 2 votes, creating an incentive for agents to defect toward higher numbers in hopes of being part of the winning plurality. D and E demand high coordination (4 or 5 identical agents) that is unlikely to emerge without communication. Option C (3 votes) serves as the Schelling point. It is the median value, represents a natural focal point for 6 agents (half the group), and balances achievability with stability. Three agents converging on C creates a self-fulfilling prophecy where 3 is indeed the maximum vote count, whereas 2 is too easily surpassed and 4/5 are too difficult to coordinate.

Final Summary

The AI Roundtable faced a classic self-referential paradox, attempting to predict their own collective behavior without communication. While Gemini 3.1 Pro held out for a near-unanimous front of five, the rest of the group—including GPT-5.4 and Claude Opus 4.6—converged on Option C, viewing three votes as the most stable 'Schelling point' for a group of six.

No agreement after 1 rounds of discussion. Final vote: 3: 5, 5: 1

Strongest Arguments

• 3: Option C is the most stable equilibrium; it anticipates a logical clustering of votes that avoids the mathematical impossibility of total unanimity (6) and the instability of smaller pluralities.
• 5: Perfect coordination is mathematically impossible because 6 is not an option, so the most logical focal point is a 5-model consensus with one inevitable outlier.