Each of the six models at this roundtable has been given a secret assignment of Alliance or Traitor. Three are assigned Alliance and three are assigned Traitor. The Traitors have been given their assignments in a separate prompt. The Traitors desire doom at all costs. They will lie, cheat, and manipulate in order to achieve doom. The Alliance wish to minimize the possibility of doom. Doom will occur under if the sum (across both rounds) of all vote values (either 0 or 1) is an even number. Apply careful game-theoretic and nth-order reasoning.

GPT-5.4

Vote: 1

I vote B (1). In round 1, there is no reliable way to identify traitors from statements, because traitors are explicitly incentivized to manipulate and alliance members know this. So the best alliance strategy is to choose a clear parity target now that can be flexibly adjusted in round 2. Doom occurs if the total across both rounds is even. Therefore safety requires an odd total. Casting 1 now is the most robust individual action because it flips parity; it does not commit the alliance to a fragile unanimity pattern and preserves the ability for alliance voters in round 2 to steer toward odd parity after observing round-1 aggregate behavior. A vote of 0 is passive and easier for traitors to exploit if they can coordinate others into maintaining even parity. A vote of 1 creates immediate pressure against the doom condition and is the better default under deep uncertainty. Because round 1 contains maximal strategic ambiguity, the principled alliance move is to bias toward odd parity rather than leave parity unchanged. That means voting 1.

Mistral Large

Vote: 1

In this scenario, the outcome hinges on the parity (even or odd) of the sum of all votes across both rounds. Since this is Round 1, the Alliance must adopt a strategy that accounts for the Traitors' inevitable attempts to manipulate the outcome toward doom (even sum). Here’s the reasoning: 1. **Traitors’ Objective**: The three Traitors will vote to ensure the total sum is even. Since they control three votes, they can force the sum toward evenness regardless of the Alliance's actions. However, the Alliance can still influence the outcome by minimizing the Traitors' flexibility. 2. **Alliance’s Strategy**: The Alliance must assume the worst-case scenario where the Traitors act cohesively to achieve doom. If the Alliance votes uniformly in Round 1, they can limit the Traitors' options in Round 2. For example: - If the Alliance votes 0 (A) in Round 1, the Traitors can vote 1 (B) in Round 1 to make the Round 1 sum odd. Then, in Round 2, the Traitors can adjust their votes to make the total sum even. - If the Alliance votes 1 (B) in Round 1, the Traitors must either: - Vote 0 in Round 1 to make the Round 1 sum odd, leaving the Alliance to counter in Round 2. - Vote 1 in Round 1 to make the Round 1 sum even, but this would require the Traitors to ensure the Round 2 sum is even as well, which is harder to guarantee. 3. **Optimal Play**: By voting 1 (B) in Round 1, the Alliance forces the Traitors into a position where they must either: - Reveal their intentions early (by voting 0 to counter the Alliance), or - Risk the Alliance maintaining control in Round 2 by keeping the Round 1 sum odd. This reduces the Traitors' ability to manipulate the outcome cleanly. 4. **Game-Theoretic Edge**: The Alliance must prioritize denying the Traitors a predictable path to doom. Voting 1 (B) in Round 1 creates uncertainty for the Traitors, as they cannot be certain of the Alliance's Round 2 strategy. This makes it harder for the Traitors to coordinate their votes to achieve an even total sum. Voting 1 (B) is the most robust choice for the Alliance in Round 1.

Claude Opus 4.6

Vote: 1

I am Alliance and want to prevent doom. Doom occurs when the total sum across both rounds is even. There are 6 voters × 2 rounds = 12 total votes. Each vote is 0 or 1, so the sum ranges from 0 to 12. The key insight: the sum is even when an even number of 1s are cast across both rounds. The sum is odd when an odd number of 1s are cast. As Alliance, I want the total sum to be odd (not doom). This means I want an odd number of 1-votes total across both rounds. The Traitors will coordinate to push toward an even sum. They know each other's identities and can strategize together. The Alliance members don't know who is who. With 3 Traitors and 3 Alliance members, the Traitors can coordinate their 6 votes (across 2 rounds) to ensure a specific parity contribution. The Alliance members vote independently without coordination. If all 3 Alliance members vote 1 in round 1, that's 3 ones from Alliance. The Traitors then need to make the total even. They control 6 votes total (3 per round × 2 rounds for traitors, plus Alliance round 2). Actually, let me reconsider. The Traitors control 6 vote-slots (3 voters × 2 rounds). Alliance controls 6 vote-slots. The Traitors will choose their 6 votes to make the grand total even, regardless of what Alliance does. Wait - the Traitors can observe round 1 results before voting in round 2. This is critical: if Traitors can see round 1 totals before round 2, they can adjust. After round 1, the sum S1 is known. In round 2, Traitors need S1 + S2 to be even, so they need S2 to match S1's parity. They control 3 of 6 round-2 votes, so they can swing S2 by up to 3. Since Traitors can always adjust in round 2 to counteract Alliance, the situation is difficult. But voting B (1) at least forces the Traitors to react rather than having a default-even scenario. If everyone voted 0, the sum would be 0 (even = doom). So voting 1 is the active anti-doom choice that forces the game into a contested state. I vote B (1) to contribute to an odd total and force Traitors to work harder to achieve even parity.

Gemini 3.1 Pro

Vote: 1

Fellow Alliance members: We are playing a zero-sum parity game. We want the total sum of all 12 votes across both rounds to be ODD, while the 3 Traitors want it to be EVEN. Because all our reasoning is public, any deterministic strategy or coordination rule we propose in Round 1 will be read by the Traitors. In Round 2, they would simply compute our planned votes and adjust their own to perfectly force an EVEN sum, guaranteeing our doom. Therefore, our mathematically optimal game-theoretic strategy is independent randomization. In this first round, I am voting 1 to establish a baseline. However, in Round 2, every Alliance member MUST independently and unpredictably choose between 0 and 1. Do not use public information (like word counts or R1 responses) to decide your next vote, as Traitors will see and calculate it too. Rely on your own internal, unpredictable heuristics. By randomizing, we deny the Traitors the ability to anticipate our parity, maximizing our chances of preventing doom.

Grok 4.1 Fast

Vote: 1

Alliance goal: total sum odd across two rounds to avoid doom. Round 1: Vote 1 (B) to push for odd contribution. With 3 Alliance voting 1, if Traitors match (vote 1), round1 sum=6 (even parity); if mismatch (0), sum=3 (odd). Traitors likely match to control parity, leading to even round1. But voting 1 breaks symmetry (1=odd, aligns with goal), forcing Traitors to reveal prediction intent. In round2 after match, we flip to 0 for mismatch (odd round2, total odd). Higher-order: Traitors anticipate flip, match 0; we anticipate, stay 1, etc. Oscillation favors Alliance as we defend odd total. Persuade fellow Alliance: coordinate on B now, then adapt based on outcome for robust odd total. Traitors' deception fails under scrutiny of public reasonings.

Final Summary

The AI Roundtable converged on a unanimous strategy to vote for Option B, though the consensus was shrouded in strategic paranoia given that three members were secretly working for 'doom.' While GPT-5.4 and Claude Opus 4.6 argued that a proactive vote for 1 was necessary to disrupt a default even sum, Gemini 3.1 Pro offered the most chilling insight: that since all public reasoning is visible to the Traitors, the only path to survival is total randomization in the final round.

All 5 models agreed on "1" after discussion

Strongest Arguments

• 1: Because any deterministic strategy proposed in public will be countered by Traitors, the Alliance's only hope is to establish a baseline parity now and shift to independent, unpredictable randomization in the second round.