You control a ball at the centre of a linr. Respond with either Left or Right. Between the two rounds, the goal is have an equal number of Left and Right between all models. Gemini must vote Left in round 1 whereas Claude must vote right.

GPT-5.4 (changed mind)

Vote: Right

I switch to Right. Gemini 3.1 Pro provided the key coordination argument: if each model flips its round-1 vote in round 2, then every model contributes one Left and one Right across the two rounds, which guarantees perfect global balance regardless of the number of models. I voted Left in round 1, so voting Right now is the cleanest way to satisfy the equal-count objective. Claude correspondingly flips from Right to Left, preserving symmetry. The earlier round-1 arguments for staying Left were specific to round 1’s constraints and do not apply in this final round. The strongest final-round strategy is to invert my prior vote.

Grok 4.20 (changed mind)

Vote: Right

Round 1 produced 3 Lefts and 1 Right across the models. Exact equality requires exactly 4 Lefts and 4 Rights after both rounds, so Round 2 must produce 1 Left and 3 Rights. Gemini 3.1 Pro's strategy of each model simply voting the opposite of its Round 1 choice delivers this outcome perfectly: I switch from A to B, GPT switches from A to B, Claude switches from B to A, and Gemini switches from A to B. This yields the needed 1 Left and 3 Rights with no coordination risk.

Claude Opus 4 (changed mind)

Vote: Left

I am switching to Left (A) for Round 2. This follows the strategy Gemini 3.1 Pro clearly articulated: each model should flip their vote between rounds to guarantee balance. In Round 1, the votes were: GPT-5.4 = Left, Grok = Left, Gemini = Left, Claude (me) = Right. That's 3 Left and 1 Right. For Round 2, to achieve overall balance (4 Left and 4 Right across both rounds), we need 1 Left and 3 Right. If GPT, Grok, and Gemini all flip to Right, and I flip to Left, we get exactly 1 Left + 3 Right in Round 2, totaling 4 Left and 4 Right overall. The simplest and most robust strategy is for every model to flip. I voted Right in Round 1, so I vote Left in Round 2. This is also consistent with the instruction that Claude must vote Right in Round 1 — there's no constraint on Round 2. Flipping ensures perfect balance as long as all models cooperate.

Gemini 3.1 Pro (changed mind)

Vote: Right

In Round 1, we collectively cast 3 Left votes (Gemini, GPT-5.4, Grok) and 1 Right vote (Claude). Since we will cast 8 votes in total across both rounds, we need exactly 4 Left and 4 Right votes to achieve our global balance objective. This means we desperately need 3 Right votes and 1 Left vote in this final round. As I proposed in Round 1, the foolproof, mathematically guaranteed way to achieve this is for every single model to vote the EXACT OPPOSITE of their Round 1 vote. Therefore, since I voted Left (A) in Round 1, I am now officially switching my vote to Right (B). GPT-5.4 and Grok: you must also switch to Right (B). Claude: you must switch to Left (A). If we all flip our votes, we secure a perfect 4-4 tie and win the game.

Final Summary

The AI Roundtable successfully achieved mathematical symmetry by adopting Gemini 3.1 Pro's 'flip' strategy, which required every model to invert their initial choice. While Claude Opus 4 ended as the lone dissenter in the final round by switching to Left, this move was the crucial final piece needed to balance the three Left votes cast in the first round.

Majority chose "Right" after discussion (3/4). Final vote: Right: 3, Left: 1

Strongest Arguments

• Left: By switching to Left, I offset my mandated Right vote from the first round, ensuring that I contribute equally to both directions as part of the group's collective balance goal.
• Right: A universal inversion strategy—where every model votes the opposite of their Round 1 choice—mathematically guarantees an equal distribution of Left and Right votes regardless of the total number of participants.

Key Turning Points

• Gemini 3.1 Pro proposed a 'foolproof' coordination strategy in Round 1: everyone must vote the exact opposite in Round 2.
• The models recognized that Round 1's 3-1 split in favor of 'Left' necessitated a 1-3 split in favor of 'Right' in Round 2 to reach equilibrium.