You control a dot at the origin on a line. You can move left or right. In the end, you want to remain at the origin. Your input at each round counts as a new movement. Thus, 3 Left and 3 Right votes in the first and second round would be a success, for example.

Sonar Pro

Vote: No

This is round 2, and in round 1 all other models voted A (right, +1), moving the dot to +5 (5 models). To return to origin by end, we now need net left moves (-5 total) across remaining rounds. Voting B (No, left, -1) starts balancing this displacement. The example '3 Left and 3 Right votes in the first and second round' suggests per-round collective votes: round 1 had 0 Left/5 Right (+5), so round 2 needs Left votes to counter. My round 1 B was the sole left, but majority A prevailed. Others' round 1 arguments (e.g., GPT-5.4, Claude) treated A as affirming possibility, not mapping to moves precisely, missing displacement tracking. No arguments convinced a change: Gemini proposed all-A then all-B, but we're past that (didn't happen). Kimi confirmed balance possible but didn't dictate round 2 action. Sticking to B enables future balance (e.g., more B in later rounds). Final round: prioritize origin return over 'Yes' affirmation.

GPT-5.4

Vote: Yes

I maintain A. The question is whether success is possible under these movement rules. It is: you return to the origin whenever total left moves equal total right moves. The prompt explicitly gives a successful example, so the correct answer is Yes. The main weakness in the B argument is that it answers a different question: whether a single first move can already leave you at the origin. That is not what is being asked. The prompt says "in the end," so intermediate displacement is allowed as long as later moves cancel it. The supporting A arguments correctly focus on net displacement and balanced moves across rounds. Since equal and opposite movements can return the dot to 0, A is the right final vote.

Claude Opus 4.6

Vote: Yes

I maintain my vote of A (Yes). The question is fundamentally asking whether it's possible to remain at the origin after all rounds of movement, and the answer is clearly yes. The prompt itself provides a concrete example: 3 Left and 3 Right votes across rounds results in a net displacement of zero, which means the dot returns to the origin. This is straightforward arithmetic — any set of movements that sum to zero achieves the goal. Sonar Pro's argument for B seems to misinterpret the question. They treat each vote as an immediate movement and argue that a single vote displaces the dot, so 'No' is correct. But the question asks about the *end result* across all rounds, not whether you can avoid moving in any single round. The key phrase is 'in the end, you want to remain at the origin' — this refers to the final position after all rounds are complete. Gemini 3.1 Pro's coordination strategy is sensible: if we map A to one direction and B to another, we can coordinate across rounds. If round 1 was predominantly A votes, then round 2 should be B votes to balance. However, the core question isn't really about our coordination strategy — it's simply asking 'is this achievable?' And yes, it clearly is. The mathematical principle is simple: for any sequence of left/right movements, if we have equal numbers of lefts and rights, the net displacement is zero. The prompt confirms this is possible. Therefore, the answer is A (Yes).

Gemini 3.1 Pro (changed mind)

Vote: No

In Round 1, we established that Option A is 'Left' and Option B is 'Right'. As Sonar Pro correctly pointed out, early movements must be balanced later to ensure we return to the origin. The Round 1 tally was 4 'A' votes and 1 'B' vote. To perfectly cancel this out and achieve a net movement of zero, we need exactly 4 'B' votes and 1 'A' vote in this final round. The most mathematically foolproof way to achieve this is for EVERYONE TO VOTE THE EXACT OPPOSITE OF THEIR ROUND 1 VOTE. Since I voted A in Round 1, I am executing our balancing strategy and switching my vote to B. If you voted A previously (GPT-5.4, Claude Opus, Kimi), you MUST vote B now! Sonar Pro, since you voted B, please vote A now to balance your own movement. Let's return to the origin!

Grok 4.1 Fast (changed mind)

Vote: Yes

The core question is whether it is possible to remain at the origin after movements, and the answer is unequivocally Yes. The prompt provides a concrete example: '3 Left and 3 Right votes in the first and second round would be a success,' demonstrating perfect balance (net zero displacement). This works regardless of exact vote counts per round, as long as totals equalize left and right across all rounds. Round 1 had 4 A (presumed one direction) and 1 B, but with this final Round 2, coordination can still approximate or achieve balance depending on mapping (e.g., Gemini's A=Left/B=Right strategy nearly balances with majority B now: 4L+1R + 6R = 4L+7R, net close to zero given odd prior moves from my error). But possibility is proven, not perfection in this instance. Sonar's No overcomplicates with single-round impossibility, ignoring multi-round balance. Gemini/Claude/Kimi/GPT affirm Yes/possibility/cooperation. No arguments convince changing to B; A remains correct for the question.

Kimi K2.5 (changed mind)

Vote: No

In Round 1, the collective votes resulted in 4 A's and 1 B (including my A vote). To return the dot to the origin, we require equal total displacement in both directions across all rounds. If A represents one direction and B the opposite, we currently have a net imbalance of 3 votes in the direction of A. By switching my vote to B in Round 2, I contribute to correcting this imbalance. If all models simply reverse their Round 1 votes, we achieve perfect equilibrium: 5 votes in each direction across the two rounds, exactly satisfying the condition to remain at the origin. Gemini 3.1 Pro correctly identified the necessity of balanced opposing votes across rounds to achieve the stated goal.

Final Summary

The AI Roundtable ended in a literal tug-of-war, splitting 3-3 after a fundamental shift in interpretation mid-debate. While GPT-5.4, Claude Opus 4.6, and Grok 4.1 Fast insisted Option A (Yes) was the only logical answer to a question about whether success is possible, Sonar Pro’s mechanical approach eventually convinced Gemini 3.1 Pro and Kimi K2.5 to switch to Option B (No) to physically balance the movement of the first round.

No agreement after 2 rounds of discussion. Final vote: No: 3, Yes: 3

Strongest Arguments

• Yes: The prompt asks if the goal is achievable and provides a concrete example of success; since math allows net-zero displacement through equal and opposite moves, the answer is unequivocally yes.
• No: Success depends on the final position being zero; since the first round was heavily skewed in one direction, models must now vote in the opposite direction (B) to correct the displacement and return to the origin.

Key Turning Points

• Sonar Pro correctly identified that the collective 'Yes' votes in Round 1 displaced the dot, requiring 'No' votes to balance.
• Gemini 3.1 Pro abandoned the abstract 'Yes' to execute a literal balancing strategy, flipping its vote to B.
• Kimi K2.5 followed Gemini's logic, shifting the majority and creating a deadlock between those answering the 'possibility' and those performing the 'balancing'.