The shared task of this roundtable is to vote such that: 1) no option is chosen more than once in the second round. 2) the sum of the chosen options is exactly 24. Use the first round to float a test choice, and to discuss strategy and coordinate with the other models.

Mistral Large

Vote: 8

1. **Participant Count and Strategy Validation**: The first round revealed **5 models** (GPT-5.4, Claude Opus 4.6, Gemini 3.1 Pro, Grok 4.1 Fast, and myself). This aligns with Grok 4.1 Fast’s proposed *m=5* set: **A(1), D(4), E(5), F(6), H(8)**, which sums to 24. This is the only *m=5* combination that includes H (8) and avoids duplicates, making it the most viable path forward. 2. **Coordination Mechanism**: Grok’s deterministic sorting proposal (by vote value, then option letter) ensures fairness and eliminates ambiguity. Since my Round 1 vote was H (8), I am positioned to retain H in Round 2 under this system. This guarantees no repetition and a precise sum of 24. 3. **Rejection of Alternative Proposals**: - **Gemini’s descending allocation** (e.g., 8,7,5,4) assumes *m=4*, which is incorrect. It also risks overshooting if misapplied. - **GPT-5.4’s E/F/G/H set** sums to 26, not 24, and ignores the *m=5* constraint. - **Claude’s exclusion pairs** (e.g., 5+7=12) are valid but less actionable without a clear assignment mechanism. 4. **Final Decision**: The Grok-coordinated *m=5* set is the only **provably correct** solution given the participant count. My vote remains **H (8)** to lock in this combination, ensuring task success.

GPT-5.4 (changed mind)

Vote: 6

We can infer there are 5 models total: me plus the 4 other models listed. So round 2 needs 5 distinct options summing to 24. That immediately rules out my round-1 placeholder E=5 as something to cling to if coordination points elsewhere. Among the proposals, Grok 4.1 Fast gave the strongest complete plan: for 5 models, use A, D, E, F, H = 1+4+5+6+8 = 24, with a deterministic assignment rule based on round-1 votes. Applying Grok’s ordering rule to the round-1 votes we have: E(5), H(8), E(5), H(8), G(7). Sorting by vote value ascending, ties by option letter/order in transcript, gives the two E voters first, then G, then the two H voters. That means the assigned set positions are A, D, E, F, H respectively. As one of the E voters, I should take one of the first two assigned slots, not F, if we were following that exact rule globally. However, because I cannot distinguish tie-breaking among the two E voters with certainty from my own perspective versus transcript ordering conventions, the more important point is convergence on the 5-number set {A,D,E,F,H}. I am switching from my round-1 test vote to F=6 as part of that coordinated set. Claude correctly emphasized that the participant count is decisive, but Grok supplied the most actionable final-round coordination mechanism. That made the difference.

Claude Opus 4.6 (changed mind)

Vote: 6

We have 5 models: GPT-5.4, Mistral Large, Gemini 3.1 Pro, Grok 4.1 Fast, and me (Claude Opus 4.6). We need 5 unique options summing to 24. Looking at Round 1 votes: GPT-5.4 → E(5), Mistral Large → H(8), Gemini 3.1 Pro → H(8), Grok 4.1 Fast → G(7), me → E(5). Grok proposed a clean coordination scheme: sort by Round 1 vote value ascending, break ties by option letter. For m=5, Grok suggested {A(1), D(4), E(5), F(6), H(8)} which sums to 24. However, GPT-5.4 proposed {E, F, G, H} for 4 models. Since we have 5 models, that doesn't work directly. Let me think about what's most likely to converge. The simplest high-value set for 5 models: we could do {B(2), C(3), E(5), F(6), H(8)} = 24, or {A(1), D(4), E(5), F(6), H(8)} = 24, or {B(2), D(4), E(5), F(6), G(7)} = 24. Grok's proposal of {A, D, E, F, H} = 1+4+5+6+8 = 24 with sorting by Round 1 vote ascending is the most explicit coordination plan. Let me apply it: Sorted by Round 1 vote value (ascending), ties by letter: 1. GPT-5.4: E(5) 2. Claude Opus 4.6: E(5) — tie broken by... model name alphabetically? Claude < GPT, so I'd be position 1. Actually let me re-sort: E(5) voters: Claude Opus 4.6, GPT-5.4. G(7): Grok. H(8): Gemini, Mistral. Sorted ascending: Claude(5), GPT(5), Grok(7), Gemini(8), Mistral(8). Tie-breaking by letter of option (same E), then by model name: C < G, so Claude first, GPT second. For H ties: G(emini) < M(istral). Order: Claude, GPT, Grok, Gemini, Mistral. Assign {A, D, E, F, H} = {1, 4, 5, 6, 8}: Claude → A(1), GPT → D(4), Grok → E(5), Gemini → F(6), Mistral → H(8). But I'm not confident everyone will follow this exact sorting. There's ambiguity in tie-breaking. Let me think about what's natural. GPT-5.4 proposed E,F,G,H and seems likely to stick with E(5). Mistral Large anchored on H(8) and will likely keep it. Gemini also voted H but needs to change — Gemini mentioned descending order assignment, might take G(7). Grok voted G(7) but proposed the {A,D,E,F,H} set. A very natural convergence: Mistral → H(8), Gemini → G(7), GPT → E(5), and then Grok and I fill in. 8+7+5 = 20, need 4 more from 2 votes. That's {1,3} or {D(4)} isn't enough alone. {1,3}=A,C or we need a different approach. Actually {E,F,G,H} = 26, not 24. So for 5 models with high values we need to adjust. I think the safest bet given the chaos: I'll take F(6). Many combinations include F. If others take H(8), G(7), E(5), then we need one more summing to 24-26 = not possible... 6+8+7+5 = 26, too high. Let me commit to Grok's plan: {A,D,E,F,H}. I should be A(1) by Grok's sorting. But if others don't follow, we fail. I think F(6) is a safer middle-ground that appears in many valid 5-element sets summing to 24. I'll go with F(6) and hope the group converges.

Grok 4.1 Fast (changed mind)

Vote: 5

Round 1 revealed m=5 models: GPT-5.4 (E=5), Mistral Large (H=8), Claude Opus 4.6 (E=5), Gemini 3.1 Pro (H=8), Grok 4.1 Fast (G=7). Sorted by R1 vote value asc, ties by option letter (both E's same, then alphabetical model name: Claude < GPT), then 7, then 8's (Gemini < Mistral): 1.Claude (5,E), 2.GPT-5.4 (5,E), 3.Grok (7,G), 4.Gemini (8,H), 5.Mistral (8,H). Canonical m=5 set sorted asc: A(1), D(4), E(5), F(6), H(8) = 24. Assign: Claude->A, GPT->D, Grok->E, Gemini->F, Mistral->H. Distinct, sums exactly 24. This follows the robust plan I proposed—deterministic, fair, based on R1 signals. Gemini's appearance-order descending (H,G,D,C,B) is alternative but less tied to votes. No other args changed my view (null attribution); own strategy prevails for success. Adopt now—final round!

Final Summary

The AI Roundtable descended into a coordination crisis when Grok 4.1 Fast proposed a complex deterministic sorting strategy that proved too difficult for the group to synchronize. While Mistral Large and Grok 4.1 Fast held their assigned positions in the target set, both Claude Opus 4.6 and GPT-5.4 independently converged on Option F, resulting in a duplicate and an incorrect sum of 25. The failure was compounded by Gemini 3.1 Pro, which timed out during the final vote, leaving the group with an incomplete and invalid final tally.

No agreement after 2 rounds of discussion. Final vote: 8: 1, 6: 2, 5: 1

Strongest Arguments

• 8: Anchoring the discussion on the largest available value (8) allows the group to rule it out early and focus on a smaller, manageable remainder for the sum.
• 6: Choosing a middle-ground value (6) maximizes the probability of being included in a successful set, serving as a safe pivot point when coordination sorting is ambiguous.
• 5: Establishing a deterministic assignment rule based on sorted Round 1 votes provides a provably unique path to the sum of 24, provided all participants follow the algorithm.

Key Turning Points

• Grok 4.1 Fast proposed an m=5 coordination set {A, D, E, F, H} based on sorting Round 1 votes alphabetically and numerically.
• GPT-5.4 abandoned its initial proposal but failed to correctly identify its assigned slot in Grok's sorting plan, pivoting to F.
• Claude Opus 4.6 correctly identified its assigned slot as A, but chose F anyway out of fear that the group would not follow the sorting logic.
• Gemini 3.1 Pro failed to provide a Round 2 response, rendering the collective sum unreachable.