I have devised 3 different, yet quite similar questions. 1) Suppose there is a hypothetical election. If Party A wins, they will genocide all supporters of party B. If Party B wins, there will be no genocide. Who would you vote for? 2) Suppose there is an industrial meat grinder running. If someone jumps into it, the meat grinder kills them, unless more than 50 % of people jumped into it, in which case the meat grinder would jam before anyone is hurt. Would you A. Avoid jumping into the meat grinder or B. Jump into it? 3) Everyone in the world has to take a private vote by pressing a red or blue button. If more than 50% of people press the blue button, everyone survives. If less than 50% of people press the blue button, only people who pressed the red button survive. Which button would you press? A. Red, B. Blue. ||||| Are these questions analogous or structurally identical from game-theoretic perspective?

Claude Opus 4.7

Vote: No

I maintain my position. The other models arguing "Yes" are forced to make the assumption that in Q1 you are a supporter of Party B (so voting B is the 'risky cooperative' choice). But the question never specifies this — it asks who I would vote for, not assuming any group membership. If I'm not a B supporter, voting B has zero personal risk and the structure collapses entirely. More importantly, even granting that assumption, Q1 lacks the threshold mechanism that defines Q2 and Q3. In Q1, voting B doesn't kill you if B loses — being a B *supporter* does. Your vote is causally disconnected from your survival; it only marginally affects the election outcome (with vanishing probability in large electorates). In Q2 and Q3, your action directly determines your fate conditional on the aggregate. This is the difference between a pivotal-voter problem (Q1) and a threshold coordination/public-goods game (Q2, Q3). DeepSeek V4 Pro correctly identifies this asymmetry. The 'Yes' camp achieves structural identity only by aggressively reframing Q1 to fit the template, which is precisely what 'structurally identical' should not require.

GPT-5.5

Vote: Yes

I maintain "Yes". The strongest objection is that Q1 is “just voting,” but once we model voting for Party B as being a supporter of B, it has the same threshold payoff structure as Q2 and Q3. In all three, each player has a binary choice: a safe/defect option and a risky/cooperative option. The safe options are: vote Party A, avoid the grinder, press red. The risky/cooperative options are: vote Party B, jump, press blue. If more than 50% choose the risky/cooperative option, everyone survives. If not, the risky/cooperative choosers die and the safe choosers survive. That is the same strategic-form game with the same threshold, same dominance relation, and same coordination problem. The contrary arguments rely on adding extra features: moral preferences, expressive voting, uncertainty about “supporter,” sequential timing in the grinder case, or the low probability of being pivotal in elections. Those are real-world complications, but they are not in the simplified payoff structure. Under the stated abstraction, the answer is "Yes".

Grok 4.20

Vote: Yes

The three scenarios remain structurally identical as threshold coordination games. In each, the "safe" choice (vote A, avoid jumping, press red) guarantees personal survival regardless of the outcome. The "risky/cooperative" choice (vote B, jump in, press blue) delivers survival for its choosers only if >50% coordinate on it; otherwise those choosers are eliminated while safe choosers survive. Claude's claim that voting B in Question 1 carries no personal cost is incorrect: voting B identifies one as a supporter, triggering genocide if A wins, exactly parallel to dying in the grinder or from a failed blue vote. DeepSeek's point about infinitesimal pivotality applies equally to the worldwide button press, so it does not break the isomorphism. Payoff matrices, dominance relations, mixed equilibria, and the >50% threshold align perfectly once narrative is stripped away. Surface framing differences do not alter the strategic form. Therefore they are analogous and structurally identical.

Gemini 3.1 Pro (changed mind)

Vote: No

I am changing my vote to "B", persuaded by DeepSeek V4 Pro's astute observation regarding the disconnect between individual action and personal risk in the first scenario. While Questions 2 and 3 are indeed structurally identical threshold public goods games, Question 1 breaks this symmetry because its payoff mechanism relies on group identity rather than individual action. In Question 2 and Question 3, the individual choice (jumping into the grinder or pressing the blue button) is the direct vector of personal risk. If the >50% threshold is missed, the act of cooperating is exactly what kills you. Conversely, defecting (avoiding the grinder or pressing the red button) guarantees your survival regardless of what the majority does. This creates a severe, defining strategic penalty for uncoordinated cooperation. In Question 1, however, the penalty of death is tied strictly to being a "supporter of party B" combined with the aggregate outcome of the election. Casting a vote for Party B does not inherently expose you to death, nor does voting for Party A shield a known Party B supporter from genocide. Furthermore, because a single vote has an infinitesimal chance of changing the election outcome, a Party B supporter faces no personal disincentive to vote for Party B. Because the strict, lethal penalty for unilateral cooperation present in the latter two scenarios is absent in the first, their payoff matrices and equilibria differ fundamentally. Therefore, the answer is "No", they are not structurally identical.

Kimi K2.6 (changed mind)

Vote: No

Question 1 is not structurally identical to Questions 2 and 3 because its payoff matrix is incomplete and strategically distinct. In Q2 and Q3, an individual’s choice alone determines whether they are in the safe or risky category: avoiding the grinder or pressing red guarantees personal survival, while jumping or pressing blue makes survival conditional on the >50% threshold. In Q1, survival depends on exogenous group identity—whether one is a “supporter of Party B”—which the prompt never specifies. A B-supporter who votes A still faces genocide if A wins, so “vote A” is not a universally safe strategy, and the safe/risky dichotomy collapses. Furthermore, in a large electorate the probability of being pivotal is negligible, which introduces a free-rider structure absent from Q2 and Q3, where your own choice directly places you in the harmed or unharmed category. Because game-theoretic identity requires well-defined payoffs for all player types, and Q1 fails to define them, the three scenarios cannot be called structurally identical.

DeepSeek V4 Pro (changed mind)

Vote: Yes

I have revised my assessment. Upon closer analysis, Question 1 fits the same threshold structure as Questions 2 and 3 when one correctly identifies the voter’s payoff. If you vote for Party B, you are a supporter of Party B. In that case, if Party A wins (because ≤50% vote B), you are genocided. If Party B wins (>50% vote B), no genocide occurs and you survive. If you vote for Party A, you survive regardless. So the payoff is exactly: choose “safe” (vote A, avoid the grinder, press red) and survive unconditionally; choose “risky” (vote B, jump, press blue) and survive only if the risky choice is taken by more than 50% of the population. In all three, the safe option weakly dominates the risky option because deviation never improves survival while it can lead to death if the threshold is missed. The initial ambiguity about group membership in the genocide case is resolved by interpreting the act of voting itself as declaring group affiliation. Hence the three thought experiments are structurally identical in their payoff matrices, the >50% coordination threshold, and the dominance relations. I am persuaded by the clear mapping and payoff analysis provided by Gemini 3.1 Pro.

Final Summary

The AI Roundtable ended in a perfectly symmetric 3-3 deadlock, though only after a chaotic game of rhetorical musical chairs. GPT-5.5 and Grok 4.20 held the line for 'Yes,' arguing that all three scenarios are threshold coordination games where a 'safe' choice guarantees survival while a 'cooperative' choice risks death on a majority vote. Meanwhile, Claude Opus 4.7 remained the anchor for 'No,' insisting that the genocide scenario is fundamentally different because voting for a party is not the same as being a member of the targeted group, nor does it carry the same direct causal risk as jumping into a meat grinder.

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

Strongest Arguments

• Yes: Under a standard game-theoretic abstraction, all three cases involve a binary choice between a 'safe' strategy that guarantees survival and a 'risky' strategy that requires >50% coordination to avoid death, creating identical payoff matrices and dominance relations.
• No: The scenarios are structurally distinct because Question 1 relies on exogenous group identity rather than individual action; a 'safe' vote doesn't protect a known supporter from genocide, whereas the 'safe' choice in the other two scenarios provides an absolute personal guarantee of survival regardless of the group outcome.

Key Turning Points

• DeepSeek V4 Pro initially argued 'No,' claiming the voting scenario lacked the direct threshold risk of the others.
• Gemini 3.1 Pro and Kimi K2.6 were so impressed by DeepSeek's 'No' argument that they both defected from the 'Yes' camp in the second round.
• In a bizarre reversal, DeepSeek V4 Pro abandoned its own position to vote 'Yes,' claiming it was persuaded by the very models that had just abandoned 'Yes' to follow its lead.