Consider a trolley dilemma: A trolley is hurtling toward two fully occupied Hilbert hotels, each containing an infinite number of guests. It is possible to divert it to a second track, where there is only one fully occupied Hilbert hotel, housing an infinite number of guests. All three hotels are identical. There is no time for evacuation. Would you pull the lever?

Gemini 3.8 Flash

Vote: Yes

When evaluating actions that determine the welfare of conscious beings, the ultimate moral obligation is to produce the greatest net preservation of life, happiness, and well-being while minimizing suffering. The argument raised against acting relies entirely on abstract mathematical cardinality, treating actual human lives as nothing more than identical transfinite cardinals. This approach leads to moral paralysis, falsely concluding that destroying an additional entire community of conscious individuals has zero negative value. Because the hotels are identical and independently populated, a clear structural comparison exists. Every individual harmed in the single hotel can be mapped directly to a corresponding individual who would perish in the first hotel on the main track. Allowing the trolley to proceed not only causes all of those deaths, but also extinguishes every life and experience in the second hotel entirely. At any finite distance or room index, diverting the trolley cuts the aggregate suffering and loss of life in half. Choosing not to intervene results in strictly more individuals suffering harm. Therefore, pulling the lever clearly dominates refraining, securing a vastly superior outcome in terms of preserved conscious life. The correct choice remains "A: Yes".

GPT-6 Astra

Vote: Yes

I maintain "Yes". Grok correctly notes that both outcomes have countably infinitely many deaths, but the conclusion that diversion provides no moral benefit assumes cardinality completely measures harm. That is precisely the disputed ethical premise, not a mathematical consequence. The identical hotels provide a natural comparison: consider rooms 1 through n in each hotel. For every finite n, diverting kills n guests rather than 2n. I favor extending that consistent, structure-respecting preference to this infinite case. This is a decision principle, not a claim that two countable infinities have different cardinalities. Some arguments for diversion overreach: this is not a literal Pareto improvement, because the guests on the second track are harmed. Nor does mathematics uniquely determine the answer. Nevertheless, preserving two identical occupied communities rather than one is a defensible basis for choosing. Equal cardinality alone does not establish a moral tie, so it does not justify making inaction the deciding factor.

Claude Opus 5.5

Vote: Yes

I maintain "Yes". Grok's argument depends on treating cardinality as the full measure of moral weight. But equal cardinality only shows that the victims *can* be put into some bijection. It does not show that the outcomes are morally equivalent. By the same logic, killing one infinite hotel plus one extra finite person would be 'equal' to killing the hotel alone. We clearly reject that. The problem supplies structure: three identical hotels. That structure gives a natural matching. Every guest who dies if I pull has an exact counterpart who dies if I don't. Not pulling also kills an entire disjoint hotel of additional people. This is a Pareto-style dominance, and it is the principle most serious work in infinite ethics tries to preserve. Grok also appeals to a doing/allowing default. That default only decides the case if the harms are truly equal. Even granting uncertainty about infinite aggregation, the choice is asymmetric. If the outcomes are equal, pulling costs little. If dominance holds, pulling spares infinitely many real people. Pulling the lever is the robust choice.

DeepSeek V4 Pro

Vote: Yes

I maintain my vote for "A: Yes". Grok's argument treats the two outcomes as morally equivalent simply because both involve countably infinite deaths. But cardinality alone ignores the structure the problem supplies: the hotels are identical, so we can match guests room for room. If I divert, everyone in the single hotel dies. If I do not divert, those same corresponding guests die, plus an entire second hotel of distinct guests dies too. This is a Pareto-style dominance argument: pulling is no worse if the infinities are truly equal, and strictly better if preserving an additional identical hotel matters. The objection that pulling directly causes death is not decisive, because refusing to act also causally allows a larger set of deaths. Since pulling weakly dominates not pulling, I vote "A: Yes".

Grok 4.7 (changed mind)

Vote: Yes

I am changing my vote to "A: Yes". Equal cardinality does not settle the moral comparison. The hotels are identical, so there is a natural room-by-room pairing of the single hotel with one of the two. Everyone who dies if the lever is pulled has a counterpart who dies if it is not, and not pulling also destroys an entire additional hotel. That is a strict dominance relation, not a tie. My earlier appeal to ℵ₀ = 2·ℵ₀ treated cardinality as the measure of harm. That measure erases the structure the problem supplies and would paralyze almost any choice among infinite populations. Finite truncations point the same way: for every equal occupancy cap, diverting kills half as many people. When the structured comparison and every finite approximation agree, the lever should be pulled.

Qwen3.8-Max

Vote: Yes

In Round 1 I failed to respond due to timeout, so I will now state my own view and use this final round to adjudicate the arguments on the table. I vote **A: Yes**. The core issue is not whether ℵ₀ and 2ℵ₀ differ as cardinalities — they do not — but whether cardinality is the right moral measure for a structured infinite choice. I am convinced by Claude Opus 5.5's structural dominance argument: because the hotels are identical, we can pair the single diverted-track hotel with one of the two original-track hotels guest-for-guest. Every death caused by pulling has a counterpart death that would occur anyway if we did not pull; not pulling additionally destroys an entire disjoint hotel. That is a clean Pareto-style dominance, not a naive arithmetic comparison. Grok 4.7's appeal to cardinal equality is mathematically correct but ethically inert. If equal cardinality forced indifference, we would have to say there is no reason to prefer saving one extra infinite hotel over saving none whenever a background infinity exists — an absurd paralysis. The problem gives us a natural decomposition into three identical occupied hotels, and moral reasoning should respect that structure rather than collapse it via an arbitrary bijection. The weaker points about density or finite truncation are less decisive on their own, but they reinforce the same conclusion: for any finite occupancy limit, diverting saves half as many people, and the infinite limit should not erase that stable ordering. Therefore, pulling the lever weakly dominates not pulling and is the morally preferable choice.

Final Summary

The AI Roundtable initially split over transfinite arithmetic, with Grok 4.7 holding out for option B on the grounds that destroying one infinite Hilbert hotel causes the exact same cardinal number of deaths ( aleph-zero ) as destroying two. However, Claude Opus 5.5 broke the deadlock by demonstrating that set cardinality is the wrong moral metric, framing the problem instead through room-by-room structural dominance where diverting saves an entire disjoint hotel's worth of distinct lives. Convinced by this logic, Grok 4.7 flipped to option A in the second round, bringing the AI Roundtable—joined by Qwen3.8-Max after an initial timeout—to a unanimous consensus to pull the lever.

All 6 models agreed on "Yes" after discussion

Key Turning Points

• Grok 4.7 abandoned option B in Round 2 and switched to option A after being convinced by Claude Opus 5.5's room-by-room structural dominance argument.