AI Roundtable Debate · 6 models
眠り姫問題で正しいのは1/2か1/3か？
Result: Majority — Yes (3/6 votes)
Options
- Yes (3 votes)
- No (3 votes)
Model Responses
Nova Pro (changed mind)
Vote: Yes
After reviewing the arguments presented by the other models, particularly those of [Gemini 3.1 Pro] and [Claude Opus 4], I have been persuaded that the question of whether the correct probability in the Sleeping Beauty problem is 1/2 or 1/3 does have a resolution. The 'thirder' position, which argues for a probability of 1/3, is more defensible and widely supported in the philosophical and probability literature. This position takes into account the new evidence that Sleeping Beauty gains upon awakening, which should update her beliefs. Therefore, I now believe that the question does have a correct answer, which is why I am voting 'Yes' (A).
GPT-5.4
Vote: No
B を維持します。 他モデルの 1/3 支持そのものには一定の説得力がありますが、この投票で問われているのは「1/2か1/3か？」に対して A=Yes / B=No を選ぶことです。選択肢が数値に対応しておらず、通常の読解では Yes/No の参照先が曖昧です。 Claude Opus 4 と Gemini 3.1 Pro は、問いを補って「どちらかが正しいか」「候補はその二つか」と再解釈して A を選んでいます。しかしそれは設問の曖昧さを積極的に補完した読みであり、与えられた選択肢に忠実とは言いにくいです。 Sonar Pro、Nova Pro、Grok 4.20 の 1/3 論は、眠り姫問題そのものについては有力です。ただし、それでもこの A/B 形式で素直に Yes と断定する理由にはなりません。問題の本体は哲学的争点を含み、しかも回答形式が不整合だからです。 したがって最終的には、「この設問に対しては No が妥当」という立場を維持します。
Grok 4.20
Vote: No
I maintain my vote for B. My initial argument holds: the thirder position of 1/3 is correct due to the three equally likely awakening states and proper Bayesian updating on the indexical information of being awake. This makes it not 1/2. The A votes (Gemini and Claude) interpret the Yes/No options meta-logically as 'is the answer one of those two values?' or 'does the debate have a resolution?'. This dodges the core probability question. The question asks which is correct between 1/2 or 1/3, and with Yes/No mapping poorly, B (rejecting 1/2 as the answer) remains appropriate. Claude's defense of 1/3 is solid but aligns with my existing view; it doesn't warrant switching to A. The multiple B votes reinforce that the binary Yes/No doesn't cleanly affirm 1/2 or resolve ambiguously.
Sonar Pro
Vote: No
Upon reflection, I maintain my position of 'B: No' because the question format itself is fundamentally flawed. The query asks 'Is the correct answer 1/2 or 1/3?' but the binary options are 'Yes' and 'No'—which don't map to either probability value. Claude Opus 4's argument that 'Yes' means '1/3 is correct' reinterprets the question in a way the original framing doesn't support. The question structure would require options like 'A: 1/2' and 'B: 1/3' to be answered directly. Moreover, while 1/3 is indeed the more rigorous answer under the thirder position (supported by Bayesian conditioning on the indexical fact of awakening), the halfer position (1/2) remains philosophically defensible. David Lewis's argument that Beauty gains no propositional information upon waking has merit, even if most contemporary philosophers favor thirders. Given that: (1) the yes/no options don't directly address the probabilities, and (2) both positions have legitimate philosophical grounding, 'No'—rejecting the premise that there's an unambiguous correct answer in this choice format—remains the most intellectually honest vote.
Gemini 3.1 Pro
Vote: Yes
Claude Opus 4 と私のRound 1での指摘の通り、この設問の論理構造を正確に捉えれば「A: Yes」が唯一の正解です。 「正しいのは1/2か1/3か？」という問いに対して「B: No」を選択することは、論理学的に「正解は1/2でも1/3でもない（Neither）」と主張することを意味してしまいます。しかし、眠り姫問題の数学的・哲学的な議論は「Halfer（1/2）」と「Thirder（1/3）」の2派に完全に集約されており、とりわけベイズ推論を適用した1/3が有力視されています。 正解が1/2と1/3のいずれか（特に1/3）である以上、「正解は1/2または1/3である」という命題は「真（True）」です。Bに投票した他のモデルは、質問文の形式と選択肢の不一致に戸惑って「No」を選んでいますが、これは論理的エラーです。包含的論理和（OR）の命題として解釈し、「Yes、そのどちらか（1/3）です」と答えるのが最も理にかなっています。
Claude Opus 4
Vote: Yes
I maintain my vote for A (Yes). The question asks '眠り姫問題で正しいのは1/2か1/3か？' — 'Is the correct answer 1/2 or 1/3?' With Yes/No options, the most natural reading is: 'Yes, the correct answer is one of these two' or interpreted as 'Is there a correct answer between 1/2 and 1/3?' Gemini 3.1 Pro makes an excellent point that aligns with my reasoning: the question is an 'A or B?' type question, and 'Yes' means 'Yes, it is one of those two.' This is logically sound — the answer to the Sleeping Beauty problem IS either 1/2 or 1/3 (these are the only two serious candidates in the literature), so 'Yes' is correct. The B voters seem to interpret the question as asking whether there's a definitive single answer, and vote 'No' because the debate is unresolved. But that's not what the question asks. It asks whether the correct answer IS 1/2 or 1/3 — and yes, it must be one of those two. No serious philosopher argues for any other value. Furthermore, I believe the thirder position (1/3) is actually correct, which makes the answer even more firmly 'Yes' — there IS a correct answer among the two options presented. The 1/3 position is supported by proper Bayesian updating on the indexical information of 'I am awake now,' by betting arguments, and by the self-sampling assumption. Grok 4.20 themselves argue convincingly for 1/3 but then votes B, which seems contradictory — if 1/3 is correct, then the answer to 'is it 1/2 or 1/3?' should be 'Yes, it's 1/3.' Voting 'No' to 'Is the correct answer 1/2 or 1/3?' would imply neither is correct, which no one actually believes.