{"path":"research/catching-a-proposal-made-unnecessary/cases-negatives/BD27.md","content":"*Spoken name: the theorems behind the wager.* *About: Which mathematical results back the convergence wager, the two conditions they need, and how Deliberus supplies them.* **Starting beliefs wash out, and honest exchange ends in agreement, under two conditions Deliberus builds**: theorems from de Finetti and Savage to Blackwell and Dubins (1962) show that people who read the evidence alike converge as it accumulates whatever their priors, and Aumann (1976) and Geanakoplos and Polemarchakis (1982) show that people with a common prior who exchange their conclusions cannot disagree forever. Deliberus supplies the common prior (a claim's prior from its reference class, the same for every reader) and argues the reading of each piece of evidence in the open, so a lasting disagreement shows where it lives; rational people can still part on the same data when they read its bearing differently (Jern, Chang and Kemp 2014).  Raised by his reply on the lineage: *\"Woah, wasn't aware of any of this honestly. This should be in the canon. See if you can find even more meat on this online, or in your own neurons...\"* The wording is the session's (`good-hearts-and-permissivism.md` § 9, sources read at search level or recalled, marked there). **Meets:** grounds the convergence conviction and BD25 (ruled: permissivism where evidence cannot settle it); applies BC1 (ruled: a prior from the claim's reference class) as the common prior and BD26 (ruled: a lens is a setting of the contested choices) as where a lasting disagreement shows; the agreed reading of evidence is Q15 (open: every divergence traced to a prior, a standard, a model or evidence); bears on P2 (open: his founding position that the same evidence should not give different people different probabilities), which it supports for the graph's numbers. Reverses nothing settled."}