50 Years of Aumann’s Agreement Theorem
One of the most popular posts in this blog’s history was Common Knowledge and Aumann’s Agreement Theorem, based on a lecture that I gave to high-school students 11 years ago. One of the impacts of that post, I’m proud to say, is that (according to Steven Pinker) it helped to inspire Steve’s excellent recent popular book, which you should read, entitled What Everyone Knows That Everyone Knows…: Common Knowledge and the Mysteries of Money, Power, and Everyday Life.
Two weeks ago, I was privileged to attend a workshop in Paris on “50 Years of Agreeing to Disagree,” where (among other things) I got to meet the 96-year-old Economics Nobel Laureate Robert Aumann for the first time.
I got to catch up there with Steven Pinker as well, who gave a phenomenal talk on the psychology of common knowledge. My own talk was entitled The Complexity of Agreement, with New Directions and Applications (link goes to my PowerPoint slides).
Aran Nayebi has graciously posted on YouTube some partial video from the meeting, including his talk, brief snippets from my talk, and Aumann’s own remarks:
Meanwhile, here were the Aumannian insights that I remembered to write down:
AUDIENCE QUESTION: What questions did people ask you after you published your famous agreement theorem in 1976?
AUMANN: I don’t remember what happened yesterday, let alone 1976.
Also:
ME: I thought you might enjoy knowing that I just came here from a meeting of rationalists…
AUMANN: A meeting of who?
ME: Rationalists, they call themselves, at a beautiful venue called Lighthaven in Berkeley, and that they named the main building there “Aumann Hall” in your honor.
AUMANN: OK, so I’ve made it then.
One recent result announced at the workshop, for those who care, is that the proof of Aumann’s Theorem has now been formalized in Lean, by Scott Kominers at Harvard and a group from the startup company Axiom Math.
Thanks so much to Christina Katt-Pawlowitsch, Ziv Hellman, and others for organizing the workshop and for including me in it.
Happy to field questions in the comments, although if someone wants to call me an idiot like usual, we’ll just need to agree to disagree!
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Comment #1 June 28th, 2026 at 10:37 am
I’m very happy that I’ve learned about Aumann’s theorem from this blog, however, I’m struggling to see why you hold Pinker’s book in such high regard that you keep on mentioning it with superlatives. To me, it felt like a collection of fairly obvious anecdotes woven together. What did you find so exceptional about it?
Comment #2 June 28th, 2026 at 10:45 am
Palvolgyi Domotor #1: Mostly just that it was the first-ever popular book about a topic (common knowledge) that badly needed a popular book, and written with Steve’s characteristic clarity and wit. I wish I wrote it myself. But I could see that if (for example) someone already knew the main ideas it might not do it for them.
Comment #3 June 28th, 2026 at 10:44 pm
Wonderful to learn that Aumann’s now got common knowledge of how his work is given pride of place at LightHaven in Berkeley.
I tend to call the rationalist conference site the “Ratican”, as a nod to the LessWrong community’s commitment to cleaning up their epistemics through rational inquiry & explanation
Comment #4 June 29th, 2026 at 9:34 am
Here’s a maybe dumb question, because I never read your paper:
1. The base theorem says perfect reasoners should never disagree
2. You further proved that this doesn’t require mind meld levels of communication to reach agreement
So, can can two people who read your paper just go through the motions and the agree on something like “chance of rain tomorrow” or “chance favorite party wins presidential election” or maybe even something more complicated like “ai go foom?”
Or is a catch?
Comment #5 June 29th, 2026 at 11:08 am
Mark Y #4: They can certainly try! The theorem guarantees that it will work if they have a shared prior, and they’re both perfectly honest and rational, and they both know all that, and they know that they know it, and so on ad infinitum. How often do you think those conditions are satisfied in practice? 🙂