By James White and Victor Haghani¹
ESTIMATED READING TIME: 6 min.

What happens when brilliant minds clash on their beliefs about the future? In this interview with Victor and James, Nobel Prize winner Robert Aumann explains his groundbreaking mathematical proof that rational, truth-seeking people simply cannot “agree to disagree” – and what this means for markets, conflict, and human cooperation.

The Agreement Theorem isn’t just abstract mathematics – it’s a blueprint for how rational minds can work together toward truth. In a world often divided by seemingly intractable disagreements, Aumann’s work offers hope.

What you’ll hear:

• The remarkable story of Aumann’s “aha moment” 50 years ago
• A simple story that makes complex game theory accessible
• Why enormous trading volumes puzzle economists
• The concept of “common knowledge” and why it matters (Aumann was the first to formally define the concept of “common knowledge.”)
• Real implications for resolving disagreements
• Professor Aumann shares how his three-page paper sparked thousands of research articles and fundamentally changed how we think about conflict and cooperation. This conversation explores both the mathematical elegance of the Agreement theorem and its practical applications for anyone interested in how rational minds can work together toward truth.

Some additional resources if you want to go deeper:

• Common Knowledge and Aumann’s Agreement Theorem by Scott Aaronson (2015)
• Are Disagreements Honest? by Tyler Cowen and Robin Hanson (2001)
• Common Knowledge by John Geanakoplos (1994) Journal of Economic Perspectives
• The Big Questions, by Steven Landsburg. Chapter 8 is an excellent discussion of the Agreement theorem
• “Agreeing to Disagree” by Robert Aumann (1976) – the 3 page article itself
• Steven Pinker and Tyler Cowen discuss the Agreement theorem, Common Knowledge and more on Conversations with Tyler podcast (September 2025)
• Steven Pinker and Sean Carroll discuss the Agreement theorem and Common Knowledge on Mindscape podcast (September 2025)
• Pinker’s forthcoming book, When Everyone Knows That Everyone Knows: Common Knowledge and the Mysteries of Money, Power, and Everyday Life

Excerpts from Pinker/Carroll discussion:

Sean Carroll: There’s a very famous theorem called the Aumann Agreement Theorem that says roughly speaking that if you have two perfectly rational agents with common shared priors about a set of claims that could be true or false in the world… then they should … come to agreement. They should basically update their own priors on the basis of the fact that this (other) perfectly rational person has updated their priors, and there is a right place to come to. … There can be give and take. But you should not, according to Aumann, if you’re both perfectly rational and you start from the same beliefs, you should not be able to agree to disagree. You shouldn’t even be able to just disagree and maintain the fiction that both you and the other person are perfectly rational.

Steven Pinker: … argument is like war. “I demolished his position, he tried to defend it, but I found the weak spot.” And we use the language of war in talking about arguments. … “Well, do we have to think about argument as war? Why don’t we think of it as like a dance?” And as it happens, the sequence of reaching agreement in Aumann’s construction is in some ways more like a dance than like a battle. … So this esoteric mathematical (Aumann agreement) theorem might actually have some insight. And again, just to tie it to implications we ought to draw, you know and I know that probably a lot of arguments among academics, or among politicians, are kind of pissing contests. It’s like, who’s going to win? Often people use dirty debating tricks. They set up a straw man. They look for a loophole that the person just neglected to mention. It’s not the best way of arriving at the truth to make it a combat sport because the truth is the truth. It doesn’t care about your ego. If all you’re doing is trying to win, that’s not the same as trying to get to the truth. And so Aumann’s theorem in some ways is an exercise in humility, in epistemic humility, and might press back against the bad habit that we have of seeing an argument as something that we want to win.

Carroll: And is there a feeling that, given this theorem, that maybe this can inspire us to take more seriously the opinions of others? I’m thinking there’s a common move you get in the media or social media where people will say, “oh, look, I said this, and everyone disagrees with me, I must be onto something,” which is sort of the opposite of what Aumann would have us believe.

Pinker: … there is a widespread tendency in science journalism, but also in science journals and among scientists, to over-update in response to a single data point. I think that’s probably a bad habit. Going back to Aumann and what does it mean? You’ve heard of the so-called rationality movement, which is, you know, how could that be a movement? Aren’t we all supposed to be rational all the time…

So the rationality movement (official headquarters are in Berkeley) is the attempt to call attention to the fallacies and biases that cognitive psychologists and behavioral economics have documented, to try to overcome them, often with Bayesian reasoning. Sometimes the rational community is called Bayesians, but they have kind of canons of argumentative hygiene or best practices, which include things like stating your degree of credence, your posterior as a quantity between zero and one, instead of saying, you know, this is right, that’s wrong, saying I have about 0.7 confidence in this. “Steel-manning” rather than “straw-manning” your opponent, that is don’t set up a straw man that’s easy to knock down, but argue against the strongest version you can imagine. Engage in adversarial collaborations where you get together with your worst enemy and decide a priori what would settle the issue to both of your satisfactions and then go out and gather the data. So all of these practices, which are kind of in the spirit of Aumann, so much so that the conference center in Berkeley that was set up as kind of the home for rationality conferences, its main meeting room is called Aumann Hall.

About Robert Aumann:

Robert Aumann won the 2005 Nobel Prize in Economic Sciences for his groundbreaking contributions to game theory and our understanding of conflict and cooperation. He is Professor Emeritus at the Hebrew University of Jerusalem and one of the most influential economists of our time. (Note: in the interview we mistakenly say that Aumann left Germany in 1930, but he actually left in 1938, 7 weeks before the Kristallnacht pogrom.)

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