02/08/2026
https://press.uchicago.edu/ucp/books/book/chicago/P/bo266592965.html
The Problem with Personalization
A respected voice on technology shows how seemingly simple ads help dismantle democracy and public discourse.Whether you’re intentionally shopping or casually browsing social media, something is following you: ads. Their creators seem to know your income bracket, politics, age, location, medical c...
15/06/2026
On February 28, 1926, Joseph Stalin’s only daughter, Svetlana, was born. The baby girl would go on to live an inconceivably strange life, which was retold, in 2014, by Nicholas Thompson, then the head of The New Yorker’s website. Known in childhood as “the little princess of the Kremlin,” Svetlana would suffer family trauma and lose the love of her life to her father’s labor camps before becoming, at the age of 41, “the Cold War’s most famous defector.”
Thompson, now the C.E.O. of The Atlantic, got to know Svetlana when she was in her 80s, living in a senior center in Wisconsin and subsisting on welfare checks. (“Thanks be to FDR,” she wrote.) Thompson was researching a book about the former Ambassador and Soviet Union expert George Kennan; Svetlana, who used the last name Alliluyeva, was physically fragile but wielded a fiery personality. Stalin’s favorite child, she had spent almost exactly half her life on each side of the twentieth century’s greatest geopolitical divide. “Reading her story—the fraught parentage, political intrigues, and romantic travails—it’s nearly impossible to name the most surprising part,” Nathan Burstein writes. “She’s a sweet, gentle, vulnerable woman,” Svetlana’s daughter pointed out to Thompson, “who is followed around by demons.” Revisit the story from our archive: https://newyorkermag.visitlink.me/D_Eg9B
15/06/2026
https://x.com/sapinker/status/2065198715170668988
Aumann’s famous theorem—the Agreement Theorem—states the following core idea:
If two rational Bayesian agents start with the same prior and their posterior beliefs about an event are common knowledge, then they cannot “agree to disagree.” Their posterior probabilities must be identical.
This is one of the most important results in game theory and epistemic logic because it formalizes how shared information and rationality force belief convergence.
🧠 What the theorem actually says (the concise version)
Two agents:
* share the same prior over possible states of the world,
* update beliefs using Bayes’ rule,
* and have common knowledge of each other’s posterior beliefs,
must end up with the same posterior probability for any event.
If they seem to disagree, then at least one assumption (shared priors, Bayesian updating, or common knowledge) must be violated.
🔍 Why “common knowledge” is the key
Common knowledge means not just:
* A knows B’s belief,
* and B knows A’s belief,
but also:
* A knows that B knows that A knows… and so on, ad infinitum.
Aumann showed that once this infinite hierarchy holds, differing posteriors are impossible.
This is the deep mathematical insight: the structure of knowledge partitions forces belief alignment.
🧩 Intuition: Why can’t they disagree?
Imagine two rational investors, Alice and Bob, who start with the same prior about a startup’s success.
If Alice says “I think the probability is 70%” and Bob says “I think it’s 40%,” and this becomes common knowledge, then:
* Alice knows Bob’s number,
* Bob knows Alice’s number,
* each knows that the other knows, etc.
Given shared priors and Bayesian updating, these numbers themselves reveal information.
Each agent must incorporate the fact of the other’s belief into their own belief.
This recursive updating forces convergence.
🧱 The formal model (light version)
Aumann models:
* a finite state space Ω,
* a shared prior p,
* each agent’s private information as a partition of Ω,
* and common knowledge as the finest common coarsening of these partitions.
If an event E has different posteriors for the two agents, and these posteriors are common knowledge, then the set of states where this happens must have probability zero—contradiction.
Thus, the posteriors must be equal.
📌 Why the theorem matters
* Economics: It underpins no‑trade theorems—if rational traders with shared priors disagree, the disagreement itself reveals information that eliminates the incentive to trade.
* Political science: Suggests that rational, fully transparent debate should lead to consensus.
* Epistemology: Challenges the idea of persistent rational disagreement.
* Game theory: Introduces the modern formal definition of common knowledge.
🧠 Non-obvious insight
The theorem does not say people in practice must agree.
It says: If they don’t agree, then at least one of the idealized assumptions is false.
In real life, disagreements persist because:
* people have different priors,
* information is not fully shared,
* beliefs are not common knowledge,
* or people are not perfect Bayesians.
This is why the theorem is philosophically provocative: it isolates exactly what must break for disagreement to exist.
Steven Pinker (@sapinker) on X
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