Common Knowledge and Aumann’s Agreement Theorem

Two people of indeterminate gender—let’s not make any assumptions here—go on a date.  Afterward, one of them says to the other: “Would you like to come up to my apartment to see my etchings?”  The other says, “Sure, I’d love to see them.”

This is such a cliché that we might not even notice the deep paradox here.  It’s like with life itself: people knew for thousands of years that every bird has the right kind of beak for its environment, but not until Darwin and Wallace could anyone articulate why (and only a few people before them even recognized there was a question there that called for a non-circular answer).

In our case, the puzzle is this: both people on the date know perfectly well that the reason they’re going up to the apartment has nothing to do with etchings.  They probably even both know the other knows that.  But if that’s the case, then why don’t they just blurt it out: “would you like to come up for some intercourse?”  (Or “fluid transfer,” as the John Nash character put it in theBeautiful Mind movie?)

.. The crucial concept here is common knowledge.  We call a fact “common knowledge” if, not only does everyone know it, but everyone knows everyone knows it, and everyone knows everyone knows everyone knows it, and so on.

.. The moral is that the mere act of saying something publicly can change the world—even if everything you said was already obvious to every last one of your listeners.  For it’s possible that, until your announcement, not everyone knew that everyone knew the thing, or knew everyone knew everyone knew it, etc., and that could have prevented them from acting.

.. But real humans tend to be unable to reason reliably past three or four levels in the knowledge hierarchy.

.. (My favorite Soviet joke involves a man standing in the Moscow train station, handing out leaflets to everyone who passes by.  Eventually, of course, the KGB arrests him—but they discover to their surprise that the leaflets are just blank pieces of paper.  “What’s the meaning of this?” they demand.  “What is there to write?” replies the man.  “It’s so obvious!”  Note that this is precisely a situation where the man is trying to make common knowledge something he assumes his “readers” already know.)

.. The kicker is that, to prevent something from becoming common knowledge, all you need to do is censor the common-knowledge-producing mechanisms: the press, the Internet, public meetings.  This nicely explains why despots throughout history have been so obsessed with controlling the press, and also explains how it’s possible for 10% of a population to murder and enslave the other 90% (as has happened again and again in our species’ sorry history), even though the 90% could easily overwhelm the 10% by acting in concert.  Finally, it explains why believers in the Enlightenment project tend to be such fanatical absolutists about free speech—why they refuse to “balance” it against cultural sensitivity or social harmony or any other value, as so many well-meaning people urge these days.

 

 

The Hypocrisy of ‘Helping’ the Poor

To me, globalization is the search for a new plantation, and cheaper labor; globalization means that, by outsourcing, it is possible to impoverish an American community to the point where it is indistinguishable from a hard-up town in the dusty heartland of a third world country.

.. The strategy of getting rich on cheap labor in foreign countries while offering a sop to America’s poor with charity seems to me a wicked form of indirection. If these wealthy chief executives are such visionaries, why don’t they understand the simple fact that what people want is not a handout along with the uplift ditty but a decent job?

The Downsizing of the American Dream

The American dream has long been equated with moving up the class ladder and owning a home. But polling leading up to the 2012 election revealed something new—middle-class Americans expressed more concern about holding on to what they had than they were with getting more. Echoing these concerns, Pew reported in 2015 that when asked which they would prefer—financial security or moving up the income ladder—92 percent selected security. This is a seven percentage point increase since just 2011, when 85 percent selected security over economic mobility.

.. people are downsizing their definition of the American dream. Today, the desire to own a home or to move up economically is often replaced by a desire to be debt free and to have financial stability.

These developments point to a possible change in the underlying psychology of the American dream, and thus for the country more broadly. When people are more concerned about falling down than they are with moving up, planning ahead and having big goals is not only pointless but painful, since time and again something outside of one’s control comes along and upends their plans. There are grave consequences to this: People stop making investments in their education; they delay or never have children; they stop buying homes, they are less likely to take entrepreneurial risks; and they defer their dreams, often indefinitely.