I know. I know that I know. For as long as human race existed, knowledge embodied power. In the life of a society, however, what becomes even more important is the fact that we share certain knowledge with fellow human beings, and that we, moreover, are aware of each other’s knowledge. This special type of awareness is termed common knowledge: I know that you know that I know that you know - and so on to infinity.
In theory, common knowledge is surprisingly hard to achieve. One of the classic examples is the Coordinated Attack Problem, where two armies need to coordinate on the timing of the attack. If they attack separately, they fail. Sending a courier with a message to the other army’s camp seems like a very simple solution to the problem. But, there is a very small probability that a courier does not reach the other camp. How would Camp One know that the friendly Camp Two in fact received the message? Of course, Camp Two can send a courier back confirming the receipt. But again, there is a small probability that the courier does not reach the destination. If he doesn’t then Camp One would not know whether Camp Two knows the timing of the attack, and therefore will not attack at the specified time. If, however, Camp One successfully receives the message, they would need to once again confirm by sending a courier back to Camp Two. This exchange can go on forever, and paradoxically the armies will not be able to coordinate, no matter how many couriers cross the valley between the camps.Thus, in the world, where achieving common knowledge is a virtually impossible task, we seem to be destined to live with ambiguity.
In practice, of course, we do not need to send and receive infinite confirmations to coordinate on a certain equilibrium. Dalkiran and Hoffman (2011) for example, argue that all we need to do is to believe with sufficiently high probability that the other person knows that we know and so on. A public announcement about an event, or a publicly visible symbol, would facilitate this kind of common belief. Without the announcement, however, it is possible that we will end up having only mutual knowledge of the event (I know that I know and you know that you know, but we are not aware, or not sure, that the other knows as well).
It is surprising how the ambiguity about what others know can and has been exploited in public life throughout centuries – sometimes with very significant social consequences. The disconnect between mutual knowledge and common knowledge has been used to perpetuate the power of the ruling elite, in campaigns of disinformation, to make the public believe in something that was contrary to what people privately knew or observed. In the Soviet Union, for example, public announcements have been used very skillfully to perpetuate the myths of efficiency and prosperity, contrary to what people witnessed in their everyday life.
Like any weapon, however, the ambiguity can be used to topple as well as perpetuate. Consider for example that in order for me to rise against the regime, I need to know that sufficiently many others share my discontent. Can I do it without the risk of publicly speaking my mind? I can certainly show up on a public square carrying a rose, a carnation, wearing an orange scarf or a tri-color cockade. It is quite possible, that this is precisely what I felt like wearing on that day regardless of my political beliefs - no regime could fault me for that. But when all of a sudden I see another person carrying the same symbol, once our eyes meet, the ambiguity is removed. The civic society, the common knowledge, the revolution is born: I know that you know, that I know, that you know that I know. All the way to infinity.
Comments
"In theory, common knowledge is surprisingly hard to achieve." - well, not really
In theory it is done by one simple assumption that defines modern mainstream micro. I believe it is practice where it is hard to achieve!
Perhaps both are :-) - but we don't normally care - we don't need the common knowledge in its pure form for most practical coordination tasks. Where it becomes interesting in when we can exploit the ambiguity to avoid certain undesirable social equilibria by for example "looking the other way", pretending not to hear, avoiding eye contact, or simply "playing dumb" :-)
Now we finally understand why revolutions start by taking control of TV towers (or telegraph, back in 1917). We also understand why dictatorial regimes may tolerate some autonomy on local and provincial TV stations but not on the central ones.
I remember being puzzled by the public announcement of election results back in the Soviet era (I was 10-11 years old). I was surrounded by 8 adults in our summer cottage (dacha) and not a single one of them voted on the election day. According to the radio announcement, 99.97 of the people voted (all unanimously supporting the communist party candidate(s)). I figured out that my family must have been the only family that did not participate in the election. Now I understand that there must have been many other families and 10 year old boys going through the same calculations.
Very true. In the Soviet Union it was always admissible - and even encouraged - to criticize the "shortcomings" of the local small fish bureaucrats - the building, hotel or restaurant managers, heads of collective farms, etc. But the higher you aimed, the more difficult it was to avoid censorship.
I suppose part of the game was to acknowledge that absurdities created by the lack of incentives to work did exist - but also to convince people that these were "local", not "global" phenomena.
December 21, 1989 in Bucharest, Nicolae Ceausescu's last speech. It started as a support rally for Ceausescu (aka the genius of the Carpathians or Conducator), with him driveling on about the imperalist being behind the demonstrations in Timisoara, and promising pay rises to everyone. Initially the crowd cheered and waved banners.
But then something extraordinary happened. At the edges of the demonstration there were some disturbances. It is unclear what exactly happened. Some claim that shot were fired. But whatever caused the commotion at the edges of the rally, it changed the course of history. Ceausescu stopped his speech, and then unsuccesfully tried to get back control of the crowd (shouting Allo, tovarish). But Ceausescu so visibly loosing control made it common knowledge that Ceausescu was done. The support rally had turned into a protest rally, all caused by a disturbance at the edge.
See this video http://www.youtube.com/watch?v=TcRWiz1PhKU&feature=related, from a great documentary Videograms of a Revolution (highly highly recommended documentary).
He was quite visibly afraid when the skirmishes started. Probably the fact that this moment was still aired on live TV contributed greatly to his demise. Once people start feeling their power, the dictatorship cannot survive.
This is also why Putin had to win the election in the first round, with at least 60+ percent. They may have learned from the experience of the Orange revolution in Ukraine. In our case, the opposition won the popular vote in the first round in October 2004 (without winning majority) even despite the falsifications and severe voting irregularities. The fact that the Yanukovych, the establishment candidate, failed to win outright under such favorable conditions clearly showed the weakness of the system and the magnitude of the popular discontent.