In the Google Age, it is hard not to take the easy way out and just google the answer to many a question which one could have otherwise enjoyed solving and learn a lot from the exercise. I hope that some gave at least a few brain cycles to figure out the puzzle mentioned in the post “The Theater of the Absurd: The War Log edition.” Here’s the follow up to that post.
The solution to the puzzle is in the wikipedia entry on “Common Knowledge.” You may wish to check it out before continuing with this post.
In that section of the entry for common knowledge in the wikipedia, it says,
“What’s most interesting about this scenario is that, for k > 1, the outsider is only telling the island citizens what they already know: that there are blue-eyed people among them. However, before this fact is announced, the fact is not common knowledge.”
I think that that is an incomplete explanation. I will go into what’s missing in a bit. For now, here’s how I like to think about common knowledge.
Imagine that I send you an email saying, “Roses are red.” Clearly, I know that roses are red. Perhaps you also know that roses are red. But I don’t know that you know that roses are red. Even after I send you the email, I still don’t know if you know that roses are red. Perhaps you have not read that email or maybe it was not delivered.
When you do read my email, you know that roses are red (if you did not know before) and you know that I know that roses are red. Now you send me an email saying “Thanks.” When I get that reply from you, I know that you know that roses are red, and that you know that I know that roses are red.
But you don’t know that I know that you know that roses are red. You only get to know that bit if I were to email you saying “Thanks for replying to my email about roses are red”, and you were to read that email.
To cut a long story short: only if we have an infinite number of back and forth emails does “Roses are red” become common knowledge with regards to you and I.
Now imagine that we are sitting in the same room intently watching TV. It’s a nature program and David Attenborough breathlessly declares that roses are red. I hear it and also note that you too heard that astonishing pronouncement. Now I know that roses are red; I know that you know that roses are red; I know that you know that I know that roses are red; . . . ad infinitum. No need for an infinite number of emails required in this case.
(Note that instead of David making that statement, either one of us could have said “roses are red” and it would have become common knowledge for us.)
General knowledge is when some information is known to all concerned. Common knowledge is when some information is not just known to all but all concerned also know that that information is known to all.
Coming back to the logic problem. Everyone knows that there are blue-eyed people in the village. There’s an exception. If there is only one blue-eyed person in the village, all she sees are brown-eyed people and so cannot know for sure if there is a blue-eyed person in the village or not.
When the visitor — perhaps David Attenborough there to make a documentary on people’s eye color — announces loudly before the entire assembled village that not all villagers are brown-eyed (meaning there is at least one blue-eyed villager), the fact becomes common knowledge. This means that all villagers know that all villagers know. It also means that if the village had only one blue-eyed resident, that resident now knows that there is a blue-eyed person in the village, and can now logically deduce her eye color.
Now here’s the interesting bit. Attenborough’s announcement did more than just make general knowledge about eye-color into common knowledge. It implicitly announced a “Day 1″ for the logical process to get started and made that “Day 1″ common knowledge. Why was this important? Because without a date on which to anchor the start of the logical deduction, it would not be possible for people to logically deduce their eye color if there were more than one person with blue eyes.
The thing to note is that the logical process of deduction requires a “coordinating signal” which says, “People, you may start figuring this one out from today.” It’s the coordinating signal function of Attenborough’s announcement that solves the problem.
All this is fine and interesting, you may say. But what does it have to do with economic development in general and with India’s economic development in particular, you may ask.
Economies have huge number of economic agents (individuals, households, firms) and in any complex economy larger than a one-person economy (aka Robinson Crusoe economy), there arise numerous coordination problems. Devices, associations, institutions, and various other methods have been invented to solve these coordination problems.
Money is one of them. So are markets. Communication channels too, the latest of which is the internets (or the web.) There’s eBay and Craigslist. There are institutions such as central banks, and constitutions, and political parties, and Olympic associations, etc. All of these and many more solve coordination problems.
Coordinating signals are necessary to make things happen. A society could have all the necessary bit to get something done but without a credible coordinating signal, it will not get done. Economies need the equivalent of coxswains in rowing, someone who “coordinates the power and rhythm of the rowers.”
I have pondered this matter of coordination and coordinating signals in the case of India’s development. Some years ago I figured out a simple model for the development of rural India, called RISC–Rural Infrastructure & Services Common. (Google RISC)
What RISC does is solve a coordination problem — that infrastructure providers find users missing, and users find infrastructure missing.
And now for the conclusion of this thread. In the post about wikileaks (same link as the one at the top of this post), I wrote “that what the wikileaks did by publishing the Afghan War Logs is that it made what was general knowledge into common knowledge.”
The US government knew what was in the wikileaks since it was their secret. They knew, for instance, that Pakistan was using American taxpayer money to kill American soldiers. Pakistani leaders knew that too. Many journalists and researchers also knew that. What wikileaks did was, first of all, to make that information more generally known. But more than that, it made the US leaders know that the American public knows, and the public knows that the US leaders know that the public knows.
The wikileaks also provided a coordinating signal of sorts for all to get started with solving the problem. Suddenly a lot of different people started looking at the problem thus compelling the US leadership to take action instead of pretending that all was hunky-dory.
As of CBS News puts it in his column, it’s “Time Start Demanding Answers From Pakistan“:
[Thanks to Rohit and others who commented or wrote to me about the logic puzzle and its solution.]