- Joined
- 9/18/07
- Messages
- 4
- Points
- 11
Once upon a time there was a village in which there lived many married
couples. There were certain qualities about this village, though, that made
this village unique:
Whenever a man had an affair with another man's wife, every woman in the
village got to know about the affair, except his own wife. This happened
because the woman who he had slept with talked about their affair with all
the other women in the village, except his wife. Moreover, no one ever told
his wife about the affair.
The strict laws of the village required that if a woman could prove that her
own husband had been unfaithful towards her, then she must kill him that
very day before midnight. Also, every woman was law-abiding, intelligent,
and aware of the intelligence of other women living in that village.
You and I know that exactly twenty of the men had been unfaithful to their
wives. However, as no woman could prove the guilt of her husband, the
village life proceeded smoothly.
Then, one morning, a wise old man with a long, white beard came to the
village. His magical powers, and honesty was acknowledged by all and his
word was taken as the gospel truth.
The wise old man asked all villagers to gather together in the village
compound and then announced:
"At least one of the men in this village has been unfaithful to his wife."
Questions:
1. What happened next?
2. And what this got to do with stock market crashes?
Answer 1:
After the wise old man has spoken, there shall be 19 peaceful days followed
by a massive slaughter before the midnight of the 20th day when twenty women
will kill their husbands.
Proof:
We will use backward thinking for the proof. Indeed, the very purpose of
this post is to demonstrate the utility of the backward thinking style.
Let's start by assuming that there is only one unfaithful man in the village
- Mr. A. Later, we shall drop this assumption.
Every woman in the village except Mrs. A knows that he is unfaithful.
However, since no one has told her anything, and she remains blissfully
ignorant. But only until the old man speaks the words, "At least one of the
men in this village has been unfaithful to his wife."
The old man's words are news only for Mrs. A, and mean nothing to the other
women. And because she is intelligent, she correctly reasons that if any man
other than her own husband was unfaithful, she would have known about it.
And since she has no such knowledge in her possession, it must mean that
it's her own husband who is unfaithful. And so, before the midnight of the
day the old man spoke, she must execute her husband.
Now, let's assume that there were exactly two unfaithful men in the village
- Mr. A and Mr. B.
The moment the old man speaks the words, "At least one of the men in this
village has been unfaithful to his wife," the village's women population
gets divided as follows:
Every woman other than Mrs. A and Mrs. B knows the whole truth;
Mrs. A knows about philanderer Mr. B, but, as of now, knows nothing about
her own husband's unfaithfulness, so she assumes that there is only one
unfaithful man - Mr. B - who will be executed by Mrs. B that night; and
Mrs. B knows about philanderer Mr. A, but, as of now, knows nothing about
her own husband's unfaithfulness, so she assumes that there is only one
unfaithful man - Mr. A - who will be executed by Mrs. A that night.
As the midnight of day one approaches, Mrs. A is expecting Mrs. B to execute
her husband, and vice versa. But, and this is key, none of them do what the
other one is expecting them to do!
The clock is ticking away and passes midnight and day 2 starts. What happens
now is sudden realization on the part of both Mrs. A and Mrs. B, that there
must be more than one man who is unfaithful. And, since none of them had
prior knowledge about this other unfaithful man, then it must be their own
respective husbands who were unfaithful!
In other words, the inaction of one represents new information for the
other.
Therefore, using the principles of inductive logic requiring backward
thinking, both Mrs. A and Mrs. B will execute their respective husbands
before the midnight of day 2.
Now, let's assume that there are exactly three unfaithful men in the
village- Mr. A, Mr. B., and Mr. C. The same procedure can be used to show
that in such a scenario, the wives of these three philandering men will kill
them before the midnight of day 3.
Using the same process, it can be shown that if exactly twenty husbands are
unfaithful, their wives would finally be able to prove it on the 20th day,
which will also be the day of the bloodbath.
Answer 2: Connection with Stock Market Crashes
If you replace the announcement of the old man with that provided, by say,
SEBI, the nervousness of the wives with the nervousness of the investors,
the wives' contentment as long as their own husbands weren't cheating on
them with the investors' contentment so long as their own companies were
not indulging in fraud, the execution of twenty husbands with massive
dumping of stocks, and the time lag between the old man's announcement and
the killings with the time lag between the old man's announcement and the
market crash, the connection between the story and market crashes becomes
obvious.
*Information Asymmetry *
One of the most interesting aspects about the story is the role of
information asymmetry.
You and I knew that there were exactly twenty unfaithful men in the village.
We had complete information about the number of unfaithful men in that
village but not their identity.
On the other hand, every woman in the village knew the identity of at least
nineteen unfaithful men. For example, if you were Mrs. A, you would have
known about nineteen unfaithful men, but not about your own husband's
unfaithfulness. And, if you were one of the women whose husband was
faithful, then you'd know the identity of twenty unfaithful men.
But the old man did not say that there were twenty unfaithful men in the
village. All he said was that there was at least one unfaithful man in the
village. So, his statement, did not add anything to the knowledge of any
individual woman because each of them knew of at least nineteen unfaithful
men!
And yet, his statement caused the bloodbath after twenty days!
The lesson is simple: It's not necessary for any new information to cause
havoc in the stock market. Sudden realizations about the stupidity of gross
overvaluations and dubious accounting practices followed by some companies
in bubble markets can and do occur simultaneously in the minds of the
crowd. And that sudden realization can cause markets to crash!
couples. There were certain qualities about this village, though, that made
this village unique:
Whenever a man had an affair with another man's wife, every woman in the
village got to know about the affair, except his own wife. This happened
because the woman who he had slept with talked about their affair with all
the other women in the village, except his wife. Moreover, no one ever told
his wife about the affair.
The strict laws of the village required that if a woman could prove that her
own husband had been unfaithful towards her, then she must kill him that
very day before midnight. Also, every woman was law-abiding, intelligent,
and aware of the intelligence of other women living in that village.
You and I know that exactly twenty of the men had been unfaithful to their
wives. However, as no woman could prove the guilt of her husband, the
village life proceeded smoothly.
Then, one morning, a wise old man with a long, white beard came to the
village. His magical powers, and honesty was acknowledged by all and his
word was taken as the gospel truth.
The wise old man asked all villagers to gather together in the village
compound and then announced:
"At least one of the men in this village has been unfaithful to his wife."
Questions:
1. What happened next?
2. And what this got to do with stock market crashes?
Answer 1:
After the wise old man has spoken, there shall be 19 peaceful days followed
by a massive slaughter before the midnight of the 20th day when twenty women
will kill their husbands.
Proof:
We will use backward thinking for the proof. Indeed, the very purpose of
this post is to demonstrate the utility of the backward thinking style.
Let's start by assuming that there is only one unfaithful man in the village
- Mr. A. Later, we shall drop this assumption.
Every woman in the village except Mrs. A knows that he is unfaithful.
However, since no one has told her anything, and she remains blissfully
ignorant. But only until the old man speaks the words, "At least one of the
men in this village has been unfaithful to his wife."
The old man's words are news only for Mrs. A, and mean nothing to the other
women. And because she is intelligent, she correctly reasons that if any man
other than her own husband was unfaithful, she would have known about it.
And since she has no such knowledge in her possession, it must mean that
it's her own husband who is unfaithful. And so, before the midnight of the
day the old man spoke, she must execute her husband.
Now, let's assume that there were exactly two unfaithful men in the village
- Mr. A and Mr. B.
The moment the old man speaks the words, "At least one of the men in this
village has been unfaithful to his wife," the village's women population
gets divided as follows:
Every woman other than Mrs. A and Mrs. B knows the whole truth;
Mrs. A knows about philanderer Mr. B, but, as of now, knows nothing about
her own husband's unfaithfulness, so she assumes that there is only one
unfaithful man - Mr. B - who will be executed by Mrs. B that night; and
Mrs. B knows about philanderer Mr. A, but, as of now, knows nothing about
her own husband's unfaithfulness, so she assumes that there is only one
unfaithful man - Mr. A - who will be executed by Mrs. A that night.
As the midnight of day one approaches, Mrs. A is expecting Mrs. B to execute
her husband, and vice versa. But, and this is key, none of them do what the
other one is expecting them to do!
The clock is ticking away and passes midnight and day 2 starts. What happens
now is sudden realization on the part of both Mrs. A and Mrs. B, that there
must be more than one man who is unfaithful. And, since none of them had
prior knowledge about this other unfaithful man, then it must be their own
respective husbands who were unfaithful!
In other words, the inaction of one represents new information for the
other.
Therefore, using the principles of inductive logic requiring backward
thinking, both Mrs. A and Mrs. B will execute their respective husbands
before the midnight of day 2.
Now, let's assume that there are exactly three unfaithful men in the
village- Mr. A, Mr. B., and Mr. C. The same procedure can be used to show
that in such a scenario, the wives of these three philandering men will kill
them before the midnight of day 3.
Using the same process, it can be shown that if exactly twenty husbands are
unfaithful, their wives would finally be able to prove it on the 20th day,
which will also be the day of the bloodbath.
Answer 2: Connection with Stock Market Crashes
If you replace the announcement of the old man with that provided, by say,
SEBI, the nervousness of the wives with the nervousness of the investors,
the wives' contentment as long as their own husbands weren't cheating on
them with the investors' contentment so long as their own companies were
not indulging in fraud, the execution of twenty husbands with massive
dumping of stocks, and the time lag between the old man's announcement and
the killings with the time lag between the old man's announcement and the
market crash, the connection between the story and market crashes becomes
obvious.
*Information Asymmetry *
One of the most interesting aspects about the story is the role of
information asymmetry.
You and I knew that there were exactly twenty unfaithful men in the village.
We had complete information about the number of unfaithful men in that
village but not their identity.
On the other hand, every woman in the village knew the identity of at least
nineteen unfaithful men. For example, if you were Mrs. A, you would have
known about nineteen unfaithful men, but not about your own husband's
unfaithfulness. And, if you were one of the women whose husband was
faithful, then you'd know the identity of twenty unfaithful men.
But the old man did not say that there were twenty unfaithful men in the
village. All he said was that there was at least one unfaithful man in the
village. So, his statement, did not add anything to the knowledge of any
individual woman because each of them knew of at least nineteen unfaithful
men!
And yet, his statement caused the bloodbath after twenty days!
The lesson is simple: It's not necessary for any new information to cause
havoc in the stock market. Sudden realizations about the stupidity of gross
overvaluations and dubious accounting practices followed by some companies
in bubble markets can and do occur simultaneously in the minds of the
crowd. And that sudden realization can cause markets to crash!
