Real-life observations of the blue eyes puzzle phenomenon?

post by HonoreDB · 2011-08-08T17:10:32.957Z · score: 2 (7 votes) · LW · GW · Legacy · 18 comments

The Blue Eyes Puzzle (solution) depicts a paradox: people engage in coordinated action despite having no new information, when "I know you know he knows" reaches a critical mass. Apparently the formal system invented to address this is called Common Knowledge.

Duncan Black complains:

I wonder if any serious investor could actually explain what new information "the market" has which could explain why DJIA should be worth 11% less than it was 2 weeks ago.

The typical, compelling, explanation for this sort of thing is herd behavior.  In the absence of new information, the market is modeled as a random walk, and when the amplitude of its swing happens to get high enough, people see a trend, anticipate it continuing, and thereby create the trend and cause a massive swing.

I wonder if you could instead model stock market swings, or other seemingly unmotivated coordinated activity, as common knowledge reaching critical mass.  Say new information was injected into the market two weeks ago, and it took that long to reach a blue eyes catastrophe.

I have no evidence for this other than random pattern matching.

18 comments

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comment by DanielLC · 2011-08-08T22:36:19.526Z · score: 10 (12 votes) · LW(p) · GW(p)

The Blue Eyes Puzzle requires you to be rational, trust others to be rational, trust others to trust others to be rational, and so on for a huge number of levels. This is not how the market behaves. Your average person doesn't go through "I know you know I know" even once when deciding on whether to buy or sell stock.

The market merely averages everyones predictions, weighted towards those who are more sure and did better in the past. This makes it better than normal people in a lot of ways, but it isn't going to go through mental hoops that the investors can't fathom. Ergo, if it was working like this, everyone would know it.

Besides that, the common knowledge is merely that people are fairly rational. The time frame isn't discrete. If there's some mechanism that would make it's direction turn based on whether the timing is even or odd, it will average out to nothing very quickly. If it's just a question of how high it goes, it will go up now until it no longer is.

comment by shminux · 2011-08-08T18:00:32.046Z · score: 4 (4 votes) · LW(p) · GW(p)

Trying to predict market behavior is a thankless job, unless you are paid handsomely to do it regardless of the outcome.

Given that getting it right better than chance has such a high payoff, so much money and so many bright minds are already thrown at the problem as to make any model (including the delayed reaction model you are suggesting) that does not consider the resulting feedback completely useless. And these bright minds with resources to spare surely try to take this into account, resulting in multiple levels of feedback. Due to the competitive nature of the enterprise the algorithms employed to squeeze any useful prediction are kept secret, so mapping the market territory is probably one of the lowest payoff-to-effort ratio problems out there, unless you are a market mover and can game the system, in effect creating the territory to match your map, and know how to skirt the insider info laws.

Of course, there are plenty of cases where people/organizations manage to beat the market in the short term, and comparatively few cases where they beat the market consistently, just like someone always wins any given lottery. In the hindsight these people (Soros, Buffett etc.) may sound like geniuses, and maybe some of them are, there is no way to know.

comment by SilasBarta · 2011-08-08T18:12:51.454Z · score: 3 (3 votes) · LW(p) · GW(p)

There is a similar common-knowledge-based argument regarding the difficulty in beating the market, based on an isomorphism to a similar logic problem.

This is the logic problem:

"There is a village of 100 couples, where each wife has the unusual ability to know when any man except her husband has been unfaithful, and she knows all other wives have that ability, but they cannot directly communicate. Each woman must also publicly kill her husband [EDIT: at noon the next day] if she can deduce he has been unfaithful. All women are also perfect logicians, capable of deducing everything that can be."

"It also happens to be the case, that every man has been unfaithful. One day, the queen, whom everyone trusts, announces that at least one man has been unfaithful. Then, all women kill their husbands. Why?"

The answer basically involves each wife doing a proof by contradiction by assuming her husband has been faithful, while leads her to believe that there exists one woman who believes all other wives believe their husbands faithful, which must be false per the queen's announcement [EDIT: once they notice no executions next noon], rendering the initial assumption of husband faithfulness false.

So, the connection to bias in investment:

"Each woman is capable of seeing other husbands' infidelity, but not her own." --> "Each active investor is capable of seeing other active investors' likelihood of underperforming the market, but not their own."
"If a woman can deduce her husband unfaithful, she kills him." --> "If an investor can deduce they are incapable of beating the market, they switch to index funds."
"Every man is unfaithful." --> "All investors are incapable of beating the market."
"Queen announces presence of one unfaithful man." --> "Market statistics announce the presence of some underperforming investors."
"Each woman does proof by contradiction that her husband has been unfaithful. --> "Each investor does proof by contradiction that they will underperform if they actively manage rather than use an index fund." (???)

comment by gjm · 2011-08-10T12:10:55.422Z · score: 5 (5 votes) · LW(p) · GW(p)

The unfaithful-husbands problem isn't merely similar to the blue-eyes problem; it's exactly isomorphic. ("I have blue eyes" = "My husband is unfaithful".) In particular, that proof by contradiction involves the same sort of recursive unwinding as in the blue-eyes problem. The only difference is that the blue-eyes problem is synchronous and the unfaithful-husbands problem is asynchronous (which, actually, makes it not work without some further hypothesis about how quickly the women make their deductions, and how well they know that, and how well they know that, etc.).

But this sort of problem seems to me to depend on very fragile details -- perfect reasoning, common knowledge, absolutely predictable behaviour, and so forth. Even a small deviation from those details can make the catastrophe (mass exodus or execution, or mass movement to index funds) not happen.

... But it's "can make", not "will definitely make". For instance, let's modify the blue-eyes problem slightly by allowing for a little uncertainty: everyone starts off with Pr(I have blue eyes) = 1/2; if that probability reaches p then they leave with probability q (both these probabilities are very close to 1). Leave everything else the same. What then? Well, it turns out that here the catastrophe still happens, with probability very close to 1, for any n; the uncertainty doesn't expand exponentially and break the inferences.

There's another difficulty in matching up the cuckolded wives (hmm, I think "cuckolded" is a gender-specific term; is there a word for a female victim of marital infidelity?) with the underperforming investors: the very first parallel in your list states, in effect, that investors are extremely irrational when contemplating their own performance, which is hard to square with making them all perfect logicians who make all available inferences.

[EDITED to add: it turns out that the wife of an unfaithful husband is a "cuckquean"; the word is obsolete and has many variant spellings. And there's an old joke: the word for a man whose wife is unfaithful is "cuckold"; the word for a woman whose husband is unfaithful is "wife".]

comment by SilasBarta · 2011-08-12T01:39:23.538Z · score: 1 (1 votes) · LW(p) · GW(p)

Good points, all. You're right that I didn't get the 100 wives problem phrased completely; it would need to stipulate that the killing happens at e.g. the next day's noon, just as the blue eye problem has departures at discrete intervals. Then each wife expects that some wife will kill at the first chance after the announcement, and when none do, they can all conclude that their initial assumption of husband faithfulness is false.

comment by jmmcd · 2011-08-09T12:52:12.114Z · score: 1 (1 votes) · LW(p) · GW(p)

Very nice!

Typo near the end: "Queen announces presence of one faithful man": faithful -> unfaithful.

comment by orthonormal · 2011-08-11T00:40:56.015Z · score: 1 (1 votes) · LW(p) · GW(p)

In the hindsight these people (Soros, Buffett etc.) may sound like geniuses, and maybe some of them are, there is no way to know.

Buffett has been so good for so long that the only plausible way it could be random chance is if he secretly possesses a doomsday device that he activates whenever his investments go sufficiently sour.

Agree for most other successful investors, though.

comment by nazgulnarsil · 2011-08-11T23:56:28.461Z · score: 0 (0 votes) · LW(p) · GW(p)

If I start flipping a coin and half the population guesses heads and half tails and I eliminate the half that guesses wrong, I will eventually wind up with one person with an unprecedented prediction streak.

comment by orthonormal · 2011-08-11T23:58:29.323Z · score: 4 (4 votes) · LW(p) · GW(p)

Yes, but Buffett continued his success for a long time after he'd already been publicly noticed. If you start with a million people, it shouldn't surprise you if someone gets 20 heads in a row- but if they get 30, you need to look for other hypotheses.

comment by nazgulnarsil · 2011-08-12T00:45:29.989Z · score: 1 (1 votes) · LW(p) · GW(p)

I'm not saying buffet isn't a good investor. Just that he is far less good than the popular narrative. Investor success follows a pareto distribution. There's always going to be someone like Buffet.

comment by [deleted] · 2011-08-09T12:15:21.510Z · score: 3 (3 votes) · LW(p) · GW(p)

This might link back to the market via the Greater Fool Theory. The idea behind the blue eyes puzzle is that everyone else is modeled with less information than you, and they model everyone else with less information than THEM, and they have models of everyone else who model everyone else with less information than THEM, etc. Another way of expressing that someone has less information than you is that they are a greater fool. In essence, everyone believes that there is a huge chain of "Greater fools" to take advantage of who think "I know this stock isn't worth this much, but I also know there is another person who DOESN'T know this, and I can make a dollar more by selling it to him."

But once it's common knowledge, you no longer think there are greater fools to take advantage of, and the economic bubble crashes.

There are definitely some similarities, but I'm not sure if you can actually make any better predictions of stock prices off of this. If you think you have come up with a testable prediction, you can certainly try it out in one of the free test markets that are available to see if it works out.

comment by gwern · 2011-08-09T00:07:04.268Z · score: 1 (1 votes) · LW(p) · GW(p)

I like anime because everyone has big eyes KAWAIIIIII

comment by [deleted] · 2011-08-09T00:07:07.629Z · score: 0 (0 votes) · LW(p) · GW(p)

I like anime because everyone has big eyes KAWAIIIIII

comment by Incorrect · 2011-08-09T00:05:29.542Z · score: 0 (0 votes) · LW(p) · GW(p)

I like anime because everyone has big eyes KAWAIIIIII

comment by Incorrect · 2011-08-09T00:01:21.298Z · score: 0 (0 votes) · LW(p) · GW(p)

test

comment by Incorrect · 2011-08-09T00:00:42.537Z · score: 0 (0 votes) · LW(p) · GW(p)

test

comment by Incorrect · 2011-08-08T23:48:10.986Z · score: 0 (0 votes) · LW(p) · GW(p)

test

comment by Incorrect · 2011-08-08T23:47:06.563Z · score: 0 (0 votes) · LW(p) · GW(p)

a