Crowd sourcing, mass psychology, and the market

Once upon a time I was teaching a math class, and posed a famous problem to the students that went something like this.

You are boarding a plane, which seats 500 passengers. Every passenger has been assigned a seat. All seats are booked. The first passenger boarding the plane misplaces his boarding pass, and so he chooses a random seat. Every other passenger sits in their designated seat, unless it is full, in which case they select a random (presumably unoccupied) seat. What is the probability that you, the last passenger in line, will arrive at your designated seat to find it unoccupied?

It happened to be one of those days when everyone was feeling lazy and uninspired, and nobody had any ideas on how to approach the problem, so I decided to try an experiment in crowd-sourcing. I asked each student to guess the answer, wrote them all down, and calculated the average. Surprisingly, it was very close to the correct answer (which appears at the bottom of the post).

What I found very surprising was that no guesses were particularly close to the correct answer. There were also a couple of idiots who guessed numbers larger than 1. My conclusions were that crowd-sourcing does seem to work--but requires a few idiots among the crowd to work properly.

Which brings me to the market.

In some past articles I discussed the topological equivalence between some common methods of technical analysis and the sort of dynamical analytical techniques I have written about in numerous other postings. The reason that TA can be used at all has to do with the importance of mass psychology in setting share prices, as opposed to economic fundamentals.

An area of stability in a phase space reconstructed from a time series tells us that the system is dominated by negative feedbacks, which tend to stabilize values in the time series within a relatively narrow range of values. A crowd-sourced price for a stock could be such a value--if the majority of market participants believe that $1 is the correct price for shares in a certain company, they will tend to sell when the price is higher and buy when the price is lower.

No matter how long the game plays, the price may remains a crowd-sourced number. It can change in response to fundamentals--for instance, when Atna recently placed the Pinson mine on care-and-maintenance, the crowd decided on a dramatically lower price for a share of Atna.

As in all crowds, there are a number of idiots who influence the price so much that they can temporarily overwhelm the fundamental case, until they either suddenly realize they have made a mistake or run out of money. If the crowd-sourced price is a mean of a population, that value can be exaggerated by a few idiots greatly overestimating (or perhaps underestimating) the real value of a stock or commodity.

For example:

Huldra Silver Inc., one year chart. I plead innocent--I never owned it.

Atna Resources Ltd., one year chart. I was one of the idiots who overvalued this one. 
Both charts from TSX site.

I tend to reject the efficient-market hypothesis. I think the market is almost always wrong, mostly because the majority of market players are missing some information. Sometimes the idiots are too high; sometimes they are too low.

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The solution is 0.5. Explanation.

Update on dengue in Singapore

After peaking in late June, the number of cases has fallen by more than half, to about 340 last week. Total number of cases this year is about 13,500.

Identifying stability in complex systems

No, this is not about Egypt.

I use the term "stability" a lot, as in area of stability. Sometimes I describe the stability of systems projected into phase space as "Lyapunov-" in nature. It may have been awhile since I discussed the criteria for determining whether we observe stability in a system--the Case-Shiller index, for instance.

I've just noticed that I didn't label the axes on the lower figure--but they are the same as in the upper figure.

Why are the yellow blobs, and the large cluster of points at the lower left of the second figure, areas of stability, whereas the small cluster near the top of the lower figure is not?

One clue is whether we see many points that occur close together in time also close in phase space. A lot of points clustered in one area means that whatever measurement we are looking at is not changing much over a long period of time--just what we mean by stability, no?

Areas of stability can only occur in certain places on a time-delay phase space reconstruction.

Same figure as above, but with the "y = x" line plotted. Points along this line would represent points where the value of the Case-Shiller index is the same as it was four years earlier. Areas of stability will straddle the line. The system cannot remain in one spot for long if it is off this line. That doesn't mean that the system has to report to the line. It can meander away from the line for long periods of time (twelve years already)--but while it is doing so, it is not stable.

What about the point where the state crosses the y = x line at the first quarter of 2008?

The first quarter of 2008 would be about where the arrow was. The index was at the same level in early 2004--but we would not say that that was a point of stability because of what the index did during that interval.

Time-derivative phase space reconstructions are topologically equivalent--but perhaps more intuitive, as in this case the system dynamics are reconstructed by plotting a measurement against its rate of change.

In this different projection--time-derivative state space portraits (of the gold-silver ratio)--in which I have plotted the GSR vs its first time derivative, all points of stability must lie along the dr/dt = 0 line. But why doesn't every point on this line represent stability (for example, the point where the curve crosses 0 when GSR = 96)?

You may recall from calculus that apart from critical points of inflection, rates of change also reach zero at local maximum and minimum points. So once again, the fact that a point plots on an area that may represent stability does not mean the system is stable at that point. You need to see a lot of other points, which are close neighbours in time, in the same area.

The Friday OT - Brazil

An old favourite of mine at one of their last performances.

The cancer of Progressivism

There is outrage over the recent revelations that aboriginal children in Canada were subjected to crude experiments (consent kindly granted by the government of Canada) studying the effects of malnutrition. Some children under government care (term used incautiously) had their milk rations cut in half, while required vitamin supplements were withheld. At the same time, dental care was withheld because the deterioration of the gums was a key indicator for malnutrition, and normal dental care would have interfered with the experiment.

A word that is being kicked around a lot this morning is "paternalism". The government had a paternalistic attitude, and handed its wards over to be abused in the name of science.

The real word that should be bandied about is "Progressivism". That is the real cancer--the notion that the government should use its "power" to "improve people's lives". These people, evidently, are too foolish to make their own choices--so let government-trained experts make their choices for them.

For example, in Ghana there are any number of young men like the one depicted below, who live hand-to-mouth, day by day. He has a small plot on which he grows a few yams or plantain, and once in awhile he gets a spot on a fishing boat and works for a share of the catch. Sometimes we hire him as a casual labourer for a few days at a time, where he has helped cut lines, dig pits, pilot our research vessel.

He owns no car, no phone, no TV, no DVD player (he has said he would like to be able to buy such things), but on the whole he is about as happy as anyone else in the village. If he is sick or down on his luck, he has friends and neighbours and relatives to help him. On the whole he has a life that is more real and vital than those lived by the people in suits here who want to turn him into a real-estate broker or investment adviser, so he can commute for an hour each day to work, and develop ulcers and pay taxes like a civilized human being.

The reason that Progressivism is like a cancer is that its practitioners do not stop. Not ever. Because they are doing it for you.