[From Bruce Abbott (2008.11.0755 EDT)]
This week’s run on the stock market is an excellent
example of how millions of perfectly good negative feedback loops (a.k.a.
control systems) can add up to one nasty aggregate positive feedback loop. Investors
in the stock market presumably have a reference for maintaining a positive
income stream and investing in stocks is one action they use to achieve this,
buying them when the market is going up and selling off when the market is
declining. (I’m oversimplifying here, but I don’t want to
make the exposition too complicated.) Whether the market is advancing or
retreating depends on the aggregate behavior of millions of investors. If
the market is advancing, individual investors act to increase their income
streams by purchasing more stocks; when the market is declining, they may sell off stocks in order to reduce
losses. (Because the market is subject to short-term fluctuation, their
portfolio-value input functions tend to ignore short-term losses unless they
become large or the rate of loss gets high. Also, the loop gain varies
among investors; those with relatively low loop gains will not begin to sell
until the error becomes relatively large.) As the market average
declines (and especially as the rate of loss accelerates), more and more
investors sell off, causing further and faster declines in the market average,
resulting in more investors selling off. When, as in this case, a change
in a variable feeds back to further amplify the change (rather than opposing the
change), we have positive feedback. So millions of perfectly good
negative feedback control systems, acting to oppose the effect of declining
stock values on their incomes, create an aggregate positive feedback loop that
produces losses for almost everyone. It’s a nice example of the
phenomenon that has been termed “the tragedy of the commons,” which
refers historically to the overgrazing and resulting destruction of community
pastures (the commons) that resulted when it was to each individual farmer’s
advantage to graze his or her animals on the commons before doing so on the
farmer’s own land. What was good in the short run for each farmer individually
was bad in the long run for them all.
Bruce A.
[From Rick Marken (2008.10.11.1010)]
Bruce Abbott (2008.11.0755 EDT)--
This week's run on the stock market is an excellent example of how millions
of perfectly good negative feedback loops (a.k.a. control systems) can add
up to one nasty aggregate positive feedback loop.
I'm not sure that stock traders are really in negative feedback loops
with respect to the variables they are trying to control. I think they
in conflict. Each wants to buy low and sell high. I agree that one
thing all are controlling is their income and/or the first derivative
thereof. But I don't think any trader, individually, can control their
income stream in the way one controls a variable in the physical
world.
What one does to affect one's own income is a disturbance to what
another does to control his or her income. My guess is that this is
always a fairly unstable situation, always on the verge of a runaway.
I think we need a simulation to see how variables affect it. But the
instability of such market's has already been noted; that's why they
have been regulated -- to stop the runaway conditions. I believe that
is why markets are never really "free".
I think it would be worthwhile to try to model a stock market; I don't
think you would need that many traders to show how it can go south
(or, for that matter, "bubble"). I think Bill already has the start of
such a model (a model of traders in a market). My only point here is
to suggest that traders in a market, though they are control systems,
are not in a true negative feedback relationship with respect to some
of the variables they are trying to control because they are in
conflict with other control systems (who are, therefore, also not in a
true negative feedback relationship with respect to the variables they
control).
Best
Rick
···
Investors in the stock
market presumably have a reference for maintaining a positive income stream
and investing in stocks is one action they use to achieve this, buying them
when the market is going up and selling off when the market is declining.
(I'm oversimplifying here, but I don't want to make the exposition too
complicated.) Whether the market is advancing or retreating depends on the
aggregate behavior of millions of investors. If the market is advancing,
individual investors act to increase their income streams by purchasing more
stocks; when the market is declining, they may sell off stocks in order to
reduce losses. (Because the market is subject to short-term fluctuation,
their portfolio-value input functions tend to ignore short-term losses
unless they become large or the rate of loss gets high. Also, the loop gain
varies among investors; those with relatively low loop gains will not begin
to sell until the error becomes relatively large.) As the market average
declines (and especially as the rate of loss accelerates), more and more
investors sell off, causing further and faster declines in the market
average, resulting in more investors selling off. When, as in this case, a
change in a variable feeds back to further amplify the change (rather than
opposing the change), we have positive feedback. So millions of perfectly
good negative feedback control systems, acting to oppose the effect of
declining stock values on their incomes, create an aggregate positive
feedback loop that produces losses for almost everyone. It's a nice example
of the phenomenon that has been termed "the tragedy of the commons," which
refers historically to the overgrazing and resulting destruction of
community pastures (the commons) that resulted when it was to each
individual farmer's advantage to graze his or her animals on the commons
before doing so on the farmer's own land. What was good in the short run
for each farmer individually was bad in the long run for them all.
Bruce A.
--
Richard S. Marken PhD
rsmarken@gmail.com
[From Bruce Abbott (2008.11.1425 EDT)]
Rick Marken (2008.10.11.1010)--
I think it would be worthwhile to try to model a stock market; I don't
think you would need that many traders to show how it can go south
(or, for that matter, "bubble"). I think Bill already has the start of
such a model (a model of traders in a market). My only point here is
to suggest that traders in a market, though they are control systems,
are not in a true negative feedback relationship with respect to some
of the variables they are trying to control because they are in
conflict with other control systems (who are, therefore, also not in a
true negative feedback relationship with respect to the variables they
control).
I agree that constructing a model is the way to test these ideas, but at
present I have too many things on my plate to get involved in doing that in
any serious way. But I'd still like you to clarify what you mean that
investors are "not in a true negative feedback relationship with respect to
some of the variables they are trying to control." Specific examples would
be helpful.
When writing my previous post I found it somewhat difficult to state what
investors might be controlling without making the exposition overly complex.
"Net worth" might be one, but then people are willing to expend their cash
to purchase certain goods and services. Of course, spending money to
satisfy some goals acts as a disturbance to a system that is attempting to
maintain or achieve some reference level of net worth. But establishing and
maintaining a positive income stream can be achieved even if one is also
expending money for goods and services, so I settled on that for my example.
That's incomplete at best, and certainly even a more complex model for one
person's system organization would likely not be correct for other
individuals. Even worse (for model building) is that people will be acting
on their perceptions and these perceptions often are not in sync with a
rational analysis, as when one sells after the market suffers huge losses
because of fear that even worse losses will follow (the aim being to
preserve what little is left). This action locks in those losses, whereas
the greatest probability is that the market will eventually recover, and
with it the value of one's stock portfolio (at least if it's sufficiently
diversified).
Bruce
[From Rick Marken (2008.10.11.1210)]
Bruce Abbott (2008.11.1425 EDT)]
I agree that constructing a model is the way to test these ideas, but at
present I have too many things on my plate to get involved in doing that in
any serious way.
I'll give it a try later today but but I bet Bill posts something
sooner. He already has a model of buyers and sellers interacting.
But I'd still like you to clarify what you mean that
investors are "not in a true negative feedback relationship with respect to
some of the variables they are trying to control." Specific examples would
be helpful.
I just meant that they are in a conflict where the variable in
conflict is money. I want to buy X for very little and sell it back
for a lot. So I am in conflict with other buyers (to pay as little as
possible but still more than they do for X) and with other sellers (to
change as much as possible for X but not so much that it won't be
sold). A model would have to work out these relationships clearly but
I think what you would come down to is the fact that traders are in a
conflict with each other where what one does to get more money for
himself decreases what the other gets, and vice versa. This is just
like a tug of war, where the position of the flag corresponds to the
money in the trading situation. It's not a negative feedback control
situation because when I act to bring the flag towards me (working
against the disturbance to the flag that is pulling it the other way)
I actually increase the disturbance. So my efforts to reduce my own
error result in increases in the environmental influences that create
that error. So the feedback loop is not really negative.
I can't wait to hear what Bill says about this. These are my
non-quantitative ideas but I believe that I did work out a
quantitative analysis of conflict that shows that, when there is
conflict, the feedback loop is no longer a control (negative feedback)
loop.
Best
Rick
···
When writing my previous post I found it somewhat difficult to state what
investors might be controlling without making the exposition overly complex.
"Net worth" might be one, but then people are willing to expend their cash
to purchase certain goods and services. Of course, spending money to
satisfy some goals acts as a disturbance to a system that is attempting to
maintain or achieve some reference level of net worth. But establishing and
maintaining a positive income stream can be achieved even if one is also
expending money for goods and services, so I settled on that for my example.
That's incomplete at best, and certainly even a more complex model for one
person's system organization would likely not be correct for other
individuals. Even worse (for model building) is that people will be acting
on their perceptions and these perceptions often are not in sync with a
rational analysis, as when one sells after the market suffers huge losses
because of fear that even worse losses will follow (the aim being to
preserve what little is left). This action locks in those losses, whereas
the greatest probability is that the market will eventually recover, and
with it the value of one's stock portfolio (at least if it's sufficiently
diversified).
Bruce
--
Richard S. Marken PhD
rsmarken@gmail.com
[From Bill Powers (2008.10.11.1344 MDT)]
Rick Marken (2008.10.11.1210) --
I can't wait to hear what Bill says about this. These are my
non-quantitative ideas but I believe that I did work out a
quantitative analysis of conflict that shows that, when there is
conflict, the feedback loop is no longer a control (negative feedback)
loop.
You and Bruce A. are talking about the same thing. If your action intended to control your own variable calls forth a disturbance (from someone else) that is larger than the effect of your action, the net effect of your action is to increase the error instead of decreasing it. So the feedback becomes positive; it's as if you've reversed the sign in the environmental feedback function.
Best,
Bill P.