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Re: [Swarm Modelling] Re: The "Art" of Modeling
From: |
Jason Alexander |
Subject: |
Re: [Swarm Modelling] Re: The "Art" of Modeling |
Date: |
Sun, 16 Feb 2003 11:09:38 +0000 |
Breaking the phenomena into the smallest pieces possible has
tremendous advantages. Parsimony is obvious. If we can explain a lot
with a little, we have a great model.
Writing from the point of view of a philosopher of science (don't shoot
me) two questions which I'd like answers to, and which I don't see
discussed in your message, are (1) what you mean by "explain" and (2)
what criteria must be satisfied for an purported explanation to be
considered a "good" or "adequate" explanation.
Although you write that a "great model" can "explain a lot with a
little," this statement still needs further explication since it is
perfectly compatible with both instrumentalism and realism.
Let me think like an old-school philosopher for a minute by supposing
that explanations have to satisfy something like Hempel's
deductive-nomological model of explanation --- so an explanation
consists of a set of general laws and initial conditions from which one
can deduce the thing to be explained. Let's set aside for the moment
the view that agent-based models provide a theory of explanation which
is different in kind from this one because the burden of proof for that
claim lies with the agent-based modeler; agent-based models consist of
general laws (the various bits of code that specify the dynamics of the
model, which may be simple or complex, but which nonetheless constrain
and determine, either deterministically or indeterministically, the
future state of the model) and initial conditions (the parameter space
which we sweep through), so agent-based models satisfy the conditions
of the DN-model of explanation. [Epstein has an article in, I think,
Complexity, which talks about the connection between agent-based models
and "old school" theories of explanation.]
Now, on the DN-model, the only difference between explanation and
prediction is a temporal one. Explanations address phenomena which have
already occurred and predictions address phenomena which have not yet
occurred. In my experience, many alleged explanations of agent-based
models, if they try to target real phenomena at all, only concern
themselves with explanation and not prediction. That is, they try to
show how particular phenomena can be reproduced (deduced) from a
particularly simple model (a small set of laws or code). I'm thinking
of the "Boids" model, among others.
If all that's required of a "good" model is that it be capable of
reproducing phenomena (without any prediction), then we are well on the
road to instrumentalism. All we care about is finding the simplest set
of general laws -- which need not map onto any real causal processes in
the world -- that serve to reproduce the actual phenomena. To give a
crazy example of the kind philosophers are known for, suppose we want
to explain a recurring social phenomena in which everyone paints their
face blue. We can get an amazingly accurate reconstruction of the
phenomena by using a model in which the only general law (bit of code)
looks like
[actionGroup createActionForEach: agentList action:
M(setFaceColorBlue)];
but this need not map onto or model any real causal process at all.
Does this explain? Well, if all we require is that the phenomenon is
reproduced, we'd have to answer "Yes." So we now can explain all
social phenomena to arbitrary degrees of accuracy by following and
extending the above approach! Thus, we'd explain individual behavior
in market interactions by cooking up (by any means necessary) a model
which reproduces it.
Let me address one objection. One might say that, even though we don't
get an explanation of why people paint their face blue by writing
[actionGroup createActionForEach: agentList action:
M(setFaceColorBlue)];
we *do* (in some sense) get an explanation of individual behavior in
market interactions if we can reproduce it. This view seems mysterious
to me - why should reproduction of a complex phenomenon by following
method M produce an explanation when reproduction of a simple
phenomenon by following method M does not? (To foreshadow, I think the
reason why one might think this is that, for a complex phenomenon, the
mere fact that you can reproduce it [in a model] means you've
identified, in some sense, the underlying causal laws, mechanisms, or
processes which really did serve to produce that phenomenon. This
"complexity implies convergence to the truth" view requires an
argument.)
Anyway, I take it that the above account of why people paint their face
blue *doesn't* provide an explanation because it doesn't hook up the
general laws (bits of code) with actual laws, mechanisms, or processes.
Good models and simulations explain, therefore, insofar as they
identify general laws and mechanisms (perhaps even to a first
approximation) that really do exist. Given this, a good model should
be able to predict (at least in sufficiently similar circumstances, for
sufficiently short periods of time) future states of the system, at
least to certain degrees of accuracy.
When you write
A parsimonious model may only explain some portion of the phenomena of
interest, but my experience is that in the process of cutting out
everything not absolutely essential, what remains is essential in the
sense that it is the essence of the problem thus important for many
other related problems.
although I agree that "cutting out everything not absolutely essential"
implies that "what remains is essential," I don't see why a successful
parsimonious model ("successful" here meaning "reproduces the
phenomenon in question" and "parsimonious" meaning "minimal or
sufficiently small set of general laws") will identify "the essence of
the problem" in the sense of identifying even one general law,
mechanism, or process that maps onto the real world. If successful
parsimonious models generally *do* this, I suspect it's an artifact of
a semi-deliberate process of selection on the modeler's behalf in
setting up the model. In constructing the model, you've already ruled
out from consideration models whose general laws don't fit into some
underlying theoretical framework.
With the lessons on simplicity firmly in mind, I attended a talk by a
weather scholar at UCLA. He described the hundreds of differential
equations in his program and how dramatic the improvements over former
attempts have been. This made me incredibly nervous. Hundreds of
differential equations seemed to lead right into the problems of
atheoretic uninterpretability that Achen warns about. In response,
our weather expert said "our aim with this model is to save people's
lives and get them out of the way of floods and disaster, not to
'understand' tornados."
The weather scholar seems to be advocating an instrumentalist view over
a realist view. If the ultimate goal is saving lives, then one will use
any "black box" model which offers the best prediction of the future,
regardless of whether it helps us "understand" tornados (where
"understanding" a tornado means that we have an accurate description of
the general laws, mechanisms, and processes which serve to produce
tornados).
But we then face the standard problem of instrumentalism: it seems that
the only justification we can give for why a "black box" model should
offer accurate predictions is that it employs, in some way, a
description of the general laws, mechanisms, and processes which are
really at work in the world. If so, then the best way in which to cook
up the "black box" model is to just go out and try to identify the
general laws, mechanisms, and processes that really exist, i.e., we get
a call for realism.
How much understanding do we need? How much predictive power do we
need? I think that a good modeling process looks back and forth from
one goal to the other because advances in one area facilitate advances
in the other.
I'm inclined to agree with this, provided that by a "good modeling
process" you mean one that seeks to provide predictions of future
phenomena and not reproductions of previously observed phenomena. As
the blue-faced people example shows, the simplest ways of reproducing
past observed phenomena may very well employ bogus laws that just
redescribe what happened in a different language. Successful prediction
at least gives us some reason to think that the general laws we've
identified (incorporated into the model) map onto the world, at least
to some degree.
If there isn't the requirement that a "good model" hook up to the world
by employing correct general laws, then I see no reason for thinking
that "advances" in reproducing phenomenon should lead to advances in
prediction.
A final thought is the importance of ambitions. ...
If I was writing a model with a prisoner's dilemma at the core, I
would parameterize it so that I could easily transform it into another
game by just changing the payoff structure. I would also make all the
agents have their own payoff matrices so that I could change to
heterogeneous payoffs once I understood how homogeneity worked. Thus,
in a later version, I might think that we are playing a battle of the
sexes while you think we are in a prisoner's dilemma.
I agree with this. Although it is important to keep ambitions in check
otherwise everything becomes parameterized and the model spirals out of
control. (I.e., agents have to interact according to some dynamic.
But why *that* dynamic? Presumably that could be parameterized as well
but, in doing so, you are well under way to recreating a
general-purpose agent-based modeling system within your particular
agent-based model.)
Cheers,
Jason
--
Dr. J. McKenzie Alexander
Department of Philosophy, Logic and Scientific Method
London School of Economics and Political Science
Houghton Street, London WC2A 2AE