Re: [Swarm Modelling] Re: The "Art" of Modeling

[Jason Alexander]

> 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