RE: [Swarm-Modelling] foundation of ABMs

[Christopher J. Mackie]

Darren; I have no quarrel with anything that promotes humility and courage, but 
are relativism and objectivism the best two touchpoints for your argument? I'm 
not clear about how they're the kind of indirect motivation to improve 
empirical adequacy that I understand you to claim them to be, or (pace Kant) 
that contemplating the noumena is sufficient to keep you on course between 
Scylla and Charybdis.  How is it different from contemplating your navel, or 
the face of God?

As (at least) one alternative, what about my favorite philosophy of science, 
van Fraasen's "constructive empiricism"?  I see that as much closer in spirit 
to the perspective you attribute to McKelvey than is Kant--and you don't have 
to postulate unseeable, unknowable thingies to get there. Start by 
acknowledging inescapable subjectivity, don't pretend to rely on what you can't 
possibly know, and strive always for higher levels of empirical adequacy: that 
sounds like 'humility and courage', and it also sounds like 'model-centered 
science'.  


Pablo; I may want to argue with Darren a bit regarding how to understand and 
evaluate what we're about, but fundamentally I'm in agreement with him and some 
of the other views expressed here: ABMs may be less 'mathematically rigorous', 
but mathematical rigor (especially in a narrow interpretation) is not the only 
or necessarily even the best evaluative standard to apply to the needs of 
*empirical* modeling.  One point worth adding is that, in fact, the difference 
between the two approaches is not as stark as it is usually made out to be: 
especially in social modeling, analytical solutions are often obtained by the 
employment of assumptions that are difficult or impossible to map well to 
specific empirical situations, so the higher degree of 'rigor' may be much more 
apparent than real. As Darren notes, formal proofs are small consolation when 
those assumptions turn out to have been poorly mapped.

Put another way, analytical solutions are great where you can find them, but 
the inability to wrestle a problem into a closed-form solution should not 
preclude serious, systematic investigation.  As one might expect from the fact 
that I subscribe to this list, I'll take an impossible-to-prove but usefully 
detailed and robustly analyzed ABM over an elegantly solved but 
too-assumption-constrained-to-map-to-reality mathematical theory almost every 
time. 

--Chris


-----Original Message-----
From: address@hidden [mailto:address@hidden On Behalf Of Darren Schreiber
Sent: Tuesday, April 05, 2005 6:04 PM
To: Swarm Modelling
Subject: Re: [Swarm-Modelling] foundation of ABMs


The value added is humility and courage.

I postulate (along with Kant) that there is a world as it actually is and that 
the phenomena have some correspondence with the nourmena.  
That I cannot observe the noumena directly, should make me humble in the face 
of the unknown consequences of the action or inaction that I choose.  That I 
cannot observe it directly should also encourage me to constantly be pursuing 
new ways of evaluating my theories, models, and observations (phenomena) of the 
world so that the choices I make are the best that I can in the circumstance.

I see this as a way through the mire of objectivism and relativism.  A "model 
centered science", to borrow a phrase from Bill McKelvey at UCLA, posits that 
we are forced to make decisions based upon our models of the world.  We don't 
assume that our models are "true" 
representations of the world or that they will ever reach that kind of 
perfection.  But, we do strive to make them good enough for the purposes we are 
evaluating them for.  On the other hand, we recognize that we do have the 
capacity to develop more and more useful models and that we can use those to 
guide our decision making.  In my view, objectivism fosters arrogance and 
relativism fosters inaction.  With a process of constantly re-evaluating our 
models of the world, we can humbly and courageously make choices about how to 
change our world.

        Darren



On Apr 5, 2005, at 5:33 PM, Christopher J. Mackie wrote:

> Hi Darren; What's the value-added of 'noumena' in your scheme?  I see 
> it in your ontology but not in your typology, and if all we can see is 
> all we can see, what role can/do noumena play?
>
> --Chris
>
> -----Original Message-----
> From: address@hidden [mailto:address@hidden
> On Behalf Of Darren Schreiber
> Sent: Tuesday, April 05, 2005 4:11 PM
> To: Swarm Modelling
> Subject: Re: [Swarm-Modelling] foundation of ABMs
>
>
> You raise some interesting questions that go to the heart of the 
> epistemological challeng with ABMs.
>
> Here is the very quick version of my thinking.
>
> 1)  There are lots of different kinds of ways to evaluate a model.  (A 
> paper that I read from the engineering literature on validation 
> catalogues 23, but there are many more, I'm sure).
>
> 2)  There are many different reasons that you want to evaluate a model.
>
> 3)  Items 1 & 2 are, or at least, should be, highly inter-related.  
> You should choose the methods (note that I use the plural, because you 
> probably want multiple methods) for evaluation (1) based upon your 
> reasons for evaluating the model (2).
>
> "Convergence to some solution" does not make sense for many of the 
> problems that I am interested in as a political scientist.  It looks 
> like progress is being made in Iraq right now, but I wouldn't contend 
> that this real world phenomena will "converge" or that there is "some 
> solution."  The social world, just isn't like that.  And, there are 
> deep problems with an ontology that constructs the world as having 
> point solutions, equilibrium, etc.  For instance, economics wanders 
> into moral quagmires when it suggests that everything will reach 
> equilibrium.  Empirically, there are reasons to believe that this is 
> not true.  Normatively, lots of people may suffer while we wait for a 
> social system to converge.
>
> I saw an interesting talk on this by Brian Skryms recently on some 
> work he's done with Robin Pemantle (a mathematician friend of mine).
> They gave an example of the stag hunt problem that can be demonstrated 
> to converge mathematically.  However, in extremely long time periods 
> (millions and millions of iterations) the problem doesn't converge.
>
> So what kind of conclusions would we draw from a mathematical 
> convergence and a lack of computational convergence?  For problems 
> where people might suffer and die due to policy choices that are made 
> based upon our models, this actually matters a lot.
>
> I have a paper that I would be glad to send out to those interested 
> that argues for a four part ontology (theory - model - phenomena -
> noumena) and then takes this ontology to organize the various methods 
> we might use for evaluating a model.
>
> The Ontology
> Theory -- the ideas that we have in our heads about how the world 
> works Models -- a specification of the ideas we have in a tangible 
> form (e.g a mathematical model, a computer simulation, a narrative in 
> a book chapter, etc.) Phenomena -- the observations we make of the 
> world Noumena -- the world as it truly is
>
> Typology of Model Evaluation
> Theory - Model tests:  face validity, narrative validity, Turing 
> tests, surprise tests, etc.
> Model - Model tests:  docking, mathematical convergence, analytic 
> proofs, etc.
> Model - Phenomena tests:  historic data validity, predictive data 
> validity, out of sample forecasts, experimental validity, event 
> validity Theory - Model - Phenomena tests (aka robustness):  extreme 
> bounds analysis, global sensitivity analysis, automated non-linear 
> testing system, validating substructures, degenerate tests, traces, 
> animation tests
>
> "Rigor" means very different things to different people.  I dare you 
> to fly on a plane that has only been evaluated with analytic proof.
> Or, to take a drug that only passes the face validity test.  Or, to 
> forecast your return on investment using only historic data.
>
> I agree that we have a big epistemological problem in agent-based 
> modeling.  The good news is that we have lots of many interesting ways 
> of solving it.  The even better news is that serious thinking about 
> the big epistemological problems in ABMs should cause other fields to 
> re-evaluate the often ad-hoc standards used to define rigor in their 
> disciplines.  And the great news is that I think this re-evaluation 
> promises a truly "new kind of science" if we seriously consider 
> integrating empirical and theoretic concerns with the normative 
> motivations that can inform our research.
>
>       Darren
>
>
>
> On Apr 5, 2005, at 2:07 PM, Pablo Gomez Mourelo wrote:
>
>>
>> Dear all:
>>
>> I am an engineer very  interested in agent-based modelling. I have a 
>> question for you all, related to justification/foundation of ABMs.
>> I have already read some literature and it seems to me that a 
>> justification of agent-based modelling has not been achieved (Volker 
>> Grimm).
>> One of the problems of AB-modelling is that randomness is nearly 
>> always included in our simulations, so different executions turn into 
>> different outcomes.
>> In comparison to mathematical models , it seems to me very difficult 
>> to develop a general theory (foundation) of agent based modelling. 
>> HOw do we know an ABM converges to some solution? How can we describe 
>> stability of an ABM?  Many modellers feel satisfied with the 
>> graphical output, but mathematicians always complain about the lack 
>> or rigour beneath the simulation.
>>
>>
>> My main question is: does anyone know of any paper/book giving a 
>> mathematical foundation of ABMs?
>>
>> All the best,
>>
>> --
>> +=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=
>> Pablo Gómez Mourelo
>> Departamento de Matemática Aplicada
>> ETSI Industriales
>> C/ Jose Gutierrez Abascal, 2
>> 28006 MADRID
>> SPAIN
>> Universidad Politécnica de Madrid
>> Phone: +34 91 336 3105
>> Fax:   +34 91 336 3001
>> +=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=
>>
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