The Benefits of Being Unrealistic

By Adam Elkus

As a PhD student in computational social science at George Mason University, I have biases that are understandable. I find that traditional social science methodologies downplay complexity, interaction, path dependence, randomness, network effects, emergence, nested social relations, multiple equilibria, cycles, and heterogeneity. They ignore bounded rationality and cognitive realism. The list goes on. However, I’m also going to speak up here about the benefits of being “unrealistic” — and why social science modelers ought to maintain a diverse toolkit.

The phrase “all models are wrong” and “models are maps” (not the territory) come to mind, but we can do better than that. Ultimately, what using a model as a map implies is that we are using the model as a stylized representation of reality. I’m reminded here about the controversy over Michael Chwe’s recent book on Jane Austen and game theory — Jane Austen didn’t intend to have her characters behave like John Nash or R.A. Fisher. It’s convenient for us to represent Jane Austen books as games, much in the same way its convenient to represent Viking societies with graph theory. It’s an imposition of our own, and we can at least hope that we don’t do too much violence to what we’re trying to represent. Often times, however, we do exactly that:

In settings like biology, medicine — or even more ambitious: social sciences — there is no underlying analytic theory. Although we might call some parameters of the model by the same name as some things we measure experimentally, the theory we use to inform our measurement is not related to the theory used to generate our model. These sort of models are heuristics. This means that when a heuristic model is wrong, we don’t really know why it is wrong, how to quantify how wrong it will be (apart from trial and error), or how to fix it. Further, even when heuristic models do predict accurate outcomes, we have no reason to believe that the hidden mechanism of the model is reflective of reality. Usually the model has so many free-parameters, often in the form of researcher degrees of freedom, that it could have been an accidental fit. This is often a concern in ecological modeling where we have to worry about overdetermination.

So we can dispense with the idea that a model that makes more realistic assumptions in some areas we know about (cognition, rationality, social interaction, heterogeneity, feedback) is necessarily going to be more useful to us than an older model that makes less realistic assumptions in those same areas (such as representing model agents as aggregates in system dynamics). We are usually making other unrealistic assumptions in areas of equal importance merely by creating a model in the first place. There is nothing inherent in iterating the Prisoner’s Dilemma and adding genetic algorithms with tournament-style selection, for example, that necessarily makes it more realistic than a traditional one-shot PD.

It’s obvious that the question you want to answer and the kind of answer you want to get should dictate choice of methods. But it’s also less obvious how this should impact choice of how fine-grained a model you need. Such a distinction often leads to the charge of “___ is unrealistic!” (usually referring to some kind of classical game theory or choice-theoretic assumptions) followed by trotting out of the “models are maps” and “all models are wrong” cliches. While true in a banal sense, defenders of more “unrealistic” assumptions about older modeling techniques surely can make better arguments.

Consider artificial intelligence and formal computer science as disciplines. AI and algorithms have been designed to perform tasks traditionally characteristic of humans — but in ways humans obviously do not solve problems. As Scott Page points out, humans use heuristics to deal with computational problems that scale poorly when analyzed by computers or find “good enough” solutions. But understanding that a problem’s worst-case computational complexity is so daunting in the first place is useful — without it we might not understand why heuristics are being employed or why they work.

This holds true beyond the worlds of AI and analysis of algorithms. We might conclude that a true Weberian monopoly of force is logically impossible — when we say “the state” has a monopoly on force, we ignore the fact that this “monopoly” could be eroded easily if enough elites with control over the means of violence decide it is no longer in their interest to contribute to it. The “state” is, after all, an aggregation of those elites. And in many parts of the world, achieving a preponderance of force (as opposed to a monopoly) is more realistic and historically accurate. But the “ideal type” is useful for modeling (verbally) what a state with true license over lawful organized violence resembles — and measuring how far the empirical world falls from ideal case still is theoretically meaningful.

Second, as a behavioral economics textbook pointed out, merely including more “behavioral” assumptions does not necessarily ensure that an behavioral economics model is going to outperform a standard economic model. The same holds for many other related disciplines. Realistic insights about individual cognition and decision may not scale up well to social aggregates — norms, for example, are far more situational in character for the average individual than they are in society as a whole.

Finally, any subject of interest is bound to be multi-layered. We are not likely to find a way to effectively link all of those layers without either making our model either too complex to be used and properly communicated or too simplistic to be truly comprehensive.

In my own field of strategic theory, military theorists are beginning to understand that there are multiple models of strategic reasoning — because the strategist’s task itself is heterogeneous. Figuring out how to get a large mass of men, machines, and supplies across the Atlantic in time to resist a Soviet invasion is strategy. Using mathematical programming to optimize military production is strategy. Game-theoretic models of coercion and compellence are also strategy. But so are the difficult tasks of managing coalitions, sense making and problem framing in ambiguous situations, and intersubjective learning about the enemy and civilian population.

Historians that can examine a given campaign or operation in granular detail get to weave all of these together into a coherent narrative. But when we begin to talk more generally, we start to face the problem of representation. In my time as an MA student at the Georgetown Security Studies program, I took a class from Kenneth Pollack on Military Analysis. We studied World War II’s European Theater of Operation (ETO), a broad area that concerns campaigns and operations in Europe, Northern Africa, the British Islands, Russia, the Atlantic, and the Strategic Bomber Offensive.

Our task in making an counterfactual analysis of a campaign or operation was to weave together a number of levels and contexts. One had to take into account the role of coalition pressures, industrial and economic supply and production, military training and organization, terrain, feedback effects from other campaigns and operations, and leadership styles to do justice to the topic. But feeding all of that into a model is a recipe for overfitting and poor out of sample predictive value.

Parsimony may be a virtue, but it is also a cruel mistress. All generalization — including qualitative case work — involves parsimony. What “models as maps” rhetoric misses is that the social scientist is actually carrying a suitcase of maps. Instead of one big and coarse map he or she is using to find their way around a metro, they have a dozen maps of varying size, detail, and specification they have to pull out each time they change subway lines. Sometimes one map being more “wrong” will be the key to another being more “right.”

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8 thoughts on “The Benefits of Being Unrealistic”

  1. Good post.

    The only way I would expand this discussion is to consider the social forces that push researchers to make bad models. One of the curses of computing is how easy computational modeling becomes, in particular, how easy it is to bloat a model. If you take an existing model, it is simple to add a feature ” that makes more realistic assumptions in some areas we know about (cognition, rationality, social interaction, heterogeneity, feedback)”; so most people do this. It is much more difficult to analyze the model, and dig down to the fundamental assumptions that are being made, enunciate, and question them. I feel it is important to encourage this.

    I really like your suitcase of maps analogy, and think it is important. However, it is suspetible to the bad modeling I describe above. People justify a new model as “well, this is just another map, you don’t have to use it, but it’s in our suitcase now: Eventually we can barely drag our luggage, and forget to look at the maps we already had more closely, to understand the art of map-making itself.

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  2. Great post as usual, Adam.

    For a long time my response to these types of discussions is to say that we need to spend more time considering the assumptions of our models and really teasing out when and where those assumptions are non-trivial. I have a post planned for the next few days that relates to this with regards to the developing emerging markets crisis, but the point is more general. I think that Phil Arena is frequently correct that simplifying (i.e. “unrealistic”) assumptions frequently are trivial, but there will be some cases where they won’t be. Knowing the difference is difficult but important.

    But even more than that, in my opinion, is the need to do more with models than report equilibrium outcomes or central tendencies with their levels of confidence. That is, frequently we are interested in cases where all other variables will *not* be held at their mean. Where ceteris does not equal paribus, to once again employ a phrase I’ve used commonly. This is pretty easy to do but we frequently fail to do it. (I am also guilty of this at times. I hope to get better at it over time.)

    Anyway: great post.

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  3. Artem,

    I completely agree — though this was long enough of a post as is. I think that first formalizing the model *and then* making it computational is important.

    Kindred,

    Also agree.

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  4. Expanding:

    I take the point about suitcases — and sometimes I worry about a combinatorial explosion in models that will confuse everyone. Unfortunately, I’m not necessarily sure how this can really be avoided in social science. Ultimately even a formal representation is just extracting something of interest from a real-world referent system, and our intuition in whether or not we’ve captured the most essential part of the referent system is not exactly that great. We can calibrate it to existing data, parameterize it, even use automated algorithmic tools to help us design it, dock it with other model styles, etc……

    But the problem really is that there are very few analytic baselines (as Artem implies) in social science. So this introduces something of a tension when it comes to verification and validation. On one hand, making a model more realistic would seem to be an natural thing to do — do away with ceteris paribus, make them boundedly rational, etc. Unfortunately this may not help (we are missing something else of interest) or it might for reasons we barely understand make the problem worse. And the more complicated the model gets, the more difficult it is to validate.

    We could try to formalize it more, but I’m not sure how this avoids the issue of the referent system again. I come from a historical-qualitative background, so I’m very attuned to the issue of levels of representation and which kinds of assemblages seem to be privileged. Social scientists have disliked making reference to the psychological states of actors when explaining things — but if you are a military historian surely the personality of the commander in question enters into any proper description of a campaign.

    Ultimately we can’t really avoid several facts (1) the everyday reality of contingency (2) the problem of self-reference embedded in much of our understanding of social science — see the legitimacy issue (3) the fact that the process of model formulation — not the actual scientific value of the model itself — is very under explored.

    I like Artem’s work because he looks at formal properties that aren’t usually thought of when modeling (computational complexity of equilibria) and his work comes closest to the idea of a constructive proof that my PhD program values (although we call it “existence proof”). Perhaps those sort of meta-issues are probably the way forward at this point.

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    1. I take the point about suitcases — and sometimes I worry about a combinatorial explosion in models that will confuse everyone.

      This is where cstheory can really help! As I quoted from Scott Aaronson before, the beauty of mathematics is that it lets us classify the models and understand the minimal assumptions and what they do. You can see this at work in computer science all the time, for instance there are some many different models of computation and yet we know they are all equivalent, there are thousands (unreality, an infinite number) of NP-complete problems but we know all of them are effectively equivalent, and so on.

      The social sciences (and biology) really lack this: people make so many models that are formally equivalent but superficially different, but never realize it. The best way to tame this is to understand what makes models the same and figure out the ‘minimal features’, but this is best done by taking apart existing models instead of making ‘bigger’ ones.

      Unfortunately this may not help (we are missing something else of interest) or it might for reasons we barely understand make the problem worse. And the more complicated the model gets, the more difficult it is to validate.

      Actually, it can be even worse than this! A lot of people when they introduce a new feature X into the model A (call this improved model A’) and then have it match data that model A couldn’t before, assume that this has provided validation that X is reflecting or accurately describing reality, after all “it’s the only change we made”. This is completely unjustified for complex systems. In the real world, it could have been countless other mechanisms (or more likely their interaction) that caused the effect, and the more realistic X you introduced actually doesn’t reflect the features of the actual thing you were trying to introduce but by accident has the same effect as some other features you were still not considering. This can lead false confidence in X as an accurate depiction of some part of reality. Oh, overdetermination, how you haunt us!

      I see this a lot in the literature when people introduce assumptions about minimal cognition, for example.

      I like Artem’s work because he looks at formal properties that aren’t usually thought of when modeling (computational complexity of equilibria) and his work comes closest to the idea of a constructive proof that my PhD program values (although we call it “existence proof”).

      Thank you! Where can I read more about this idea that your PhD program values? Unless you mean it in the mathematical sense of the word.

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  5. I think when people charge with “unrealism,” they ultimately are saying “your assumptions don’t comport with my priors.” Some of these people have tried to claim that they don’t reduce complexity at all when thinking about the world, and they’re lying to themselves. Metaphors and analogies are models, and that’s what verbal theorists use all day to achieve parsimony.

    On this: “norms, for example, are far more situational in character for the average individual than they are in society as a whole.”

    That’s sharp. I have an idea why. Think of the master statuses from sociology: race, class, gender, nationality. These are all variously supposed to accrue ideal-typical norms that attend to those (huge) categories. Now imagine that each individual is made up of a vector of those norms, and many others that attend only to the local cluster of the much larger network they’re a part of.

    I think this view may start to illuminate why economics has worked so well to explain phenomenon — because it’s always taken for granted a potentially infinite ranking of choices, rather than having to take norm-guided or heuristic behavior for granted and focus on particular manifestations of norms (like racial biases).

    It seems to me like there *is* a general theory, micro-to-macro, of how norms work, but we just lack a sense of how any individual norm on a particular person’s “heuristic vector” obtains greater or less valence at any one time.

    Taking norms for granted does not imply that the only way to do social science is to look at tiny little case study situations and ethnography, or that we can only talk about huge-group norms that a lot of people share, like race or national identity. Indeed, I would suggest that the larger is the set of people who share a particular norm in their vector of heuristics, the more *poorly* that heuristic will correlate to other behaviors, because it is being confounded by such an enormous variation of other heuristics across that group of people. This jibes with most people’s intuition that X doesn’t C “just because he’s black” or “just because he’s American.”

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  6. “It seems to me like there *is* a general theory, micro-to-macro, of how norms work, but we just lack a sense of how any individual norm on a particular person’s “heuristic vector” obtains greater or less valence at any one time.”

    Graham, that’s the main problem. One of the main reasons I find constructivism and liberalism in IR theory very vacuous is that they posit all kinds of norm adoption, diffusion, etc but actual empirical evidence of norm transfer that would verify the theory is often fuzzy to nonexistent.

    Ultimately the implications of a “heuristic vector” is that randomness and contingency Is A Thing, and social science (paraphrasing an article by Krakaeur in Cliodynamics) assumes high regularity and low randomness.

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  7. Artem,

    Just saw your comment —

    On CS theory — I agree, that’s why I like your blogs. That said, what you are doing is very different from what this entry talks about. In social science, aside from things like Arrow’s Impossibility Theorem, most social science modeling has this cycle:

    (1) Observe something of interest in the world

    (2) Create a conceptual model

    (3) Formalize it in mathematics and/or code

    (4) Test until it satisfies some discipline-specific standard of internal and/or external validity

    I am not sure that we can deal with the basic problem that steps 1-2 are really problematic. As Weber argued in his lectures on methodology and objectivity, 1-2 are the points at which our own subjective values and interests have the most potential to wreck us.

    I think that meta-analysis of models (not statistical meta-analysis, but more of the sort of Scott Aaronson tangle-reducing you reference) is a good way to try to reduce our confusion — and my own interest in using computation to think about strategy comes from that instinct.

    In terms of your question about my program, I’ll email you.

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