From realism to interfaces and rationality in evolutionary games
November 1, 2014 12 Comments
As I was preparing some reading assignments, I realized that I don’t have a single resource available that covers the main ideas of the interface theory of perception, objective versus subjective rationality, and their relationship to evolutionary game theory. I wanted to correct this oversight and use it as opportunity to comment on the philosophy of mind. In this post I will quickly introduce naive realism, critical realism, and the interface theory of perception and sketch how we can use evolutionary game theory to study them. The interface theory of perception will also give me an opportunity to touch on the difference between subjective and objective rationality. Unfortunately, I am trying to keep this entry short, so we will only skim the surface and I invite you to click links aggressively and follow the references papers if something catches your attention — this annotated list of links might be of particular interest for further exploration.
So let’s start with naive realism, this is the stance that the world is exactly as we perceive it; we can’t be wrong. This doesn’t mean just that we can’t be wrong about understanding our sense-perceptions but that these sense-perceptions also can’t be wrong about the external world. As you can guess from the naive predicate, this isn’t a stance many hold seriously. Instead, the orthodoxy among vision scientists is critical realism (Brunswih, 1956; Marr, 1982; Palmer, 1999) — perception resembles reality, but doesn’t capture all of it. To borrow an image from Kevin Song, if naive realism is a perfect photograph then critical realism is a blurry photograph. Or, to use a metaphor more familiar to modelers instead of models: our perception is a map of the territory that is reality. Our perception, like the map, distorts, omits many details, adds some labels, and draws emphasis; but largely preserves the main structure of reality.
Such critical realism is popular among more that just vision scientists, I would wager it is the belief of most non-philosophers. But why believe it? The easiest response is that it is self-evident. But it is also self-evident that the Earth is stationary when I’m sober, and the Moon is bigger at the horizon than when it is higher in the sky; yet I don’t take either of those statements as truths about the world. A better response is that critical realism is useful, it has helped me and my ancestors avoid being eaten by tigers, alligators and pythons. A variant of this is the stance that most cognitive scientists prefer. They give the evolutionary justification that an agent whose perception did not capture the statistical regularities of the environment would fare worse at survival than one who did. Thus, evolution would push us towards more and more veridical representations of reality. Of course, this isn’t the only argument for critical realism — this position and slight variants have been held by many philosophers since the ancient Greeks without any knowledge or reliance on evolution — but it is one of the more popular current scientific arguments.
Now, I am happy to suppose that evolution would select for perceptions that maximize fitness — although there are good arguments that can pull the rug out completely from under such adaptationist accounts — but why should we expect that true perceptions are particularly good at maximizing fitness? This question led Hoffman (1998; 2009) to develop the interface theory of perception. The name, and Hoffman’s favorite example, comes from computing machines. Consider your desktop screen: what are the folders? They don’t resemble or approximate the complicated sequence of changes in magnetization in a thin film of ferromagnetic material inside a metal box called your hard-drive, not even at a coarse-grained level. Nor do they show or even hint at the complicated information processing that changes those magnetic fields into the photons that leave your screen. If I had to interact with my computer at a level that accurately — or even partially — represented the underlying physical processes that carry out the information processing then — even with my years of computer science and physics education — I would not be able to write this post. It is an interface that hides the complexity that is unnecessary for my aims.
In the case of evolution, the ‘aim’ is (roughly) maximizing fitness, and thus perception doesn’t need to be truthful, but has to provide an interface through which the agent can act to maximize its’ fitness. Mark et al. (2010) built an evolutionary game theory model to show some conditions under which the interface theory is more adaptive that truthful perceptions. They looked at a game where two players meet at random and are presented with three potential foraging spots. The first agent picks one of the three spots, and then the second agent picks one of the remaining two spots. The signal that the agents receive about the fitness effects of the spot does not vary linearly with the actual effect. Instead it is a Gaussian with a patch sending a mid-level signal producing the highest increase in fitness, while patches with very low-level or high-level signals produce less of a fitness benefit for an agent that chooses them. As such, a critical realist strategy that properly reflects the structure of the signal cannot easily track fitness, while an interface theory can concentrate on the high-fitness regions of the signal, perceiving them as distinct from the lower fitness regions even if that breaks the linear order. This — plus a cost for simply perceiving the fitness effect instead of the complicated signal — leads agents with an interface theory to out-compete the naive and critical realists.
Once you have the objective effects of the game differing from the subjective experience on which agent decisions are based, you have to become much more careful about discussions of rationality. In particular, if an agent’s subjective perceptions of their actions are not in-like with the objective effects of their actions then an agent can act rationally on their subjective experience, while appearing to act irrationally from the perspective of someone that only has access to the objective effects. In theory, this is nothing new to economists: markets are supposed to be a method for rational agents acting on different subjective utilities to come to a mutual understanding and exchange. In practice, the frequent reliance on ‘representative agents’ in modeling throws away this agent heterogeneity, especially since an average of many rational agents with differing utility functions cannot itself be modeled as a rational agent. In the context of evolutionary game theory, this distinction fits into a recent trend of more carefully modeling the genotype-phenotype-behavior map (usually in EGT it is simply assumed that the genotype is the phenotype and behavior — the identity map) and through it psychological mechanisms (McNamara, 2013).
By worrying about the distinction between subjective and objective rationality, Marcel, Tom, and I have shown an even more drastic examples of the interface theory of perception (Kaznatcheev et al., 2014). We had the agents interact in pair-wise prisoner’s dilemma games in a structured population, and let their subjective perceptions of the payoffs evolve. In this context, a naive realist would be an agent that evolves subjective perceptions that are in exact numeric agreement with the objective effects of the game on fitness. A critical realist would be an agent that evolves a subjective perception that is of the same type of game, but maybe with slightly different numbers. An interface theorist would evolve a subjective representation that is a game with completely different payoff structure that leads to a different kind of behavior. In highly competitive environments our agents arrive at critical realism, and in friendlier (but still competitive) environments they evolve an interface. This interface allows them to cooperate and thus maximize overall well-being.
The drastic difference in our work is not just that we don’t tax a cognitive cost for true perceptions — in fact, we could tax a small cognitive cost for building interface and still arrive at the same qualitative results — but that our interfaces don’t maximize individual fitness. Instead, the interfaces that agents evolve in the friendlier environments allow them to maximize inclusive fitness — thus, I prefer to call these representations as social interfaces. They allow the society of agents to interface with the world in such a way that misrepresenting reality allows them to maximize the coherence and the well-being of the society and not just the short-term interests of the individual.
Consider, for example, religion as an example of such a social interface. People often see a tension between the praise of religion for promoting cooperative and moral behavior and the criticism for delusional beliefs. Our model resolves this tension by showing how a delusional interface can arise in order to facilitate cooperation among subjectively rational agents. Our simplistic model can apply to both moralizing and non-moralizing gods and be used to describe some of the earliest social interfaces with reality present in ancient cultures. Of course, these are tentative connections to the cognitive science of religion, but I hope they can serve as the first steps to further exploration by co-opting evolutionary game theory as a modeling tool.
Brunswik, E. (1956). Perception and the representative design of psychological experiments. University of California Press, Berkeley.
Hoffman, D.D. (1998). Visual intelligence: How we create what we see. W.W. Norton, New York.
Hoffman, D.D. (2009). The interface theory of perception. In: Dickinson, S., Tarr, M., Leonardis, A., & Schiele, B. (Eds.), Object categorization: Computer and human vision perspectives. Cambridge University Press, Cambridge.
Kaznatcheev, A., Montrey, M., & Shultz, T.R. (2014). Evolving useful delusions: Subjectively rational selfishness leads to objectively irrational cooperation. Proceedings of the 36th annual conference of the cognitive science society. arXiv: 1405.0041v1
Mark, J.T., Marion, B.B., & Hoffman, D.D. (2010). Natural selection and veridical perceptions. Journal of Theoretical Biology, 266(4): 504-515.
Marr, D. (1982). Vision: A computational investigation into the human representation and processing of visual information, Henry Holt and Co. Inc., New York, NY.
McNamara, J.M. (2013). Towards a richer evolutionary game theory. Journal of the Royal Society, Interface, 10(88).
Palmer, S. E. (1999). Vision science: Photons to phenomenology. The MIT press.