Thursday, May 07, 2009

Economics, ant farmers and free will theorems

Wow, it's been almost a week since my last post. I was pretty busy at the Perimeter Institute -- my brain is occupied trying to digest all the new things I've learned :-)

The conference had its origins in an essay Can science help solve the economic crisis? written by several of the organizers. The essay received responses from several prominent thinkers, and led to an exchange between Stanford economist Paul Romer and mathematician turned quant Eric Weinstein (see further down the page at the link above). Romer agreed to debate Weinstein, but then failed to show up! [Note added: in a private communication to me, Paul Romer writes that there was a misunderstanding and he never agreed to participate in a debate.]

The meeting went full speed from 9 AM until late at night for four days. The attendees were a mix of theoretical physicists (with particle physics and complexity theory, especially the Santa Fe Institute, well represented), practitioners from Wall St. (often from a math or physics background), academic economists (Barkley Rosser, Richard Freeman, etc.) and evolutionary biologists. See here for video recordings of talks. There were many good talks but I especially recommend Doyne Farmer's for the physicist's complex systems view of economics.

Too much ground was covered for a short summary, but one area of interest for almost all attendees was the possibility of going beyond the neoclassical paradigm via simulations of interacting agents. Examples of such simulations were discussed in several of the talks, including by Santa Fe "ant farmers" Bruce Sawhill and Jim Herriot, who used agents to model air traffic for the ambitious DayJet startup (see here and here).

The technology is certainly there to do some massive, quasi-realistic simulations of an actual economy (as opposed to an isolated financial market or sub-economy). The main problem, which wasn't given as much attention as I might have liked, is that the results are limited by the quality of the individual agents, who must have at least rudimentary learning capabilities to be realistic. Hence one is led full circle back to problems related to AI, machine learning and even psychology or cognitive science.

When I wasn't at the conference I managed to have several interesting physics discussions. Below are links to some recent work by John Conway and Simon Kochen that came up in two separate conversations I had at Perimeter -- one with Rob Spekkens (he and I were discussing related issues, although he didn't mention these papers specifically) and with Nima Arkani-Hamed, who was visiting from IAS.

The Free Will Theorem

On the basis of three physical axioms, we prove that if the choice of a particular type of spin 1 experiment is not a function of the information accessible to the experimenters, then its outcome is equally not a function of the information accessible to the particles. We show that this result is robust, and deduce that neither hidden variable theories nor mechanisms of the GRW type for wave function collapse can be made relativistic. We also establish the consistency of our axioms and discuss the philosophical implications.

See also the Strong Free Will theorem.

I feel the name of the theorem is a bit misleading, but inevitably so as it is quite difficult to define free will. The main feature of the papers is the great clarity of thought and presentation. In content, they are not so different from the older GHZ result which was formulated in terms of what the authors called local realism. To be honest I don't quite agree with Conway and Kochen's interpretation of their own results -- it's obvious that the results are easily consistent with many worlds quantum mechanics, which does not (at least from my spacetime perspective) allow for free will.

Here are 6 lectures on the theorem and related topics, given by Conway recently at Princeton. See also 'tHooft's response to their result.


Chris said...

A remark that sticks with me occurred in Emanuel Derman's talk, which I found as absorbing as Andrew Lo's. I don't recall the exact wording, but the essence was this:

When we construct a theory of bird flight, the birds pay no attention; they just keep flying as they always have. However, when we construct economic theories—theories of how markets work—the participants in those markets might well choose to employ those theories in their decision-making, if they think (think!) this might be to their advantage.

This simple fact can lead to all kinds of mischief; it describes the essence of the social sciences' reflexivity.

Steve Hsu said...

Someone described social science as "making theories about things that make theories" :-)

Chris said...

[PS: I hadn't previously read this nice historical piece by Jeremy Bernstein from the September 2004 Commentary, which is replicated on Derman's website.]

Don said...

"if our current understanding of physical laws is correct, humans have only the illusion of free will."

I don't see how this could possibly follow. If I say, "If our current understanding of free will is correct, physical laws are only an illusion", how would we choose between the two positions?

But, at least in my view, my being subject to an illusion makes sense, since my senses can deceive me about the physical world and its workings. The alternative would be for the world to be deceived about me.

It is not possible, based on the physical world and anything in it, for me to conclude that the very assumptions, like free will, that allow me to understand the physical world at all, are an illusion. I would be left without an edifice on which to construct any theory, let alone one based on math and inference. It would be like doing math without axioms, or something like that.

Don the libertarian Democrat

anon said...

"The attendees were a mix of theoretical physicists (with particle physics and complexity theory, especially the Santa Fe Institute, well represented), practitioners from Wall St. (often from a math or physics background), academic economists (Barkley Rosser, Richard Freeman, etc.) and evolutionary biologists."

What makes these people think they are relevant?

Is it that none of them has ever run a business?

Steve Hsu said...

> Is it that none of them has ever run a business?

Some of them have :-)

But I agree with your point.

Don: could a robot discover that he is indeed a robot?

Don said...

Steve, I'll sleep on your question. I need to think about what it means to be a robot. When I looked up robot on Wikipedia, I became confused about what a robot is supposed to be, as opposed to an android, cyborg, etc.

What I will say is that it is up to us to decide if we want to say that a robot discovered that it is a robot. It would not be enough for a robot to tell me, "Hey, Don, I just discovered that I'm a robot." For example, can the robot lie? Can I respond, "I don't believe you. Someone told you that you're a robot, didn't they?"

This is what Austin and Wittgenstein meant by criteria and context. If you tell me that you're a physicist, I have criteria by which I can determine the truth or falsity of your claim. If you tell me that you're a robot, I can assess that as well. So, I need to think about the criteria I would use to assess the truth or falsity or meaning of a robot telling me that he's discovered that he's a robot.

Take care,


anon said...

Steve has run a business. Or at least he has reported he has.

He must have learned from that experience that theory is a luxury.

As Heidegger says in so many words in the Question Concerning Technology, modern science is NOT the father of nor the handmaiden of modern technology, but the remittance man of modern technology.

Physics was the easiest subject for me, but I did not pursue it because as far as I could tell it had few practical results.

Dave Bacon said...

Derman's thoughts on the conference:

So, Steve, when are you taking a sabbatical at SFI? :)

Luke Lea said...

You know, Steve, I've thought about this problem for decades. To me it seems intuitive that human behavior is too labile to model mathematically. The way individual human beings react to changes in price is influenced by whims/fashions/imperfect information in ways that are unquantifiable. Sure, the basic laws of supply and demand hold but beyond that it is like using a sponge as a lever. Economics is more like checkers than chess.

David said...

dropped into your space via MIT Tech review.

Anyhow: here is my suggestion. TAKE SERIOUSLY THE POSSIBILITY THAT AT LEAST SOME HUMANS CAN "IMAGINE IT SO"... that is: they are at times unbounded by so-called "pysical laws". What if this isn't mystical bullshit? Naturally, if true, this would shake the foundations of what humans think "reality" is... and science wouldn't be so happy either, since nothing could be pinned down very securely, for any length of time.

Mike said...

I think the question of "free will" is puzzling only because we are so involved and attached to it.

Consider an ensemble of isolated people with exactly the same genetics who have experienced exactly the same life who are faced with a decision.

Either they make the decision based on their genetics and life experiences, in which case they all decide the same, or there is an element of randomness, in which case there might be a spectrum of decisions, but the spectrum has no meaning, because the differences are due to randomness.

What more could there be? How could one member of the ensemble make a "better" decision, unless that member has more or different information than the others? This of course invalidates the hypothesis.

What gives the appearance of some independent "free will" is, I think, the fact that on this planet, no two people share the same experiences. Decisions are made based on an algorithm developed by those experiences (and genetics), and so we rightly consider our decisions to be "ours" -- they are based on the algorithm developed by our experiences, not anyone else's.

Even if we allow the possibility that decisions are not so preordained, why should that make us feel better? There is no tangible value I can add to a decision other than input from my past experiences -- if I could somehow make a different decision than my identical clone in another identical world, the difference would have to be arbitrary. Why should I cling to hope for that?

Chris said...

In an effort to return the comments on this post to the topic at hand, I offer the following:

The Last Temptation of Riskby Barry Eichengreen[Barry Eichengreen is the George C. Pardee and Helen N. Pardee Professor of Economics and Political Science at the University of California, Berkeley.]

And what is true of investors and regulators, introspection suggests, can also be true of academics. When it is costly to acquire and assimilate information about how reality diverges from the assumptions underlying popular economic models, it will be tempting to ignore those divergences. When convention within the discipline is to assume efficient markets, there will be psychic costs if one attempts to buck the trend. Scholars, in other words, are no more immune than regulators to the problem of cognitive capture.

What got us into this mess, in other words, were not the limits of scholarly imagination. It was not the failure or inability of economists to model conflicts of interest, incentives to take excessive risk and information problems that can give rise to bubbles, panics and crises. It was not that economists failed to recognize the role of social and psychological factors in decision making or that they lacked the tools needed to draw out the implications. In fact, these observations and others had been imaginatively elaborated by contributors to the literatures on agency theory, information economics and behavioral finance. Rather, the problem was a partial and blinkered reading of that literature. The consumers of economic theory, not surprisingly, tended to pick and choose those elements of that rich literature that best supported their self-serving actions. Equally reprehensibly, the producers of that theory, benefiting in ways both pecuniary and psychic, showed disturbingly little tendency to object. It is in this light that we must understand how it was that the vast majority of the economics profession remained so blissfully silent and indeed unaware of the risk of financial disaster.
I'd say he nailed it. This crisis is fundamentally about a failure to sustain intellectual honesty and professional integrity, in the face of inducements to do otherwise.

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