Tuesday, December 19, 2017

Emergence, rationality, and human behavior

Irrational mind from rational brain; illustration by Douglas Hofstadter in Godel Escher Bach. Is this a perturbation to rationality or emergent from rationality?

[Gary] Becker acknowledged that ... he was pushing the envelope. In his Nobel address he discusses this explicitly (Becker 1993). “I have intentionally chosen certain topics for my research—such as addiction—to probe the boundaries of rational choice theory. … My work may have sometimes assumed too much rationality, but I believe it has been an antidote to the extensive research that does not credit people with enough rationality”. 
Becker’s last sentence suggests an alternative definition of behavioral economics: crediting people with just the right amount of rationality and human foibles. The trick is in figuring out what is just the right amount. The approach taken by most behavioral economists has been to focus on a few important ways in which [Homo sapiens, HS] diverge from Homo economicus [HE].
That is from a recent article by Richard Thaler in JPE. Thaler's characterization suggests a particular interpretation of economic theory where real humans are perturbations from a rational Homo economicus:

(1) HS = HE + dB

Now this "behavior perturbation theory" formulation is entirely plausible. It represents the typical approach to quantum field theory where the electrons we observe are "ideal" electrons plus quantum interactions (dI):

Electron = Ideal electron + dI

However, this formulation is incorrect for thermodynamics. We do not say [1] that diffusion is an atom plus some diffusion perturbation (dD):

(✕) Diffusing atom = Atom + dD

but rather it is an entropic force that does not exist for a single atom and requires there to be an collection of a large number of atoms [7]:

Diffusion = d(Σ Atoms)

Diffusion is a pseudo-force that exists due to the possible configurations of a collection of atoms, but not for any single atom. This sets up a different paradigm from (1). Economic forces might well arise from collections of humans

(2) Economic forces = d(Σ HS)

That is to say that economic forces (macro or micro) are gradients in the state space accessible by real humans. In this paradigm, you might be able to observe many behavioral effects (dB) relative to Homo economicus that don't show up in economic forces as a simple aggregate if at all. This might explain Thaler's lament:
The field of behavioral economics has been around for more than three decades, but the application of its findings to societal problems has only recently been catching on.
Could this be because:

d(Σ HS) ≈ d(Σ HE)

(i.e. on average the idiosyncratic human behaviors dB 'cancel' such that Σ dB ≈ 0)? Or what about:

d(Σ HS) ≈ HE?

This approximation is something I speculated about awhile ago (that a rational representative agent might be emergent from irrational humans). My own particular view is that macroeconomics can be understood using (2) with the addition of perturbations due to collective behavior (CB):

(3) Economic forces = d(Σ HS) + dCB

These "collective perturbations" [6] are things like so-called groupthink or the panics that accompany financial crises that lead to correlations among Homo sapiens. This would also include information cascades (where the "conventional wisdom" undergoes a "phase transition" from thinking e.g. fundamentals justify asset prices to "this is a bubble"). Notice that you can't really have "groupthink" or "information cascades" without a collection of Homo sapiens or other agents.

Overall, there are several possible paradigms for understanding economic forces and each of these paradigms indicate which effects are important. But there's another way to organize these paradigms in terms of scales, emergence, and information theory. Erik Hoel wrote an interesting paper (or rather series of papers) that I discuss here where he uses information theory to describe how theories explain observations and data. You can think of a theory as a way to decode empirical evidence. The codes can be more or less efficient depending on how much information is lost (and whether lost information is relevant information). But it is unlikely a single code (theory) is efficient across all messages (phenomena), so you end up with specific codes that work well for collections of phenomena. The collections of phenomena are split up by what we can call scales, and so in economics we might have a macro scale (economic forces) and a micro scale (humans). There is no reason that a particular code (theory) at one scale has to have anything to do with a code at a different scale, and it also does not necessarily make sense to cross over from one scale to another because each scale has its own agents (degrees of freedom).

That may seem like a tangent, but I think it is critical to understanding the economic theory paradigms above. A behavioral theory may well describe Homo sapiens at the individual human scale, but may not apply (or have any direct analog) at the economic/macro scale [2]. Paradigm (3) keeps everything at the collective scale (collective forces with collective perturbations [3]) while paradigm (1) tells us that behavior crosses scales from individuals to economic forces among societies. Of course, either paradigm could be the most efficient way to understand economic theory, but I think there is a bit of an over-simplification in Thaler's 'Homo economicus plus behavioral perturbations' view [4]. However since economic forces at the macro scale aren't very well understood, I don't think we should limit ourselves to any specific paradigm [5] — but we should keep in mind that the connection between theories at different scales may be tenuous (or simply not informative).

At the top of this post, I have a picture of an illustration from one of my favorite books: Godel Escher Bach by Douglas Hofstadter. Hofstadter is trying to illustrate how rationality (illustrated by math facts) at one level (computer code or neuron behavior) can in fact result in irrationality (illustrated by 2+2=5) at another level (an artificial intelligence or human behavior). The connection between 10+6=16 and 2+2=5 is more than just tenuous, but complete logical disconnect. But this picture illustrates my point about how the "perturbations to rationality" view is limiting: in what sense is the irrationality of 2+2=5 a perturbation to the rationality of 10+6=16?

This disconnect could also occur when transitioning from the human scale to the economic scale in my modification of Hofstadter's illustration:



The irrationally behaving humans (made up of rationally behaving machine-like neurons) can themselves be collected into a rational macroeconomic system. With this post, I am only emphasizing that this is a theoretical possibility given the present state of understanding economic forces — something to keep in mind.

...

Footnotes:

[1] It is possible to set up an effective theory that works like this, but it would be far more limited in scope than the correct approach. Actually, I think that is a good way to think about behavioral economic formulated as perturbation theory: it functions for limited scope.

[2] This could also apply to agent based modelling. I'm not saying it is definitely true or anything like that, only that assuming agent-based modelling is the only way to answer questions is potentially flawed (more on that here).

[3] This is not to say that collective perturbations are not reducible to individual behavior, but rather I am thinking in terms of "weak emergence" where the the theory individual behavior that yields the collective behavior is not as informative or useful as just understanding the collective behavior at its own scale.

[4] Thaler may well be adopting this view for the purpose of persuasion: "economic theory is fine with some behavioral tweaks" rather than "burn it down".

[5] Individuals can limit themselves to study one paradigm if they want.

[6] These perturbations fall under the heading of "non-ideal information transfer".

[7] This "schematic" equation related directly to the gradient ("d") of entropy ("Σ Atoms") in the actual definition of entropic force.

9 comments:

  1. I like your modified picture. Nice presentation of your ideas too.

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  2. Three thoughts come to mind:

    1. Each atom occupies a unique three dimensional space. Groups of atoms are collections of individuals each carefully avoiding each-others individual space.

    2. The term '2 + 2 = 5' (to me) represents a miss-fit of a trial run. In other words, humans attempt to make sense of collections of misfitting data; they must make decisions and act despite knowing that the correct data fit (2 + 2 = 4) remains unknown.

    3. Now introduce your notion of 'scales'. The individual (measured by some scale) avoids the unique space occupied by others yet remains within the 'scale' used to measure the group. The two scales must have points of intersection, but because they are measuring different concepts (theories), they should diverge only to re-intersect when the group is considered as an individual.

    Example: [individual Human -> regional groups -> national groups -> One World] Both Individual Human and One World are uniquely defined spaces.

    Maybe I should not comment. These are certainly spontaneous thoughts!

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  3. Auld calls "rational" economic jargon, which it is, and UnlearningEcon calls (economic) rationality an unfalsifiable claim. IMX, economists themselves, in talking with non-economists, present economic rationality as not just jargon, but as normative. Also, the standard economic view of rationality is an individual attribute, not a collective one.

    Ken Burns, in his documentary series on the Dust Bowl, shows that in the year before the Dust Bowl, wheat and corn farmers overproduced so much that their market collapsed, and mounds of grain were left beside the roads to rot. One farmer, interviewed years later, said that whatever the problem was, the answer was to plant more. The overplanting was a reaction to the drop in grain prices as a result of the deepening depression. In that situation, what was rational for the individual farmer? Leaving the farm to starve in the city was not an attractive option. Collective rationality would have been for the farmers to reduce production to shore up prices and reduce costs. But for any farmer to reduce production on his own while all the others were increasing production would only reduce his share of the market. My impression is that the farmers who planted more were being economically rational, despite the reasonably predictable consequences. In multiperson game theory, I do not think that economists usually regard forming alliances as rational.

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    1. By contrast, in the 1970s when beef prices declined sharply, farmers and ranchers slaughtered cattle, and the next year supply was low and prices were high. Apparently they did this without any collusion, although surely people talked about what to do.

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    2. Hi Bill, Happy New Year!

      Yes, we get into trouble when we overload the term "rational" -- I run into similar problems with the word "information" all the time. I am using it above more in the sense that "rational" means you get supply and demand out of it. In that case, farmers planting more crops resulting in a falling price (extra supply at the same level of demand) is a "rational" result at the macro level regardless of whether (and in fact despite) farmers were rational or irrational.

      So what I'm saying above isn't so much that agents that can maximize a game theory game are emergent, but rather a mathematical description that is isomorphic to a result of rational agents (i.e. supply and demand) is emergent -- an in fact is emergent regardless of whether the underlying human agents can maximize the game or not.

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  4. Jason: “Yes, we get into trouble when we overload the term "rational" -- I run into similar problems with the word "information" all the time. I am using it above more in the sense that "rational" means you get supply and demand out of it”

    Words are important. They mean no more and no less than what we all agree that they mean. If we don’t agree what they mean, they mean nothing. I seem to recall that astronomers held a meeting a few years ago to debate whether to change the meaning of the word “planet”. Before the meeting Pluto was a planet. After the meeting it wasn’t.

    The definition of any word is a social convention. If you break the convention, no-one will understand you. One of the biggest problems in economics is that individual words don’t mean what non-economists think they mean. If you try to discern what the words mean to economists, you will find that economists often don’t seem to have clear or consistent definitions, so the entire economics edifice appears to be built on sand.

    Whatever economists mean by “rational”, it is too vague and ambiguous to be useful, and too far from the conventional view to be understood by non-economists. In the real world, group decisions are no more rational than individual decisions e.g. the election of Trump. Group decisions are CONSENSUS-based decisions, so they tend towards the centre of distributions of individual views / decisions. That’s all.

    For example, markets form when individuals put forward bid and offer prices. I might bid to buy shares for €1. You might offer to sell the same shares for €100. If we are the only people in the market, we might haggle our way to a consensus price of €40 at which we agree an exchange.

    As other people join the market, we get entire distributions of bid prices and offer prices. The consensus price is then just the price where the two distributions overlap.

    At a higher level, our share might be part of a broader stock market. The broader market value is simply a weighted average of the consensus prices of its constituent shares.

    In other areas, we employ different CONSENSUS-BUILDING ALGORITHMS (CBAs) e.g. democratic elections, jury trials. These CBAs can have their own biases. For example, the 2016 US election would have had a different result if the CBA was based on votes cast for each candidate rather than the electoral college system. This alternative result would have been no more or less rational than the conventional result – just a consequence of a different CBA convention.

    Your approach seems more consistent with my description of markets i.e. consensus prices emerge from the overlap of distributions of bid and offer prices. That’s how real markets work, so market practitioners might also respond better to such a description. Economists tend to ignore bid and offer prices. They talk about agents in markets being “price takers” of prices which are set magically by supply and demand curves. However, if there were no agents putting forward bid and offer prices, there would be no prices to take.

    IMHO the use of the word “rational” here creates confusion and detracts from your overall argument. Homo economicus (or rational agent / representative agent) is a made-up, unmeasurable concept that adds nothing to our understanding of how the economy works, and actively prevents discussion of the herding behaviours that seems to be central to most macro-pathologies.

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    1. The technical definition of "information" also doesn't mean what non-physicists or non-engineers think it means. Is that a problem? Should we abandon the entire field of information theory because people think information has meaning? That would abandon Shannon's insight that has made high data rate communication possible.

      There are a whole bunch of technical jargon word that don't mean what people outside those fields think they mean. "Charm" is a quantum number conserved by the electromagnetic and strong forces. "Gauge" doesn't mean the same thing to most people as it does to physicists.

      Now it may be argued that economists' definitions of "rational" (of which there are *many* ranging from "not deliberately trying to make themselves worse off" to "follows a mathematical equation") is not as helpful as the counterintuitive definitions of "information" or "gauge". But this kind of depends on already knowing what the correct theory of economics is. You may think the definition I used above is garbage, but what if the theory it's being used in connection to becomes the theory that explains all of economics? Not saying that is likely, but the truth is that neither you or I know whether someone's counterintuitive definition of the word "rational" will lead to insight in the same way Shannon's counterintuitive definition of the word "information" that is maximized for a random string lead to a major breakthrough.

      The fallacy here is believing the present state of any theory is complete and assuming if it hasn't been explained (i.e. "rational" hasn't been a useful explanation) that it will never be explained (i.e. that the economic definition of "rational" won't be a part of a complete theory).

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    2. I would also like to add that the way I am using it above is kind of the standard in economics, but that in the information transfer view it can be violated and represents the difference between ideal and non-ideal information transfer.

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  5. My comment was about “rational” rather than “information”. “Information” is not a problem in economics as almost everyone uses it in the sense:

    “Traders in the Apple shares market reacted to new information about Apple’s plans”.

    In economics, the term “information” is used to denote meaningful information. You are the outlier.

    You cannot just import a definition of a word into a field which uses that word in a different manner and declare that your definition is correct, and the common usage is wrong. At minimum, if you want to invoke the physics definition of “information” in economics, you need to explain, in terms that your economics audience will understand, two things:

    First, what does your definition of “information” mean in the economics world. Shannon used the term in the world of telecoms. I understand what Shannon meant. He was talking about codifying messages in a way that would allow them to be transmitted electronically effectively, efficiently and over long distances. I don’t understand what you mean because you don’t explain your version in English. Also, you appear to use the term differently from Cesar Hidalgo who is also a physicist who talks about Shannon-based “information” in economics.

    Second, you need to provide an alternative vocabulary for “information” as it would be understood by others. You also need to use this vocabulary yourself. You often use the word “information” in a way that appears to imply meaning but the fact that you don’t have an alternative term for “information with meaning” means that your writing is ambiguous.

    You say that “information” is sent from demand to supply but the information in my Apple quote is sent from Apple to both demand and supply. Additionally, the people on the demand and supply sides of an asset market are often the same people, so what does it mean for these people to send information to themselves and what does this information represent in the real-world? And why does supply not send information to demand? You need realistic examples from economics as illustrations.

    In case of ambiguity, you should read what I have written above as a challenge to you rather than as a condemnation of your concept of “information”. This goes back to differences in our usage of the word “science”. I think that science has two stages: “scientific research” and “socialisation of science”. The first stage is what you think of as science. The second stage is about communicating research results to the rest of society in a way that society understands and accepts. The second stage is essential in any science which proposes a real-world application or a change in social behaviour. In general, scientists are hopeless at socialisation. That’s why exceptions – like Richard Feynman or modern popularisers of physics such as Brian Cox (in the UK at least) – stand out from the crowd.

    Regarding “rational”, I don’t think that I am importing my own version of “rational”. I am saying that economists themselves appear to use the term ambiguously, so it’s impossible for a non-economist to understand what they mean even if you accept that economists can redefine words for their own internal purposes. Also, the term seems to be used as an alternative to observing real-world markets and writing down a realistic description of the observation.

    At best, “rational” is a modelling assumption used in a specific type of economic model which appears to have little real-world value. I don’t think that the word “standard” is a useful word here either. Joseph Stiglitz (Nobel prize winner) routinely ridicules the rational agent and its associated models. Meanwhile, as far as I can see, Paul Krugman (another Nobel prize winner and probably the best-known economist in the US) mostly ignores the concept.

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