Evolution for Everyone

Consider the following proposition: I’ll give you 1 million dollars for sure or a 50:50 chance at 2.1 million dollars. What’s your choice? If you’re like me, you’ll choose the certain 1 million. Yet, that is a violation of core economic theory that became known as the “Allais Paradox” based on the pioneering work of Maurice Allais in the 1950’s, who received the Nobel Prize in Economics in 1988.

The Allais Paradox provides a nice way to begin understanding the gap between economics and evolution. Using the notation that I introduced in E&E I, if A=the assumption that people maximize their mean expected utility and A’=the assumption that people are also sensitive to the variance in addition to the mean, then A’ is clearly superior to A as a description of our species. Call it evolution, psychology, common sense, or whatever you like. If core economic theory is a collection of assumptions (ABC), and if science is an incremental process, then the transition from ABC to A’BC should be straightforward. What Allais established would be progress, not a paradox. Instead, something about A’ made A’BC more problematic than ABC, interfering with incremental scientific progress. What was it?

Milton Friedman‘s classic paper “The Methodology of Positive Economics“, which was also published in the 1950’s, suggests at least three contributing factors:

1) An ideal of economic theory as like geometry or classical physics, complete with theorems that can be formally derived from each other. This sounds good but it can’t even be achieved for modern physics. Trying to achieve it results in such a restrictive set of assumptions that incorporating more realism is mathematically intractable.

2) The correct observation that models are simplifications that need not be realistic in every respect. A more realistic assumption is only worth incorporating into a model if it makes a difference for meaningful predictions that the model is trying to make.

3) An extremely lax set of criteria for comparing alternative models on the basis of evidence. Friedman wrote as if alternative models could be straightforwardly compared on the basis of evidence, resulting in incremental scientific change, but here is how he described the evidence for core economic theory:

An even more important body of evidence for the maximization-of-returns hypothesis is experience from countless applications of the hypothesis to specific problems and the repeated failure of its implications to be contradicted. This evidence is extremely hard to document; it is scattered in numerous memorandums, articles, and monographs concerned primarily with specific concrete problems rather than with submitting the hypothesis to test. Yet the continued use and acceptance of the hypothesis over a long period, and the failure of any coherent self-consistent alternative to be developed and be widely accepted, is strong indirect testimony to its worth.

If this isn’t a recipe for confirmation bias, what would be?

Against this background, we can begin to see why the Allais paradox posed such a threat to core economic theory. It violated the principle of maximization of returns, it could not easily be incorporated into the body of formal analytical theory, and it was a move toward realism that would definitely have consequences for economic predictions.

The lax criteria for comparing alternative models made it easy for proponents of core economic theory to ignore the Allais paradox. If risk sensitivity can’t easily be incorporated into the formal analytical framework, then it can’t become a coherent self-consistent alternative within the framework. Continued use and acceptance of a hypothesis over a long period testifies to its worth only when scientific change is incremental. An inferior paradigm can persist forever because it resists incremental change, like a local equilibrium in complexity theory or an adaptive peak in evolutionary theory. Longevity is no proof whatsoever of explanatory or predictive power.

Maurice Allais knows what it’s like for a paradigm to resist change. Here’s a passage from the entry that he wrote for the Allais paradox in the New Palgrave Dictionary of Economics (1987):

For nearly forty years the supporters of the neo-Bernoullian [expected utility] formulation have exerted a dogmatic and intolerant, powerful and tyrannical domination over the academic world; only in very recent years has a growing reaction begun to appear.” …”[The Allais paradox] is fundamentally an illustration of the need to take into account not only the mathematical expectation of cardinal utility, but also its distribution as a whole around its average, basic elements characterizing the psychology of risk.

The fact that Allais became a Nobel laureate in 1988 does not mean that he prevailed. In the next post, I will present a more recent example of how core economic theory still can’t seem to move in the direction of greater realism, even when it makes a huge difference for meaningful predictions that the models are trying to make.

I thank John Gowdy for bringing the Allais paradox to my attention, along with the other economists involved in the EI’s Nature of Regulation conference, for discussions and readings that provided the material for this post. It should be clear any field as large as economics or evolution is heterogeneous and that a sizable minority of economists are trying to move their field in the direction of greater realism, including integration with evolutionary theory. This discussion of the paradigmatic nature of economics and evolution will hopefully facilitate their efforts.

To be continued.


  1. #1 Vlad
    December 12, 2009

    Very interesting read! Glad to see economics discussed in this manner. Hopefully it’s discussions like these (and that large majority of economists you mentioned) that will push the field to be more beneficial to the studying of the human condition.

  2. #2 dcotler
    December 12, 2009

    Since, for most people, $2.1 million is much less than twice as good as $1 million, which squares with the human tendency to be risk averse for prospective benefits. The choice of a guaranteed million is the rational, and evolutionarily adaptive, choice. An animal prone to choose guaranteed sustenance vs a chance to be either oversupplied or starved is fitter. In this case those (e.g. Gigerenzer) who think it’s the psychologists who don’t know what normative is are right. Now, if you offered me $2.10/0 vs $1.00 a million times. . .

  3. #3 dcotler
    December 12, 2009

    I meant,
    Since, for most people, $2.1 million is much less than twice as good as $1 million, the choice of a guaranteed million is the rational, and evolutionarily adaptive, choice (which squares with the human tendency to be risk averse for prospective benefits). An animal prone to choose guaranteed sustenance vs a chance to be either oversupplied or starved is fitter. In this case those (e.g. Gigerenzer) who think it’s the psychologists who don’t know what normative is are right. Now, if you offered me $2.10/0 vs $1.00 a million times. . .

    Posted by: dcotler | December 12, 2009 3:02 PM

  4. #4 Russell
    December 12, 2009

    A rational actor maximizes their mean expected utility by recognizing that a second million dollars will not increase that nearly as much as the first million. The Allais paradox holds, even with dollars that have the same utility. But the situation you pose is different.

  5. #5 MichaelE
    December 12, 2009

    Thank goodness people outside of economics are finally realizing that it can be studied in the same way as all the other natural sciences.

  6. #6 Lyle
    December 12, 2009

    Re #4 a rational actor being a human calculating machine would calculate the expected value of each choice and since the 50% for 2.1 million has a higher expected value 1.05 versus the 1.00 for the sure thing case, go for the 2.1 case. The fallacy here is that humans believe to use an old phrase “a bird in the hand is worth two in the bush”, or try to minimize risk where possible.
    BTW there is a new field of Economics called Behavioral economics that takes insights from psychology and applies them to economics. Psychologists to small experiments to see how people make decisions and apply them to larger cases. Interestingly Adam Smith wrote a book called the Theory of Moral Sentiments before the Wealth of Nations that pointed a lot of this out. However in order to make the math tractable and economics like physics human behavior was replaced by the bloodless human calculating machine. (Sort of like neglecting friction when discussing falling bodies but much worse). This simplification enables the economist to build nice mathematical theory that let them feel they have become a science that is up there with physics, but their assumptions on which they base their theories are clearly wrong. (Another example we make different decisions if we are angry than if we are calm)

  7. #7 David Sloan Wilson
    December 13, 2009

    A quick reply to Lyle (6): Your diagnosis about replacing warm-blooded people with a bloodless human calculating machine, resulting in a theorem-like body of math trumping common sense, is right on. I will shift my attention to behavioral economics in future installments. To provide a preview, it takes some steps in the right direction but, with a few notable exceptions, has yet to engage seriously with evolutionary theory.

  8. #8 Sarah L.
    December 13, 2009

    To build on Russell’s comment: your opening paragraph does not give an example of the Allais paradox. It simply describes the choice of someone who is risk averse; this is easily taken into account in classical economics with a concave utility curve. (As Russell notes, in classical economics, rational actors maximize utility, not wealth.) The Allais paradox notices the inconsistency between the results of that choice and the results of a second choice, of, say, a medium chance to win a small amount of money and a smaller chance to win a large amount of money. The Wikipedia link you provide has a good example. (This does not take away from the main point of your post.)

  9. #9 bob koepp
    December 13, 2009

    One gets the impression from DSW and Lyle that simplifying assumptions are a “bad thing” in scientific modeling. But that ignores the methodological role of simplification. For example, Galilean science doesn’t “neglect” friction when discussing falling bodies. In experimental contexts it systematically minimizes the contribution of friction in order to arrive at a model of how bodies would fall in the absence of friction. This is a crucial step in the construction of a theory of motion.

    It’s possible, of course, to make incorrect simplifying assumptions, and this might well be what’s happened in economic theory. If so, we need to make corrections in the assumptions underlying theory; but we’re still going to need to start from a simplified/abstracted/idealized picture of the world.

  10. #10 Ewan
    December 13, 2009

    Regarding the part about confirmation bias… surely as an evolutionist you are aware that an absence of alternative theories *does* strengthen the orthodoxy, and that this is often legitimate.

  11. #11 Lyle
    December 13, 2009

    If the simplifying assumptions lead to models that clearly fly in the face of observations they are bad. Human beings are infinitely more complex than the laws of motion in the Newtonian range where quantum mechanics and relativity both general and special reduce to the Newtonian model.
    One does have to keep in mind that behavioral economics came out of psychology, and so the real question is how much has evolutionary theory interacted with psychology?
    In essence how much of our animal nature shows up in how we act.

  12. #12 bob koepp
    December 13, 2009

    In much the same way that behavioral economics “came out of” psychology, the notion of a “rational agent” at the heart of traditional economics is the product of philosophical theories of agency. What we get is basically an elaboration of a belief/desire model of motivated action with a normative theory of rationality grafted on. That normative theory was pretty unsophisticated — e.g., it didn’t even have a proper notion of ‘satisficing’. I think it more likely that economists were led astray because of limitations of their working notion of rational agency, not because they followed the tried and true method of employing simplifying assumptions to analyze the behavior of dynamic systems.

  13. #13 Paul Murray
    December 13, 2009

    The difficulty is that gain from money is logarithmic. The extra value you get from 2 million is not twice that you get from 1 million. I’d like to offer this choice to some groups but use a multiplier – 50/50 chance of doubling of halving the money, or various combinations thereof.

  14. #14 Julian Garcia
    December 13, 2009

    I think this is a great post to set the field for the upcoming discussion. While it is definitely true that “a sizable minority of economists are trying to move their field in the direction of greater realism” (very much against the tide of mainstream economists), in my experience, the second part of the sentence, i.e., “including integration with evolutionary theory” does not follow directly to many behavioral economists. Although they do know that ultimately there’s evolution behind their findings in the lab, they often would not invest much into unveiling ultimate causes. Why? I look forward to the rest of this series…

  15. #15 Alan Kellogg
    December 15, 2009

    First error, assuming people are rational. People are not rational, people are hopeful. People take risks in the hope a reward will follow. If gaining 2.1 million means risking the loss of 1 million, then people will risk the loss.

    I would accept the 1 million. Not because I’m rational, but because I’m pessimistic. Life experience has taught me not to take such chances. Rationally I have as much chance as anybody else of getting that 2.1 million, but personal experience and clinical depression dictate against taking the chance. I’ll take the 1 million and let other people throw the dice.

  16. #16 Alan Kellogg
    December 15, 2009

    Or to borrow an exchange from an RPG session…

    Professor: You have only a 5% chance of succeeding. What sort of man works on such odds?

    Adventurer: Heroes professor, heroes.

  17. #17 Marilyn
    December 15, 2009

    I suggest to interested rational agents check the site quoted below… in…Chile..btw: Darwin was fascinated with giant chilean barnacles

  18. #18 rickflick
    December 15, 2009

    Wait a minute. What would you rather have. 1 million dollars now, or 1 trillion billion dollars in 20 years. Assume you are now 40 years old. 50 years old. 60 years old. 70 years old???

  19. #19 InfuriatedSciTeacher
    December 16, 2009

    Alan> Not so much rational as simply applying heuristics based on the probabilities of previous events, which fits right in with your second explanation. Rationality comes second, and has been shown in the psych literature on decision making to be subsumed a bit (Tversky 1970&1994, Stupple Et al. 2009, Poletiek 2009).
    On the hopeful/risk taking thing, there is something to that. Another paper on the subject (that I can cite if I bother to look up which one) discusses how the perceived probability of a favourable outcome to an event increases when someone has a distinct goal for that event, or when the risk seems less (I didn’t have any money before, so I’m not really losing any, etc.)

  20. #20 John Atkeson
    December 22, 2009

    My first impression was the same as above: the value of your second million dollars is way less than the value of your first million.

    When you think about it, it may be a global rule of value. A ham sandwich can have near-infinite worth to a starving man, but almost none to Bill Gates. (Now we know why progressive taxation exists.)

    Trying to devise a mathematical system for this would blow the lid off of classical economics. Imagine a ‘floating dollar’ whose worth is constantly scaled against the individual’s total wealth.

    What it means though is while money may be an evolutionary improvement over barter, it is only a step along the way to some other more accurate and scalable measure of value.

  21. #21 Jannik
    December 28, 2009

    @David Sloan Wilson

    Russell & sarah are right. You have not given an example of the allais paradox. The paradox is not a problem concerning risk aversion. Expected utility theory does account for the utility associated with the variance of pay-offs.
    The paradox arises when the agent is confronted with 2 different sets of gambles and in the experimental setting, makes choices which are inconsistent according to expected utility theory.

  22. #22 Moti Michaeli
    March 18, 2010

    I hate to ruin the party, but the last comment (by Jannik), and the comments it refers to, were too gentle and considerate, albeit totally correct. To make things clear, the misrepresentation of the Allais Paradox, and the lack of distinction between max expected utility and max expected returns, render the whole post deeply fallacious. The main point of this post seems to be that economists should learn from evolution (or Psychology for that matter) that risk matters and that people are sensitive to variation, and incorporate it into their models. However, expected utility is, by definition, a model of decision under risk, where agents are sensitive to variation, and that is exactly why they maximize utility and not wealth! So this main point becomes totally insignificant. In fact, in every new classical economic model where specific utility is assumed, you will find that decision makers are assumed to prefer the 1 million over the 50% chance of 2.1 millions, due to the concavity of the utility function. I really hope that next posts will refrain from such blunt mistakes, as I was very intrigued by the whole project.

  23. #23 Steven E. Landsburg
    January 4, 2012

    Consider the following proposition: All species eventually develop antlers. If you’re like me, you’ll find this proposition implausible. Yet the inevitability of antlers is a central tenet of core evolutionary theory.

    I wonder whether you’ve twigged yet to the fact that this makes exactly as much sense as your opening paragraph.

  24. I really hope that next posts will refrain from such blunt mistakes, as I was very intrigued by the whole project.

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