Kantian Optimisation

No time to read the paper right now, but it looks great.

Kantian Optimization, Social Ethos, and Pareto Efficiency
Date: 2012-03
By: John E. Roemer (Dept. of Political Science, Yale University)
Although evidence accrues in biology, anthropology and experimental economics that homo sapiens is a cooperative species, the reigning assumption in economic theory is that individuals optimize in an autarkic manner (as in Nash and Walrasian equilibrium). I here postulate an interdependent kind of optimizing behavior, called Kantian. It is shown that in simple economic models, when there are negative externalities (such as congestion effects from use of a commonly owned resource) or positive externalities (such as a social ethos reflected in individuals’ preferences), Kantian equilibria dominate Nash-Walras equilibria in terms of efficiency. While economists schooled in Nash equilibrium may view the Kantian behavior as utopian, there is some — perhaps much — evidence that it exists. If cultures evolve through group selection, the hypothesis that Kantian behavior is more prevalent than we may think is supported by the efficiency results here demonstrated.

37 thoughts on “Kantian Optimisation

  1. For a paper that starts off by claiming support from evolutionary biology, I think it rather misrepresents the “evidence” from that discipline. Where are the references?

  2. The Maths was too much for me. However there was enough of the idea embedded in the text to get the general concept. I agree it looks quite interesting. It certainly seems intuitively correct to suggest that people frequently use Kantian equilibrium type logic in their decision making rather than Nash equilibrium type logic. It’s the only real explanation for why anybody bothers voting in a purely voluntary system or why most people refrain from littering.

    The following is my attempt at a summary.

    Logic 1. Given everybody is doing X then does it profit me to also do X. If yes we have a Nash equilibrium. eg if everybody drives on the left it profits me to also drive on the left. eg if everybody speaks English it profits me to also speak English.

    Logic 2. If everybody does X does it profit everyone. If yes we have a Kantian equilibrium. eg if everybody puts their litter in the bin does it profit everybody. eg if everybody is considerate does it profit everybody.

    To be sustainable (ie to achieve equilibrium) Kantian logic would in my mind seem to require some capacity to exclude or punish people who don’t share the logic. Either ostracism or something harsher.

  3. Sounds a bit like Socrates’ observation that people find it harder to do wrong than right.
    Is it why there seem to be so many exhausted looking people in the world?
    It seems a relief when held up to Ricardo and Ralph Nickleby.

  4. To cartoon the two, so why did the more psychopathic supportive version (Nash) get adopted as standard? Why do such a small percentage of the population get to manipulate economic theory & modelling in their favour for so long?

  5. you have an odd love-hate relation with maths, Nick. If ever there was a paper full of mathematical abstractions that will never be measured and results that wont change any policy maker’s choices or view of the world, its stuff like this. I hope you realise that with this kind of model in mind, recessions are still mass holidays because there is full information of all opportunities? You usually denounce stuff like this.

  6. Paul,

    Maths is for pursuing logical relations. As for fitting evidence to theories well that works if you have the kinds of replicable conditions you get in natural science. In social science it’s very often chimerical.

  7. Meika – Nash equilibrium isn’t widely enough understood in my view. I like the Kantian insight but I see the two as complimentary in terms of explaining social phenomena.

  8. Roemer’s paper is important for a number of reasons. I appreciate Nick’s love hate relationship with mathematics, but in this case he has spotted that it is being used to explore some of the foundations of what an alternative to the neo-classical orthodoxy would look like.
    A few words of clarification (I hope) on previous posts.
    1. It is true that if you take neo-classical economics seriously the great depression looks like the great holiday. This paper shouldn’t sink with that ship. Its whole point is to explore the alternative.
    2. I don’t think measurability matters in this context. Most of what goes into economic theory isn’t measureable. This doesn’t mean it isn’t important or doesn’t shape policy. Consider rational expectations theory. This largely provided the theoretical justification for the policies that contributed to the 2oo8 crisis.
    3. Nash got adopted as standard because it answers questions about individual optimization and this is what political economists and game theorists were interested in around the 1950,s and neo-classical economists continued to be interested in. Partly this is because this sort of optimization was all that the mathematics they had let them understand. Market equilibrium is a trivial case of a Nash equilibrium so it fitted with what was understood.
    4. So why not ditch the mathematics? Unfortunately we need it. Without some formalization we are just left guessing about how complex systems behave, and usually our guesses are horrible. It is not that mathematics works as in physics as Nick said. It just allows us to explore our ideas and their consequences.
    5. Nash and Kantian equilibria are very different so if they are thought to be complementary you would need to specify the sense of the term.
    For anyone interested, and to elaborate some of the previous points, the context of Roemer’s paper can be filled in as follows:
    1. Neo-classical economics has been heavily criticized by social scientists and philosophers for a long time for its dependence on the assumption that individuals make optimizing decisions without regard for others.
    2. Most of these criticisms don’t go a lot beyond the ‘I don’t like it’ stage. If you are really serious in replacing individual optimization with othr regarding actions of some sort you need to have some idea of what to replace it with and what the consequences might be.
    3. In this paper it is suggested we might try some idea that individuals have some sort of social ethos and this is cashed out in the Kantian imperative.
    4. If you wish to explore the Kantian imperative as a decision rule you need to know whether it could meet some simple conditions and something about its characteristics. If not it isn’t going to be interesting doing any more work on it.
    5. For example, one simple test is Pareto efficiency. Another is maximizing social welfare (as an aside the Nash equilibrium almost always fails each of these, except in trivial cases).
    6. In order to do this you have no choice to do a bit of mathematics. You could sit around and speculate and rely on guesses and intuition if you wanted. This mostly gives bad guesses and not much by way of an alternative theory.

  9. Thx Alex,

    But can people stop talking about my love hate relationship with mathematics.

    It’s a hate relationship with scientism, not a love-hate relationship with mathematics. I have the highest regard for mathematics and within economics it can offer all sorts of insights. It is not, however a higher form of insight in economics, but a particular style of reasoning that is the most powerful in certain circumstances, and – like other modes of reasoning when used badly – can be useless or (more often) worse.

  10. Look, people. Use this sort of math if you need to, but then, make the effort to translate the paper to English for the rest of us. Not fair!

  11. “2. Most of these criticisms don’t go a lot beyond the ‘I don’t like it’ stage. If you are really serious in replacing individual optimization with othr regarding actions of some sort you need to have some idea of what to replace it with and what the consequences might be.”

    That’s not really true — other areas (i.e., not economics) have entirely different starting places for dealing with individual and group behaviors and many have quite sophisticated and predictive theories. It really depends on what you are intertested in.

  12. A. The English problem.
    There is a lot of explanation in the paper that is worthwhile reading and should give the drift of things if it is well written. In princile you could translate the mathematics into English (or any other language) but, despite what you are told mathematics is not a language so the translate would not e one to one. It take 100′s, perhaps 1,000′s of pages and be completely incomprehensible since it caries a hidden burden of several 100 years of proofs and logical connections.
    B. Other disciplines.
    It is true that other disciplines have different starting places.
    There are two points here:
    1. Predictions. Other disciplines often make predictions in the inductive sense – ‘this is what happened last time so it will happen next time.’ If they didn’t then the predictions culd be expressed mathematically and some of this is done in sociology and political science. Inductive predictions are useful and interesting and mostly all we have. But they do not amount to a theory.
    2. Interest. What a lot of us are interested in is constructing an alternative to existing political-economic theory since this type of theory has a profound influence on the way in which governments behave and decisions get made. Unless you are able to formalize your ideas then you aren’t going to have much impact on the existing formal theory. Many of the most outspoken critics of formal theory, including many historians, simply run a disguised and inconsistent version of it in their writing. It is not a choice between no models and models in this debate. It is really only a choice between not very good models and very bad models. (As a personal aside Roemer taught me this after I gave up mathematics for many years to do philosophy)

  13. Sorry Vera, I was being a bit of a smartarse. For penance I’ll do my best with a bit of an intro in English.

    The paper constrasts two kinds of equilibrium (or lack thereof). One produced by autarkic optimising behaviour where each person tries to advantage themselves assuming others’ behaviour stays the same. This is Nash equilibrium and undermines cooperation (though in the kinds of circumstances that economists like to imagine are close to reality in competitive markets) perfect competition and perfect cooperation end up being the same thing. And in these circumstances they are efficient.

    However very often life isn’t like that. It isn’t like that for payment of taxes – because we pay taxes for others, and it isn’t like that in lots of other situations (for instance int he workplace where people need to cooperate or where we clean up after ourselves so we don’t impose ugliness on others). Here we are in a ‘prisoner’s dilemma’ and we can advantage both ourselves and someone else by cooperating (but we fear the other person won’t cooperate with us and so we’ll be worse off.)

    In this situation human psychology often leads us to consider doing something which – if replicated by others – would improve our own – and others’ wellbeing. We pay our taxes even though the penalty for not doing so is inadequate to get us to do so if we were heading for a Nash (autarkic) equilibrium. Here we often fancy Kant’s categorical imperative and we try to do something – or at least begin by doing something, which if others did it would make everyone better off.

    Unsurprisingly this decision rule produces more efficient outcomes in a range of circumstances, particularly where there are externalities of the kind mentioned above.

  14. “Unless you are able to formalize your ideas then you aren’t going to have much impact on the existing formal theory”

    Alternatively, you might have quite a lot of impact on reality. For example, if you take gambling as a good test case that should be amenable to theories from different areas, then whose ideas are people acting on? For example, if I look at the recent ideas for pokie reforms, which came out of formal economic theory and which came from ideas from other disciplines which like to look at gambling too (e.g., psychology)? I think the answer to this is pretty clear even though theories of gambling in psychology range from the somewhat formalized (e.g., how the reward circuits work in our brains) to the rather unformalized (e.g., theories of attitudes). I think this is a good example of why not to get too caught up with formal theories (and I’m not criticizes them here), especially if you can generate theories that predict behavior that formal theories cannot.

  15. meika, based on the predictive excellence of common economic models, I’d say you are more than welcome to use whichever theoretical approach you like. I’m curious about why you prefer one GPU to another though.

    Alex:

    Inductive predictions are useful and interesting and mostly all we have. But they do not amount to a theory.

    When they dropped the atom bomb over Japan, that was an inductive prediction. Same with the rest of science and technology. All of it.

  16. let me paraphrase Alex, the defender of the faith:


    some classic economists, who see the macro-economy as having perfect markets and populated by selfish individual decision makers, explain recessions as voluntary holidays. My former adviser is more sophisticated as he allows individuals to care about each other. Hence in his story recessions are not just voluntary holidays taken up by rational individuals. Employers consciously don’t bother these holiday makers with lucrative job offers as to not disturb their leisure.

    Really….

  17. Not sure i understand your point Paul.
    Whose faith? In what? am not a neo clasical econonomist and have no desire to defend it.
    Roemer wasn’t my advisor.
    I am only defending the use of I mathematical models asin mathematical marxism for example.
    As before I agree that neo classica economics lrafs to the interpretation of the depression you give.
    This shows how silly it starts to become when its logic is pushed.
    I can’t find any such implication in this paper, however.

  18. Alex,

    I re-labeled your personal aside about Roemer teaching you on this issue as him being your adviser on this issue.

    I am on the whole quite in favour of mathematics in economics, but dislike all pretences of mathematical edices built from ‘first principles’ (preference axioms and the like), into which this paper firmly falls. Its pretentious and lazy: you wont ever measure these preference maps or most of the other functions and yet flouts much of what we now know of both our internal psychology and economic reality. Its ‘general lessons’ are then no more than quick sand.

    Having said this, I too am a warm supporter of thinking more broadly of economic behaviour as incorporating more than greed, but it must be anchored in reality. Ever seen a policy that is a Pareto-improvement? I am afraid you have been bamboozled by the maths.

  19. Well I think we’ve flushed out something of interest here. I’m on Alex’s side – as you might imagine. Many of the most useful things about the use of Maths in economics relate to the logical structure of what you’re doing. I’ve never been much of a fan of Pareto optimality because it is – as you intimate Paul – not an interesting criterion of welfare. But it does have some worth while logical properties. It enables one to distinguish clearly between equity and efficiency – though in thoughtless hands it’s an invitation to assume that something logical has some relationship to a criterion of choice between two states when we all know that in the real world the criterion is useless choosing between them.

    But the alternative use for mathematics which involves setting up ‘hypotheses’ and then testing them? Well if there are stale relationships you may be able to get somewhere – it is for instance of interest in the current circumstances to ask how much exchange rates might be influenced by the terms of trade and how much they might be influenced by interest rate differentials over time – as well as some other causal factors. But this is pretty simple stuff. And taking further usually ends up in grief as Keynes argued to Tinbergen all those years ago. Relationships change all the time, and there are non-linearities all over the place.

    There’s not much point in building a model of positive economics from preference axioms and all that stuff – simply because they’re lousy ‘micro-foundations’ on which to understand how the economy might move from one period to another. That seems to me to be different from building a model designed to build a toy world which helps elucidate normative criteria.

  20. normative criteria to judge what real phenomena? If your toy world is based on things you cannot even by loose approximation measure, and even as a pattern it is too abstract and particular, then what is it you hope to learn?

    Perhaps Alex can give an example of where he now thinks differently about a real-world phenomenon or moral situation than before.

  21. There’s an almost identical debate to this that goes on amongst people who worry about the use of models in the cognitive science community. One of the founders of cognitive science talked about it here.

  22. How can a model be useful as a normative model if it’s not a good positive description of the world? If I’m seeking to determine whether state one is better than state two in the world, I think it’s legitimate for me to assume preferences that are “well behaved” even though we know people’s psyches aren’t so well behaved because if we’re engaged in social and political engineering – which we are all the time by default or design – we are (arguably) entitled to make that assumption.

    If we had a perfect science of taking into account the world precisely as it is we might not be justified in doing so, but we won’t ever have that luxury and so when faced with the alternative of throwing up our hands in ignorance (which we rapidly have to do if we’re trying to make predictions about what will come to pass) we can sometimes, perhaps often, make some progress in taking our ethical reasoning further in this way.

  23. Nick, Conrad,

    such as, in this case? We are just going in circles here. If you understand this model and it is useful, surely you can give me an example of its usefulness over and above existing stuff?

  24. Paul, my opinion is much more similar to yours than the article that I linked (which is basically the position of Nicholas), and I think models should, in general, go out there and collect variance etc. and not just show some interesting idea.

    However, there are exceptions to this. For example, in my area (how people process language and read), one of the computational models showed that you potentially only need one mechanism to construct the sound of a word from it’s letters (i.e., read aloud). Previously, everyone had assumed that you need two main mechanisms (which are themselves further broken down into smaller components just to complicate things further), one which is basically a mental dictionary for words that you have encountered before, and a second which is a rule-based mechanism which allows the bits of words to be read in case you haven’t seen the word before (e.g., you can read: stoddle). The interesting aspect of the model was that it allowed nonlinear aspects of the problem to be learnt, and also allowed a number of predictions to be made about how people read (both with normals and with people with acquired injuries). At the time, no-one had really tried to push this idea at all (it’s very hard to imagine how non-linear systems work and the predictions they make, let alone convince people of them if you can only do it verbally), and it led to a proliferation of experiments and data collection that helped increase our understanding of the models available and reading more generally. This was basically because the predictions it made and the data it produced were tractably understandable even though the model itself learns non-linear patterns. I imagine it is also far easier to get data to test in this area than economics (you can just run experiments ad-nauseum if you want, manipulate any old characteristics of stimuli you want and think are important, and the data you get is generally ecologically fine, even from university students).

    Now, as it turns out, the model was wrong in many ways, and when tested quantitatively, it is hopeless — it captures less various than a simple regression equation with a couple of obvious variables in it (the top model for collecting variance in this area collects more than 5 times as much). However, without that model, I imagine we would have been stuck arguing with people who believed in an even older model that whilst likely to be closer to reality than the non-linear model, isn’t as good as the newer models that had to take far more constraining data into account that otherwise wouldn’t have been collected (the older model is, however, conceptually much simpler to understand which seems to be important for convincing people it must be the best model in the social sciences!). So it seems fair to say that the non-linear model did allow people to understand how a very complex system might work in a way that they hadn’t really thought of before, even though it turned out to be wrong.

    There are in fact now a few really good models like this my area. One of the interesting things is that there are models in overlapping domains that predict different processes occur in the overlapping areas (most people only work in one domain, so this hasn’t really upset them!), so the models are good at identifying which areas are certainly falsiable for some of the models, since in these cases, either one model is more right than the other, or they are both equally wrong. So again, the models help drive experimentation in the area and thus hopefully allows us to identify aspects of problelms that are important but generally overlooked.

  25. conrad,

    agreed but this is not the kind of model we are looking above. There are thousands and thousands of papers with models with very similar structures, all built upon things that have defied (and will defy) measurement for hundreds of years, yielding completely general results in worlds that neither exist nor vaguely resemble anything you have ever seen. And the excuse for asking society to keep propping up the wages of people producing more of these things is that one day in the far future in a galaxy yet to be discovered we will see just how right and insightful each and everyone of these things are. For dont you want to know too about fairness, altruism, and the optimal allocation of all goods under all states of Nature? Sigh.

  26. “all built upon things that have defied (and will defy) measurement for hundreds of years, yielding completely general results in worlds that neither exist nor vaguely resemble anything you have ever seen.”

    It’s the public that want it — I assume here that the leading journals in economics all need “generally interesting” papers, i.e., things that don’t tackle specific issues, and doing stuff that takes years (e.g., data collection) obviously isn’t a good way to keep your output up unless you have an army of smart graduate students, and nor is it a good way to increase your citations (since how will your papers get cited lots if it takes years of data collection to extend your ideas?). The public then decides on which university they want to go to based almost entirey on this, and the government then colludes by making league tables etc. highlighting this and even how our universities compare to the rest of the world on this metric (and again, almost no others).

    I might note that I’ve got lots of sympathy for people that don’t want to play this game. Psychology has exactly the same problem as it is dominated by neuroscience because the public thinks that you learn more from that (it must be true, you have pictures of the brain!), even though in all reality, we’ve learnt SFA from it in terms of human cognition despite the billions upon billions spent.

    Here’s a true story: The guy I used to work for when I did my post-doc had a great question that he’d ask all the people doing fMRI (brain imaging) which was:”what have you learnt about language that we didn’t already know via other methods”. The response was usualy either deafening silence, or something that was incorrect. I hate to think of the billions upon billions that have been spent learning this, although admittedly it’s far worse in the US where people need to find 2 months of wages (and wasting money doing fMRI studies is an easy way to get it), than here.

  27. conrad,

    interestingly, the top journals are of the same mind as I am: new models and methods nowadays need ‘an application’ to get into the top journals, which I think is a very good development. As a result of this development, the standing of some of the more esoteric journals has dropped and the models you see in top journals are far more applied and useful than they used to be. Definitely progress. The paper above is in an area not yet subjected to that same treatment, but given the vast numbers of them I would think it wont be too long until that kind of stuff too wont get into good journals without clear examples.

    As to empirical work, one of the more interesting developments has been that research support for top economists has become absolutely fantastic. Many of us can afford several full-time RAs to gather and analyse data for us. Particularly in some areas of macro and development the average amount of data effort going into a single top publication is just phenomenal. Indeed, so phenomenal that people without that generous support don’t have a look-in. The problems are hence less those of lack of incentives for data-work, more the difficulties in interpreting actual data.

  28. Tel -
    “When they dropped the atom bomb over Japan, that was an inductive prediction. Same with the rest of science and technology. All of it.”

    The mainstream (and commonsense) view would be that induction plays a role in technology but that science theory is necessarily deductive. As is economic theory.

    You don’t see deduction anywhere at all?

  29. A. Models. The discussion seems to be conflating different sorts of models. There are at least three:
    1. Normative models attempt to make an argument that tests the logic of a moral position as in the brain in a vat model or the Wilt Chamberlain model. There is nothing to be tested here.
    2. Explanatory models try to throw some light on what is happening by constructing some sort of analogy. They also help us explore consequences of our assumptions. Examples: would it be possible to have a planned economy or would an economy in which individuals were free to pursue their own goals.
    3. Positive models are for testing.

    B. Examples of where I think differently. (I presume you mean as a result of models although logical arguments are simply models).
    1. Outside of physical phenomena I am not sure what the real world is. The only approximate real world example that comes to mind is the proof of the Poincare conjecture and its implications for understanding the shape of the universe.
    2. Interpreting reality more loosely, most of what I understand comes from models of various sorts. There are lots of examples.
    (i). Social choice theory tells me that a lot of things I thought reasonable like unrestricted domain etc etc don’t really make much sense.
    (ii) The post Sraffa proofs that the labour theory of value won’t hold under certain conditions convince me that I might need to abandon marxian political economy.
    (iii) Walrasian equilibrium theory tells me that the conditions required for stability in a pure market are so restrictive that I shouldn’t expect it and that a lot of economic analysts don’t seem to understand their own theoretical foundations.
    (iv) Together with (iii) the Cambridge capital controversy tells me that maybe I should think about returning to the marxian model in a reconstructed form (eg Sraffa, von Neumann).
    (v) Explorations in the probability of various outcomes (gambler’s ruin and all that) tell me that if you have a desert based theory of reward you need to support an extensive form of collective insurance.
    (vi) Kalia’s theorem on proportional welfare tells me that starting with pretty weak assumptions you are forced into an egalitarian outcome and this pushes me in this direction.
    (vii) From game theory I learn that as soon as you move away from a situation where the number of buyers and sellers is arbitrarily large you will almost always generate sub-optimal outcomes. This makes me suspicious of market solutions and tells me what to be suspicious of.
    (viii) In moral philosophy arguments about rights, utilitarianism, ownership, justice (many of these formalized as in the industry around the Rawsian theory of justice) etc etc
    (ix) etc etc

    C. On a few random statements
    1. Bamboozled. Do you mean you think I don’t understand the mathematics in this paper or that I don’t understand mathematics more generally?
    2. If not first principles what – second or third principles perhaps?
    3. Pareto improvement. Why would I need to see one? I haven’t seen an economy or aggregate capital, or a society, or a payoff function etc etc either. Or did you mean to say something else?

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