"Rhetorics" and post-modernism
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Itzhak Gilboa
Aug 2, 2009, 11:21:39 AM8/2/09
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Thanks for the comments!
Re "rhetotic" -- I have indeed been abusing the term a bit. I tend to think of "bad rhetoric" as the kind of tricks that make you lose a debate but come up with great answers the morning after, and of "good rhetoric" as the new ways of looking at a problem that you can take with you and convince someone else. When I think of mathematics as a rhetorical tool, I think of the latter, and didn't mean all the negative baggage.
A bit of post-modernism, btw, is not so bad, especially if it justifies interesting mathematical results :) Seriously, I think we can't ignore the fact that many of our models help us think, but are not quite as precise as we'd like them to be. The big post-modern sin we should not commit is confusing the normative with the positive: it's one thing to say that "in the social sciences, everything we say is influenced by our personal background and interests" and it's another thing to accept this normatively. As long as we strive for objectivity, it's OK to admit that we may not have achieved it, or even that we will never achieve it. In this sense, scientific objectivity is like world peace: we may be realistic and admit we'll never get there, but it doesn't mean we shouldn't try.
Tzachi
Bart Lipman
Aug 2, 2009, 11:49:57 AM8/2/09
to decision_t...@googlegroups.com
The point I really don’t understand is why axioms are supposed to be persuasion devices. If you are suggesting we are trying to persuade agents to “act more sensibly,” I think that’s a useful goal but very different from what most economists are up to. Personally, I have little inclination to try to do that.
If you are suggesting that we are trying to persuade each other to take the predictions of the model more seriously, then I think that’s closer to what we actually do, but not a good way to put the point. Instead, I would say that this aspect of the value of axioms is that it helps us understand what the model is predicting and thus to evaluate whether we think we should use it to make predictions. Similarly, we may use the axioms to argue that this is the behavior we wanted to study and therefore this model helps us think more clearly about that behavior, whether we think it is predictively accurate or not. In other words, I would say that we’re not trying to persuade anyone of anything, just trying to get to the point of having models which predict better/yield more insight.
I also agree with Marco’s interpretation of the value of axioms. On the other hand, I don’t think that we have to see testing and prediction/insight as mutually exclusive goals.
Bart
Bart Lipman
Department of Economics
270 Bay State Road
Boston University
Boston, MA 02215
phone: 617-353-2995
fax: 617-353-4449
http://people.bu.edu/blipman
Check out the latest issue of Theoretical Economics
: http://econtheory.org
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David K. Levine
Aug 2, 2009, 1:31:22 PM8/2/09
to decision_t...@googlegroups.com, decision_t...@googlegroups.com
Much as I hate methodological disputes: to understand why axioms are crucial you should look at what happens when people design theories without axioms - you might want to go reread Matt Rabin's work, for example. It's easy to design special functional forms and decision models to fit particular bits of data. The problem is they rarely turn out to make sense beyond the particular bit of data they are fit to. Axiomatic theories have the advantage that they give some assurance that the theories make at least a modicum of sense - that they don't lead to strange and bizarre behavior under circumstances other than the particular data to which they were fit. For example - it's not that you couldn't write down a theory that violated transitivity that makes sense - it's that if you just wrote down a theory that happened to violate transitivity it almost certainly wouldn't make sense.
----- On 8/02/0909 09:28 am decision_theory_foru wrote -----
The point I really don't understand is why axioms are
supposed to be persuasion devices. If you are suggesting we
are trying to persuade agents to "act more sensibly," I
think that's a useful goal but very different from what most
economists are up to. Personally, I have little
inclination to try to do that.
If you are suggesting that we are trying to persuade each
other to take the predictions of the model more seriously,
then I think that's closer to what we actually do, but not a
good way to put the point. Instead, I would say that this
aspect of the value of axioms is that it helps us understand
what the model is predicting and thus to evaluate whether we
think we should us#
David K. Levine
John H. Biggs Distinguished Professor
Department of Economics http://www.dklevine.com/
Washington University in St. Louis phone: (314) 935-9529
Campus Box 1208 office: 336 Seigle
St. Louis MO 63130-4899
Itzhak Gilboa
Aug 3, 2009, 4:50:46 AM8/3/09
to decision_theory_forum
Consider the following imaginary scenario. You're teaching an econ
class and mention the first welfare theorem. Someone asks what it is
and you explain it, mentioning "consumers who maximize utility subject
to a budget constraint". Then a few students raise their hands.
Student 1: "Excuse me, but, with all due respect, this doesn't seem
very relevant to anything. I've never made decisions this way, and
most of the people I know don't even know what 'maximization' means."
Student 2 adds: "I happen to be a psych major, and I've been told that
utility maximization has been refuted in carefully run experiments. I
can dig up the reference somewhere."
And Student 3 chimes in : "I think that only economists can think that
this is what people do. You are very selfish yourselves, and
therefore you assume that everyone else is. You actually preach
selfishness to justify your own conduct."
Then you go back and explain the axioms that are equivalent to utility
maximization. The three students, and the rest of your class,
probably find the first welfare theorem slightly more relevant to real
life than they would if such an axiomatization didn't exist.
I think of this as "good" rhetoric in the sense that it's not a trick
that's used for gaining the upper hand in a debate. It's a real
argument. I don't think that this is very different from Bart's view,
as in "we may use the axioms to argue that this is the behavior we
Btw, I try to do it in classes -- I ask the students what they think
about globalization. They're suprised because they know I know
nothing about globalization. I'm just trying to have a discussion
along the lines above and thereby motivate the rest of the class. Of
course, this is a rhetorical device as well.
In any event, the main point can be stated without reference to
rhetoric or persuasion: if the theories we had were rather accurate,
there would be less of a need to consider different representations of
the same theory. It's precisely because they're not so accurate that
we use them as ways to conceptualize the world rather than actually
predict. And we evaluate them by trying to imagine how plausible they
are, rather than measure how accurate they are. This evaluation of
plausibility can greatly benefit from having different representations
of the same theory.
Is this rhetoric-free version more palatable? :)
Tzachi
class and mention the first welfare theorem. Someone asks what it is
and you explain it, mentioning "consumers who maximize utility subject
to a budget constraint". Then a few students raise their hands.
Student 1: "Excuse me, but, with all due respect, this doesn't seem
very relevant to anything. I've never made decisions this way, and
most of the people I know don't even know what 'maximization' means."
Student 2 adds: "I happen to be a psych major, and I've been told that
utility maximization has been refuted in carefully run experiments. I
can dig up the reference somewhere."
And Student 3 chimes in : "I think that only economists can think that
this is what people do. You are very selfish yourselves, and
therefore you assume that everyone else is. You actually preach
selfishness to justify your own conduct."
Then you go back and explain the axioms that are equivalent to utility
maximization. The three students, and the rest of your class,
probably find the first welfare theorem slightly more relevant to real
life than they would if such an axiomatization didn't exist.
I think of this as "good" rhetoric in the sense that it's not a trick
that's used for gaining the upper hand in a debate. It's a real
argument. I don't think that this is very different from Bart's view,
as in "we may use the axioms to argue that this is the behavior we
wanted to study and therefore this model helps us think more clearly
about that behavior". I'm just dramatizing this a bit.
Btw, I try to do it in classes -- I ask the students what they think
about globalization. They're suprised because they know I know
nothing about globalization. I'm just trying to have a discussion
along the lines above and thereby motivate the rest of the class. Of
course, this is a rhetorical device as well.
In any event, the main point can be stated without reference to
rhetoric or persuasion: if the theories we had were rather accurate,
there would be less of a need to consider different representations of
the same theory. It's precisely because they're not so accurate that
we use them as ways to conceptualize the world rather than actually
predict. And we evaluate them by trying to imagine how plausible they
are, rather than measure how accurate they are. This evaluation of
plausibility can greatly benefit from having different representations
of the same theory.
Is this rhetoric-free version more palatable? :)
Tzachi
Daron Acemoglu
Aug 3, 2009, 12:56:44 PM8/3/09
to decision_t...@googlegroups.com
This is very enjoyable and instructive for me, who is on this forum more
as an outsider. Though not a decision theorist by any stretch of
imagination, I do grapple with these questions very often.
But I guess my answer and general approach would be somewhat different.
At the risk of appearing naïve and ill-informed in front of such a
distinguished audience, I would say two things:
1. I guess I'm more optimistic than many on this forum about the role of
empirical work (experimental, econometric, historical and based on
introspection and casual empiricism). I think at the end of the day
economics is (ought to be) an empirical discipline. Therefore, our
models have to be judged on the basis of their "empirical success" or as
inputs into other models that will in the future generate "empirical
success"--- we cannot be in a cycle in which models are judged
continuously as "fables" with no hope of ever making contact with
empirical phenomena.
So what is "empirical success"? I don't think we have much choice here:
we have to define it in terms of some type of Popperian metric (not
necessarily strict Popper, but some variant thereof). But this metric
should not be applied to every aspect of the model because the phenomena
being modeled are too complicated, and thus many features of the model
are adopted for simplicity and clarity, and are auxiliary to the main
purpose of the model. Looked at through these lenses, I don't see the
difference between "predictions" and "insights" as clearly. When you
write down a model and would like to take it to data, you would not want
to confront all of the "predictions" of the model with data (putting in
the language of econometrics, you would not want to take all of the
"moments" implied by model and match them with corresponding moments
from the data). You would choose which "moments" are central,
corresponding to be "key predictions" of the model, and which ones are
incidental or likely to be "noisy" because of omitted factors.
Therefore, perhaps what we mean by "insights" are the "key predictions"
of the model, and the distinction between insights and predictions is
not very sharply drawn. For example, in Akerlof's lemon example, the key
prediction is not that all secondhand cars that are traded will be
lemons or that the market for secondhand cars will completely break
down, but (in my reading) it is that there will be a penalty for
secondhand cars (and only if there is no credible quality verification
mechanism for used cars). Moreover, this model is extremely useful as
input to other models, because it also highlights theoretical principles
that can be applied to a variety of different situations to develop new
"key predictions"(dynamic trading under adverse selection, mechanism
design, etc.).
Incidentally, I would add that this is also my understanding of the
approach to testing adopted in physics and biology. In neither
discipline, so far as I know, one would take all the implications of a
specific mathematical model to the lab or to the field.
If this perspective has some validity, then "testing axioms" needs to be
re-thought a little bit. The above perspective says that they are
exactly the aspects that should be "tested" if the axioms are the key
"predictions" of the model. They should not be tested if they are
building blocks towards another set of "key predictions".
2. Having said all that, I think one danger is the following: we write
down models for their clarity and parsimony with lots of auxiliary
assumptions that we do not believe in. For example, in most instances,
we would write down models in which people can rationally evaluate risk
and markets function very well, because these are good simplifying
assumptions, when they do not interfere with the "key predictions" we
would like to develop and communicate. But after having written many
such models, at some point, we, or our students, start believing the
simplifying assumptions. I think this is a particularly big problem in
macroeconomic modeling, and one can argue that these dynamics have
indeed played out, and many first-rate macroeconomists have incidentally
started to believe the incidental aspects of the models (forgive the
pun). If this is a real danger, then perhaps the types of philosophical
discussions being conducted on this forum are even more useful for the
long-run health of our profession.
Thanks
Daron
as an outsider. Though not a decision theorist by any stretch of
imagination, I do grapple with these questions very often.
But I guess my answer and general approach would be somewhat different.
At the risk of appearing naïve and ill-informed in front of such a
distinguished audience, I would say two things:
1. I guess I'm more optimistic than many on this forum about the role of
empirical work (experimental, econometric, historical and based on
introspection and casual empiricism). I think at the end of the day
economics is (ought to be) an empirical discipline. Therefore, our
models have to be judged on the basis of their "empirical success" or as
inputs into other models that will in the future generate "empirical
success"--- we cannot be in a cycle in which models are judged
continuously as "fables" with no hope of ever making contact with
empirical phenomena.
So what is "empirical success"? I don't think we have much choice here:
we have to define it in terms of some type of Popperian metric (not
necessarily strict Popper, but some variant thereof). But this metric
should not be applied to every aspect of the model because the phenomena
being modeled are too complicated, and thus many features of the model
are adopted for simplicity and clarity, and are auxiliary to the main
purpose of the model. Looked at through these lenses, I don't see the
difference between "predictions" and "insights" as clearly. When you
write down a model and would like to take it to data, you would not want
to confront all of the "predictions" of the model with data (putting in
the language of econometrics, you would not want to take all of the
"moments" implied by model and match them with corresponding moments
from the data). You would choose which "moments" are central,
corresponding to be "key predictions" of the model, and which ones are
incidental or likely to be "noisy" because of omitted factors.
Therefore, perhaps what we mean by "insights" are the "key predictions"
of the model, and the distinction between insights and predictions is
not very sharply drawn. For example, in Akerlof's lemon example, the key
prediction is not that all secondhand cars that are traded will be
lemons or that the market for secondhand cars will completely break
down, but (in my reading) it is that there will be a penalty for
secondhand cars (and only if there is no credible quality verification
mechanism for used cars). Moreover, this model is extremely useful as
input to other models, because it also highlights theoretical principles
that can be applied to a variety of different situations to develop new
"key predictions"(dynamic trading under adverse selection, mechanism
design, etc.).
Incidentally, I would add that this is also my understanding of the
approach to testing adopted in physics and biology. In neither
discipline, so far as I know, one would take all the implications of a
specific mathematical model to the lab or to the field.
If this perspective has some validity, then "testing axioms" needs to be
re-thought a little bit. The above perspective says that they are
exactly the aspects that should be "tested" if the axioms are the key
"predictions" of the model. They should not be tested if they are
building blocks towards another set of "key predictions".
2. Having said all that, I think one danger is the following: we write
down models for their clarity and parsimony with lots of auxiliary
assumptions that we do not believe in. For example, in most instances,
we would write down models in which people can rationally evaluate risk
and markets function very well, because these are good simplifying
assumptions, when they do not interfere with the "key predictions" we
would like to develop and communicate. But after having written many
such models, at some point, we, or our students, start believing the
simplifying assumptions. I think this is a particularly big problem in
macroeconomic modeling, and one can argue that these dynamics have
indeed played out, and many first-rate macroeconomists have incidentally
started to believe the incidental aspects of the models (forgive the
pun). If this is a real danger, then perhaps the types of philosophical
discussions being conducted on this forum are even more useful for the
long-run health of our profession.
Thanks
Daron
Bart Lipman
Aug 3, 2009, 9:00:01 PM8/3/09
to decision_t...@googlegroups.com
Daron, you make a number of excellent points. While I
hesitate to commit to agreeing with you completely before I
have absorbed all the implications, I'm tempted to do so...
Thankfully, I know I can't agree with you on macro because
my ignorance on the subject means that I have no idea
whether you're right or not.
I think part of why many theorists refer to "fables" and
"insights" is because testing is often taken to mean the
kind of testing that you quite rightly argue against.
Personally, I don't believe preferences are complete or
transitive, much less that they would satisfy independence.
Yet I find these very useful hypotheses for thinking about
other issues. I agree with your perspective that if we adopt
simplifications like these, it doesn't make sense to test
this part of our hypotheses.
I think part of the problem is theorists like me often don't
think about which parts of the model are to be taken
seriously and which not. After all, a theorem is an
implication of the full set of assumptions, so it doesn't
come naturally to us to say we believe the conclusion but
not certain of the assumptions. Consequently, it's hard to
identify a principled way to achieve this separation.
Finally, I agree that what we call "insights" are often
predictions, albeit in a less formal and less structured
form than the axioms of the model. On the other hand, I
think there's another kind of nonpredictive insight which is
when you come to not only make a particular prediction but
understand *why* that's the prediction. Arguably, this just
means that we understand how to generalize the prediction,
so it's a tricky distinction.
Tzachi, thanks for the clarification on rhetoric. I do
think we're saying more or less the same thing in different
words.
Bart
Bart Lipman
Department of Economics
270 Bay State Road
Boston University
Boston, MA 02215
phone: 617-353-2995
fax: 617-353-4449
http://people.bu.edu/blipman
Check out the latest issue of Theoretical Economics :
http://econtheory.org
hesitate to commit to agreeing with you completely before I
have absorbed all the implications, I'm tempted to do so...
Thankfully, I know I can't agree with you on macro because
my ignorance on the subject means that I have no idea
whether you're right or not.
I think part of why many theorists refer to "fables" and
"insights" is because testing is often taken to mean the
kind of testing that you quite rightly argue against.
Personally, I don't believe preferences are complete or
transitive, much less that they would satisfy independence.
Yet I find these very useful hypotheses for thinking about
other issues. I agree with your perspective that if we adopt
simplifications like these, it doesn't make sense to test
this part of our hypotheses.
I think part of the problem is theorists like me often don't
think about which parts of the model are to be taken
seriously and which not. After all, a theorem is an
implication of the full set of assumptions, so it doesn't
come naturally to us to say we believe the conclusion but
not certain of the assumptions. Consequently, it's hard to
identify a principled way to achieve this separation.
Finally, I agree that what we call "insights" are often
predictions, albeit in a less formal and less structured
form than the axioms of the model. On the other hand, I
think there's another kind of nonpredictive insight which is
when you come to not only make a particular prediction but
understand *why* that's the prediction. Arguably, this just
means that we understand how to generalize the prediction,
so it's a tricky distinction.
Tzachi, thanks for the clarification on rhetoric. I do
think we're saying more or less the same thing in different
words.
Bart
Bart Lipman
Department of Economics
270 Bay State Road
Boston University
Boston, MA 02215
phone: 617-353-2995
fax: 617-353-4449
http://people.bu.edu/blipman
Check out the latest issue of Theoretical Economics :
http://econtheory.org
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Itzhak Gilboa
Aug 4, 2009, 3:54:04 AM8/4/09
to decision_theory_forum
Re insights and predictions: I'm very sympathetic to the idea that
"insight" can be translated into predictions, by thinking about
classes of outcomes that might arise etc. I also agree that, in
general, part of our data is a result of introspection. (This is why
I think part of philosophy -- the part I can understand -- is a social
science.)
But I still think that there is a useful distinction. (And the
distinction between black and while also has grey areas :)) One
possible way to draw the line has to do with whether you expect
another scientist to complete the job. When you have a good-enough
approximation and you, as a scientist, decide that it's not worth
delving further into fine-tuning the model, we can think of it as an
approximation, the best quantitative prediction that is worth
obtaining. By contrast, when you have a general insight such as
Akerlof's lemons, you still know that some work need to be done (by a
"scientist") before you draw implications regarding, say, the
insurance market.
Insights can be viewed as theories that tend to prefer generality and
simplicity to accuracy. But I don't think we have good measures of
this tradeoff as we do in the case of model selection in statistics.
What does this have to do with the role of axioms? I'm not sure, and
I guess that opinions vary to a large degree. How about the following
weak monotonicity rule: the importance of axioms for descriptive
models is at least as high when it comes to general insights, which
are not directly tested and quantified, as it is for specific
theories, which are -- ?
Tzachi
"insight" can be translated into predictions, by thinking about
classes of outcomes that might arise etc. I also agree that, in
general, part of our data is a result of introspection. (This is why
I think part of philosophy -- the part I can understand -- is a social
science.)
But I still think that there is a useful distinction. (And the
distinction between black and while also has grey areas :)) One
possible way to draw the line has to do with whether you expect
another scientist to complete the job. When you have a good-enough
approximation and you, as a scientist, decide that it's not worth
delving further into fine-tuning the model, we can think of it as an
approximation, the best quantitative prediction that is worth
obtaining. By contrast, when you have a general insight such as
Akerlof's lemons, you still know that some work need to be done (by a
"scientist") before you draw implications regarding, say, the
insurance market.
Insights can be viewed as theories that tend to prefer generality and
simplicity to accuracy. But I don't think we have good measures of
this tradeoff as we do in the case of model selection in statistics.
What does this have to do with the role of axioms? I'm not sure, and
I guess that opinions vary to a large degree. How about the following
weak monotonicity rule: the importance of axioms for descriptive
models is at least as high when it comes to general insights, which
are not directly tested and quantified, as it is for specific
theories, which are -- ?
Tzachi
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