Parables, Proverbs, Paradigms, and the Role of Axioms

[Itzhak Gilboa]

Economics is often criticized for producing too few scientific
theories of the type that one is used to see in the natural and life
sciences. For a rather mathematized field, economic theory produces
relatively little quantified predictions that are proved correct.
Moreover, many basic assumptions of economics were shown to be
violated in (carefully designed) laboratory experiments. Finally, the
field is criticized for being recruited for political causes, mostly
for the glorification of capitalism.

Many of us feel that, while all of the above are valid critiques that
should be taken seriously, economic theory still produces great
insights that change the way we think about social interactions, about
our personal decisions, etc. Economic theory can be viewed as
producing several types of “insights” that are not “theories”:

1. Parables: a story such as the prisoner’s dilemma or Akerlof’s
lemons resembles a parable. The listener is not supposed to think
only or even mostly about the story, but about potential analogs
thereof. The prisoner’s dilemma is not about prisoners, just as La
Fontaine fables are not about crows, foxes, and other animals that
they explicitly mention. Rather, these parables invite the listeners
to think of other cases. Which are the cases, and what is the precise
nature of the analogy are not part of the parable itself. It is thus
open to more than one interpretation. But it can clearly make the
listener view a specific case in a new light. (Ariel Rubinstein often
refers to economic models as “fables” or “tales”, though his usage is
a little different.)

2. Proverbs: a general rule, such as “information asymmetry leads to
Pareto sub-optimality” is akin to a proverb. As opposed to a parable,
a proverb aims at a generalization and is stated as a general rule.
Consequently, proverbs may explicitly contradict each other. For
example, there are contexts where one can quote both “too many cooks
spoil the broth” and “the more the merrier”, and their implications
will be in contradiction. The collection of proverbs does not provide
guidelines for the resolution of such contradictions. Still, proverbs
can be useful in organizing our thoughts, pointing out certain
regularities in our experiences, and so forth.

3. Paradigms: a general set of principles of thinking about the world,
such as utility maximization, can generate many specific theories and
is not confined to any of them. It is tempting to refer to such sets
as paradigms. (The term “paradigm” is fraught with many different
meanings, ranging from the way it’s used in philosophy of science to
the very different usage in experimental psychology. Trying to be
more precise, David Schmeidler and I referred to such constructs by
the term “conceptual framework”, but “paradigm” may be less
cumbersome.) Such a “paradigm” has a language to describe certain
situations, as well as rules for making predictions (or
recommendations) about them. For example, utility maximization refers
to a decision maker, alternatives, a utility function, and the
principle of utility maximization. Game theory, coupled with the
concept of Nash equilibrium, is another such paradigm, or “conceptual
framework”. It refers to players, strategies, outcomes, and utility
functions, and selects Nash equilibria from the set of outcomes.
Thus, these paradigms provide specific predictions (or
recommendations) in given models. But they do not specify the mapping
from the theoretical concepts to real life entities. One may commit
to use utility maximization and still have modeling choices in
specifying the alternatives: specific bundles, streams of
consumptions, etc. Similarly, applying Nash equilibria to a game
allows the modeler much freedom in specifying the players, the actions
(and the time horizon), the state space, etc

Common features of parables, proverbs, and paradigms are that they
provide us with insights, but they never commit to a specific
prediction. They are ways to organize our thoughts, but they lack the
user’s manual that would say which proverb applies when, which parable
is the most fitting, or how to translate a paradigm into theory.
Moreover, it appears that in many examples such user’s manuals will
have to be extremely messy and subject to constant adaptation to the
domain of application, as well as to the period, the culture, and so
forth. Critiques of economics may be right in expecting the domain to
do more in terms of specifying such user’s manuals that work. But it
would be wrong to dismiss the entire field because it produces more
insights than theories.

The above is relevant to the role of axiomatizations in decision
theory. We typically believe that axioms are useful from a normative
point of view because they can serve a rhetorical purpose: to convince
decision makers to make choices that they would not otherwise make.
We also appreciate the role of axioms in relating theoretical concepts
to observables, thereby delineating the scope of theories, verifying
that they are refutable, and indicating how they might be tested. But
axioms have an important role also from a descriptive viewpoint: when
we do not interpret a theory literally, different representations
thereof may appeal to us to varying degrees. For example, a theory
about people who maximize a utility function may seem highly
hypothetical. But a theory about people who make choices according to
a complete and transitive order may be deemed much more relevant.
Because, details aside, the two theories refer to the same decision
makers, a theorem that shows that equivalence is a powerful rhetorical
tool.

Axiomatic derivations therefore become more important the less
accurate we expect theories to be. Indeed, if we only measured the
degree of success of a theory by the accuracy of its predictions, say,
by an R-squared, then different mathematical representations of the
same theory would be just as useful and just as convincing. But if we
interpret the theory as a paradigm (or a “conceptual framework”),
helping us to conceptualize a particular situation, we find that
different mathematical representations make it more or less
compelling, arouse different associations, and so forth.

In other words, if we think of descriptive theories also as rhetorical
devices used in the context of a given discourse, mathematical results
about these theories may help people convince others of certain points
of view, despite the fact that the results are tautologies. In fact,
such tautologies can be viewed as a type of “framing effects”:
equivalent representations of the same object arouse different
reactions.

In the early days of mathematical economics, mathematics was perceived
by many as a tool that can help making economics more “scientific”,
generating accurate quantitative predictions regarding the behavior of
single decision makers as well as whole economies. Nowadays many
people seem to be less optimistic about the possibility of such
“scientific economics”, but they find that economic analysis is still
very useful, partly by providing insights and organizing principles.
It is interesting that, precisely when mathematics loses credence in
its ability to provide accurate numerical predictions, it gains
importance as a rhetorical tool, helping us to judge the relevance of
parables, proverbs, and paradigms.

[marco]

To me, the main descriptive role of axioms remains that of permitting
an easy, direct test of a theory by means of observable choice data
(It was only because vNM/Savage axiomatised their theories that Allais
could formulate such a beautifully clear-cut challenge). This role of
axiomatics is proving to be amazingly handy in the recent spate of
papers on 'psychological' procedural models of choice. How can you
establish whether a choice maker is using one procedure instead of
another, or any procedure at all? Well, if the observed choice data
violate the characterising axioms of a procedure, you can certainly
reject it without any further psychological musings (More challenging
is the role of axioms in accepting a theory -their power as tests-,
because of the difficulty in pinning down a suitable alternative
hypothesis).
Maybe (as Caplin argues) choice axioms can nowadays be thought as
capable of restricting not only choice data but other observable data
associated with choice, too (e.g. neurophysiological). Be that as it
may, I would prefer if we viewed axioms mainly as a bridge between
observable data and mathematically convenient formulations of a theory
(e.g. in the way GARP, Congruence etc. translate mathematically
tractable utility maximisation models into behavioural restrictions).
I am mildly worried by emphasising the aspect of rethorics. I hate the
sentence 'this axiom is not very convincing' (perhaps because it
typically is a prelude to a rejection...): let the data decide what is
convincing and what isn't, not rethorical criteria!
marco (mariotti)

[Dov]

Well put!

Instead of "paradigms" and "conceptual frameworks", why not
"discourse"? This will open the door to all the impossible possible-
worlds of pomo :) We can next talk about the various hegemonies in our
field(s), and show how they influence our discourse.

Your use of "rhetoric" (four times!) is bothering. I looked up the
dictionary and found out why this is so.

rhet⋅o⋅ric
–noun

1. (in writing or speech) the undue use of exaggeration or display;
bombast.
2. the art or science of all specialized literary uses of language in
prose or verse, including the figures of speech.
3. the study of the effective use of language.
4. the ability to use language effectively.
5. the art of prose in general as opposed to verse.
6. the art of making persuasive speeches; oratory.
7. (in classical oratory) the art of influencing the thought and
conduct of an audience.
8. (in older use) a work on rhetoric.

It doesn't matter much what meaning you give it (and obviously, being
the master you are entitled to do so). There is always the emphasis of
form over content and a hint to conning and marketing.

There is rhetoric in physics and mathematics, and it is of interest.
But it has no significance to the content of these branches of
knowledge. When rhetoric plays a major role in a scientific field, it
sounds like a bankruptcy of the field.

[Klaus Nehring]

One of the frustrations, even dangers of economic modeling, be it more
theoretical or more applied, is its looming “bad infinity”: economic
theory may appear as just “one damn model after another”.

If empirical observation would put tight and direct constraints on
which models deserve to be taken seriously at all, this combinatorial
explosion would be much less of a problem than it is in fact. I
broadly agree with Tzachi that the typically rather loose connection
between empirical observation and theories or models is central to
the epistemological predicament of economics, and should play a
central role in meta-economic discussions such as those about the role
of axioms.

An important role of axioms is to locate models – say models expressed
in terms of functional forms – in logical space. In this way, axioms
serve to generate an entire logically interrelated set of models, or
theoretical map of a space of possible models, rather than merely
informing us about one particular point in that space. This is
important not least because any particular model will be false with
near certainty (to the extent that truth-falsity of models is a
meaningful distinction to begin with). A well-developed theoretical
map informs us, for example, about the various ways a particular
putative benchmark model such as SEU may fail, and what difference
such failure would make.

In the context of decision making under uncertainty, we have a fairly
well-developed theoretical map at this point. This success is due in
no small part to the way in which the Savage axioms, for example,
break down the specificity of the SEU model into various axiomatically
described behavioral dimensions such as transitivity, probabilistic
sophistication, Independence (or better, I would suggest, utility
sophistication), that can be evaluated independently.

By contrast, to take another example, in the context of decision
making with self-control problems, we have a few models, but no
theoretical map yet. I believe that the value of the axiomatic work in
this area would be greatly enhanced if it leads to such a theoretical
map.