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Theory and Decision

Erschienen in:

04.01.2019

What are axiomatizations good for?

verfasst von: Itzhak Gilboa, Andrew Postlewaite, Larry Samuelson, David Schmeidler

Erschienen in: Theory and Decision | Ausgabe 3-4/2019

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Abstract

Do axiomatic derivations advance positive economics? If economists are interested in predicting how people behave, without a pretense to change individual decision making, how can they benefit from representation theorems, which are no more than equivalence results? We address these questions. We propose several ways in which representation results can be useful and discuss their implications for axiomatic decision theory.

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See Dekel and Lipman (2010) and Luce et al. (1990) for related discussions.

It is interesting to observe that both approaches date back to the 1950s at the latest (see, e.g., Luce and Suppes 1965 on stochastic choice), but that they recently seem to have moved to center stage after several decades in which they received less attention.

We refer to this type of justification as “meta-scientific” as it involves modeling of the work of scientists, as described in Sect. 2.2. above. It is not part of the work of the applied economist who attempts to explain or to shape economic reality; rather, it is part of the work of the philosopher or sociologist of science, who attempts to verify that the aforementioned economist does not use ill-defined terms and does not develop irrefutable, meaningless theories.

Specifically, we refer to Gilboa et al. (2009, 2012) who discuss the appeal of Savage’s axioms and the importance of the state space to which they are applied.

This is in line with our views of economic models as rhetorical devices (see Gilboa et al. 2014, 2106). Our focus here, however, is on the choice of modeling tools rather than on specific models.

Axiomatizations that are effective as rhetorical devices can also be thought of “framing effects”: a decision rule that may appear unreasonable in one representation may be more compelling in another.

As pointed out to us by Ivan Moscati, these and other leading economists varied in their motivation and in their views of expected utility as a normative and/or descriptive model of choice. We thank a referee for pointing out that economists at the time were apt to blur the distinction between normative and descriptive models. For example, Arrow (1951, p. 406) writes that, “In view of the general tradition of economics, which tends to regard rational behavior as a first approximation to actual, I feel justified in lumping the two classes of theory together.” One contribution of Kahneman and Tversky (1979) was to argue that descriptive models can be improved by not insisting they be normative.

Moscati (2018) describes early empirical investigations of the expected-utility axioms.

Among the best known violations of expected utility theory, preference reversals strike at the heart of the transitivity axiom. See Lichtenstein and Slovic (1971), Lindman (1971) and Grether and Plott (1979).

This is a real case that has not been analyzed by professional historians of science. It is based on the authors’ own impressions and personal histories.

We thank Peter Wakker for this and related observations.

Handa (1977) suggested the same formula where v was the identity.

This turned out to be a special case of Choquet expected utility theory (Schmeidler 1989).

Clearly, “convincing people” should be operationalized in a quantitative manner. Some people may be convinced to follow a decision model, while others may not; they may accept it for some applications but not for others, etc. Note that these measurement issues apply both to the term “normatively appealing” and to “objectively rational”.

Other concepts can be “qualitative probability”, “cost of temptation”, “similarity”, etc.

Famously, Savage also ridiculed his own defense by writing “I don’t mind being hanged as long as my reputation and good health are unharmed”. See Gilboa (2009) for further discussion of the delineation of applications in which state-dependent utility is unavoidable.

In the first, self-report has famously been used to measure well-being. Despite many problems with this measurement tool, “Subjective Well-Being” is still considered an important source of information. Likewise, in Aumann’s example involving the decision maker’s wife self-report would be a way to find out that the measured probability does not correspond to his beliefs.

See Moscati (2018) for a discussion of the development of utility theory.

See Cozic and Hill (2015) on axiomatizations as definitions of theoretical terms.

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Titel: What are axiomatizations good for?
verfasst von: Itzhak Gilboa
Andrew Postlewaite
Larry Samuelson
David Schmeidler
Publikationsdatum: 04.01.2019
Verlag: Springer US
Erschienen in: Theory and Decision / Ausgabe 3-4/2019
Print ISSN: 0040-5833
Elektronische ISSN: 1573-7187
DOI: https://doi.org/10.1007/s11238-018-09685-1

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