Analogy in Decision Making
نویسنده
چکیده
In the context of decision making under uncertainty, I formalize the concept of analogy: an Analogy between two decision problems is a mapping that transforms one problem into the other while preserving the problems structure. After identifying the basic structure of a decision problem, I introduce the concepts of Analogical Reasoning Operator and of Analogical Reasoning Preference. The former maps the decision problem at hand into a family of decision problems, which are analogous to the problem under consideration. The latter is the result of aggregating the various analogies. I provide several representations (in decreasing order of generality) of the analogical reasoning operators. After introducing two mild assumptions on the aggregators of analogies, I characterize analogical reasoning (AR) preferences. I give several examples of AR preferences and of the associated aggregators. These include Gilboa-Schmeidler similarities, Choquet integrals and quantiles. Finally, I show that the class of Monotone Continuous Invariant Biseparable (MCIB) preferences (which includes many popular models of decision making under uncertainty) has an important stability property: Any MCIB preference is an AR preference; conversely, every AR preference which results from aggregating MCIB preferences is an MCIB preference. Key words and phrases. Analogy, kernels, Analogical reasoning operator, Invariant Biseparable preferences, Choquet integral JEL classi cation: D81 I am grateful to Mario Ghossoub, Tzachi Gilboa, Marcus Pivato and David Schmeidler for several conversations we shared on this papers subject. 1 2 MASSIMILIANO AMARANTE
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عنوان ژورنال:
- Math. Oper. Res.
دوره 40 شماره
صفحات -
تاریخ انتشار 2015