Analogy in Decision Making

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 problem’s 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 that results from aggregating MCIB preferences is an MCIB preference.