Memory and Similarity: a Graph-Theoretic Model for Case Based Decision Theory

Most approaches to Decision Theory do not represent explicitly the fact that individuals use their memories to make their choices, i.e., that they reason by analogy with past instances of decision making. Gilboa and... [ view full abstract ]

Most approaches to Decision Theory do not represent explicitly the fact that individuals use their memories to make their choices, i.e., that they reason by analogy with past instances of decision making. Gilboa and Schmeidler's Case Based Decision Theory (CBDT) tackles this question, advancing the idea that an individual evaluates each possible alternative based on the sum of the utility levels that resulted from choosing it in previous cases stored in his memory. This sum is weighted up by the similarity between past cases and the current instance.
Effective applications of CBDT require actual representations of the similarity functions. In fact, there might exist many possible interpretations of the "similarity between cases" relation. In this paper we propose an axiomatization that allows us to represent similarity in terms of a shortest-path distance in a graph. Our goal is to provide a practical tool for the application of CBDT as well as a structural characterization of similarity. In this sense, our framework provides a constructive version of CBDT.