In this proposal, the P. I. will investigate a series of measurement-theoretical issues clustered around three types of decision-making problems: optimization problems, consensus problems, and judgments of closeness. For each class of problems, the P.I. lists a series of important applications, and identifies a series of unsolved theoretical questions, most of them related to the issue of meaningfulness. These research questions evolve around the question of whether the solution to an optimization or consensus problem or a particular judgment of closeness or distance is `meaningful,` in the sense that it is not an artifact of the particular measurement scale on which input variables were assessed.
