In a case-based reasoning system, one simple approach to assessment of similarity of cases to a given problem situation is to create a linear ordering of the cases by similarity according to each relevant domain factor. Using Arrow's Impossibility Theorem, a result from social welfare economics, a paradox is uncovered in the attempt to find a consistent overall ordering of cases by similarity that satisfactorily reflects these individual rankings. The implications of the paradox for case-based reasoning are considered.
