Making a choice between multidimensional alternatives is a difficult task. Therefore, a decision maker may adopt some procedure (heuristic) to simplify this task. We provide an axiomatic model of one such heuristic called the Intra-Dimensional Comparison (IDC) heuristic. The IDC heuristic is well-documented in the experimental literature on choice under risk. The IDC heuristic is a procedure in which a decision maker compares multidimensional alternatives dimension-by-dimension and makes a decision based on those comparisons. The model of the IDC heuristic provides a general framework applicable to many different contexts, including risky choice and social choice.