Elicitation and context effects in judgments: Fixed sum versus fixed scale frames

Two apparently similar methods for making numerical judgments about a set of objects (point allocation and direct rating) have been shown to yield different profiles of values (here, numerical judgments) attached to Ranks. Direct rating typically leads to a nearly linear relationship of Value with Rank. When using point allocation, people tend to produce a half U-shape of Value with Rank, evidenced by a positive quadratic term in Rank, which is not present for direct rating. We argue that point allocation imposes a fixed-sum frame on the judgment task. Furthermore, certain problems, such as allocating a budget, are intrinsically framed as fixed-sum. These problems also lead to quadratic curvature of numerical judgment with Rank. We discuss the implications of these effects, both in formal and informal contexts.