Unfolding theory, developed by Clyde Coombs in 1950, provides a geometric model of preference in which both persons and stimuli are represented as points in the same psychological space. A person's preference ordering over stimuli is determined by the distances from the person's ideal point to each stimulus point: closer stimuli are more preferred.
The Unfolding Model
Consider stimuli arranged along a single dimension. If person j has ideal point θⱼ, the preference for stimulus i with position sᵢ is a decreasing function of |θⱼ − sᵢ|. "Unfolding" the preference ranking recovers the joint scale of persons and stimuli. The name comes from visualizing the preference order as a "folded" version of the underlying scale, folded at the ideal point.
U(i, j) = −d(sᵢ, θⱼ)²
In one dimension: U(i, j) = −(sᵢ − θⱼ)²
Multidimensional Unfolding
The model extends naturally to multiple dimensions, where stimuli and persons are points in a k-dimensional space and preference is determined by Euclidean distance. Multidimensional unfolding recovers both the stimulus configuration and the ideal points from preference data, revealing the dimensions along which preferences vary and how individuals differ in their ideals.
Unfolding theory has been applied to political ideology (voters and candidates as points on a liberal-conservative dimension), consumer preferences, and attitude measurement. It provides a richer model than simple ranking because it explains why different people have different preference orders: they have different ideal points in the same underlying space.