An unfolding model for continuous bounded responses is proposed, derived both from a hypothetical interpolation response mechanism and from the hypothesis of two opposite sources of item refusal being collapsed. These two sources of refusal are made explicit in a three-component Dirichlet response model and then collapsed to obtain a (two-component) beta response model. The two natural parameters of the beta are interpreted as acceptance and refusal parameters and expressed as functions of person-item distances on a latent continuum. The potentially bimodal shape of the beta is exploited to model chaotic response choices among ambivalent subjects.