first, all subjects are assumed to have a utility function, determined by their individual gains from treatment and costs from treatment. based on an underlying assumption of monotonicity, the never-takers, compliers, and always-takers can be arranged on the same continuum based on their utility function. this assumes that the always-takers have such a high utility from taking the treatment that they will take it even without encouragement. on the other hand, the never-takers have such a low utility function that they will not take the treatment despite encouragement. thus, the never-takers can be aligned with the compliers with the lowest utilities, and the always-takers with the compliers with the highest utility functions.