A method is presented for helping patients who have laryngeal cancer to decide between laryngectomy and radiotherapy in cases where these treatments are deemed medically equivalent. The method is based on the model of additive conjoint measurement. The treatment with the higher utility is determined from pair comparisons among outcomes that vary in quality and quantity of life. Pair comparisons enable a (partial) test of the axioms of additive conjoint measurement. This is in contradistinction to earlier work on decision making for patients with laryngeal cancer, and most of the work in medical decision making in general, in which underlying axioms have almost never been tested. Besides testing the axioms, another important advantage of pair comparisons is that they avoid difficulties with other, risk-based, assessment procedures by presenting only riskless alternatives. Encouraging results have been found in a study among patients.