We introduce the use of negative preferences to produce solutions that are acceptable to a group of users. Using negative preference profiling, a system determines which solutions are unsatisfactory to individual users, and it is assumed that the remaining solutions are satisfactory. To satisfy all members of the group, the system can propose solutions that are not unsatisfactory to any of the ... [Show full abstract] group's members. This approach can find a large set of solutions that are acceptable to a group and simplify user profiling. To demonstrate these benefits, we implemented Adaptive Radio, a system that selects music to play in a shared environment. Rather than attempting to play the songs that users want to hear, the system avoids playing songs that they do not want to hear. Negative preferences can potentially be applied to other domains, such as information filtering, intelligent environments, and collaborative design.