This paper reports a qualitative study on students' informal reasoning on a controversial socio-scientific issue. Twenty-two students from four science classes in Norway were interviewed about the local construction of new power lines and the possible increased risk of childhood leukaemia. The focus in the study is on what arguments the students employ when asked about their decision-making and the interplay between knowledge and personal values. Five different types of main arguments are identified: "the relative risk argument, the precautionary argument, the uncertainty argument, the small risk argument, and the pros and cons argument". These arguments are presented through case studies, and crucial information and values are identified for each argument. The students made use of a range of both scientific and non-scientific knowledge. The findings are discussed in relation to possible consequences for teaching models aimed at increasing students' ability to make thoughtful decisions on socio"scientific issues. (Contains 5 figures.)