An assessment of the consequences of biological invasions and of the measures taken against must be at the base of each social decision in this field. Three forms of uncertainty can be distinguished that make such a decision difficult to take: (1) factual uncertainty, which encompasses not only risk, but also unknown probabilities of known consequences, and unknown consequences, (2) individual uncertainty, i.e. insecurity about the values to consider, and about the form how to consider them, and (3) social actor uncertainty, i.e. uncertainty about the social actors to consider and how to do it. This paper furnishes axiomatic reflections about the difficulties of assessments integrating these three uncertainties. Using this analytical separation, it restructures two main assessment techniques, and herewith shows the main differences between cost-benefit-analysis and multi-criteria decision aid in supporting public decisions about biological invasions. It is shown that the main difference between cost-benefit-analysis, the classical economic decision support, and multi-criteria decision analysis is less its mono- vs. multi-criteria approach, but its facility to be embedded in a social decision context. With multicriteria decision aid it is more facile to lay open the uncertainties in all three dimensions and to make them an explicit topic for public discourse. Therefore, it seems more suitable as an assessment method for biological invasions.