Stochastic multicriteria acceptability analysis (SMAA) is a multicriteria decision support method for multiple decision makers in discrete problems. In SMAA, the decision makers need not express their preferences explicitly or implicitly. Instead, the method is based on exploring the weight space in order to describe the valuations that would make each alternative the preferred one. Inaccurate or uncertain criteria values are represented by probability distributions from which the method computes confidence factors describing the reliability of the analysis. In this paper we introduce the SMAA-2 method, which extends the original SMAA by considering all ranks in the analysis. In situations where the “elitistic” SMAA may assess large acceptability only for extreme alternatives without sufficient majority support, the more holistic SMAA-2 analysis can be used to identify good compromise candidates. The results are presented graphically. We consider also situations where partial preference information is available. We demonstrate the new method using a real-life decision problem.