We study the biOWA model for preference aggregation and multicriteria decision making from bipolar rating scales. A biOWA is an ordered doubly weighted averaging extending standard ordered weighted averaging (OWA) and allowing a finer control of the importance attached to positive and negative evaluations in the aggregation. After establishing some useful properties of biOWA to generate balanced Pareto-optimal solutions, we address fair biOWA-optimization problems in combinatorial domains. We first consider the use of biOWA in multi-winner elections for aggregating graded approval and disapproval judgements. Then we consider the use of biOWA for solving robust path problems with costs expressing gains and losses. A linearization of biOWA is proposed, allowing both problems to be solved by MIP. A path-ranking algorithm for biOWA optimization is also proposed. Numerical tests are provided to show the practical efficiency of our models.