Adding up reasons: Lessons for reductive and nonreductive approaches

How do multiple reasons combine to support a conclusion about what to do or believe? This question raises two challenges: (1) How can we represent the strength of a reason? (2) How do the strengths of multiple reasons combine? Analogous challenges about confirmation have been answered using probabilistic tools. Can reductive and nonreductive theories of reasons use these tools to answer their challenges? Yes, or more exactly: Reductive theories can answer both challenges. Nonreductive theories, with the help of a (new?) result in confirmation theory, can answer one, and there are grounds for optimism that they can answer the other.