Responsibility and solidarity principles in sharing the costs of cleaning a polluted river

To clean a polluted river, some agents must undertake operations that incur costs. The problem is to determine a fair method to share these expenses among agents. We consider the established methods of Local Responsibility Sharing and Upstream Equal Sharing, based on the responsibility principles of Absolute Territorial Sovereignty and Unlimited Territorial Integrity, respectively. We combine these with Total Solidarity, a method based on a solidarity principle. This yields new cost-sharing methods, which we characterize axiomatically.