Sharing the cost of redundant items

•We consider a group of agents with different needs who share the cost of indivisible public goods.•Examples include edges in networks and sharing the cost of a given (perhaps inefficient) graph.•We characterize a family of cost ratios measuring the relative liability of items across agents.•This family includes cost ratios based on the canonical counting liability index.•Based on this family we then generate cost sharing rules that are additive in costs.

We ask how to share the cost of finitely many public goods (items) among users with different needs: some smaller subsets of items are enough to serve the needs of each user, yet the cost of all items must be covered, even if this entails inefficiently paying for redundant items. Typical examples are network connectivity problems when an existing (possibly inefficient) network must be maintained.We axiomatize a family cost ratios based on simple liability indices, one for each agent and for each item, measuring the relative worth of this item across agents, and generating cost allocation rules additive in costs.