An arbitration process ensures changes made by more than one node to the same data are propagated to each node holding the shared entity and applied in the same order on each node. An arbitration cycle for a particular entity is begun on a node ("instigator") when the node broadcasts a proposal message or when the node ("observer") receives such a proposal message. Multiple nodes can be instigators during a single arbitration cycle. Each node that receives a proposal message sends a response message to the corresponding instigator. After each instigator node receives all the proposals in the arbitration cycle, it determines whether it is the winner of the arbitration cycle and broadcasts a closure message if it is. Each node determines an order in which to apply the changes when it has received all the proposals. Arbitration cycles associated with different items can be running concurrently.