A facility for operating a first node in a mesh network having other nodes is described. The first node directly receives signals each encoding an identifier of one of the other nodes, at least a portion of the signals also encoding an indication that the node having the identifier has appointed itself a routing node. The facility determines a first value equal to the number of unique node identifiers encoded in signals received during a first period of time, and a second value equal to the number of unique node identifiers encoded by signals received during the first period of time that also encode the indication. The facility determines a routing score for the first node based at least upon the first value and the second value that reflects the first node's suitability as a routing node in the mesh network.