The median problem is a classical problem in Location Theory: one searches for a location that minimizes the average distance to the sites of the clients. This is for desired facilities as a distribution center for a set of warehouses. More recently, for obnoxious facilities, the antimedian was studied. Here one maximizes the average distance to the clients. In this paper the mixed case is studied. Clients are represented by a profile, which is a sequence of vertices with repetitions allowed. In a signed profile each element is provided with a sign from {+,-}. Thus one can take into account whether the client prefers the facility (with a + sign) or rejects it (with a - sign). The graphs for which all median sets, or all antimedian sets, are connected are characterized. Various consensus strategies for signed profiles are studied, amongst which Majority, Plurality and Scarcity. Hypercubes are the only graphs on which Majority produces the median set for all signed profiles. Finally, the antimedian sets are found by the Scarcity Strategy on e.g. Hamming graphs, Johnson graphs and halfcubes.

Additional Metadata
Keywords Discrete location and assignment, Distance in graphs, Graph theory, Hamming graph, Johnson graph, consensus function, halfcube, majority rule, median, median graph, plurality strategy, scarcity strategy
Publisher Erasmus School of Economics (ESE)
Persistent URL hdl.handle.net/1765/26664
Citation
Balakrishnan, K., Changat, M., Mulder, H.M., & Subhamathi, A.R.. (2011). Consensus Strategies for Signed Profiles on Graphs (No. EI2011-34). Report / Econometric Institute, Erasmus University Rotterdam. Erasmus School of Economics (ESE). Retrieved from http://hdl.handle.net/1765/26664