  We study the dynamics of exciton-polaritons in a double-well configuration.
The system consists of two weakly coupled Bose-Josephson junctions, each
corresponding to a different circular polarization of the polaritons, forming a
{\it Josephson double dimer}. We show that the Josephson oscillation between
the wells is strongly coupled to the polarization rotation and that
consequently Josephson excitation is periodically exchanged between the two
polarizations. Linearized analysis agrees well with numerical simulations using
typical experimental parameters.
