Water solvated polymeric dyes and polymeric tandem dyes are provided. The polymeric dyes include a water solvated light harvesting multichromophore having a conjugated segment of aryl or heteroaryl co-monomers linked via covalent bonds, vinylene groups or ethynylene groups. The polymeric tandem dyes further include a signaling chromophore covalently linked to the multichromophore in energy-receiving proximity therewith. Also provided are labeled specific binding members that include the subject polymeric dyes. Methods of evaluating a sample for the presence of a target analyte and methods of labeling a target molecule in which the subject polymeric dyes find use are also provided. Systems and kits for practicing the subject methods are also provided.