The importance of quantum mechanical exchange in determining the electronic properties of molecules has long been appreciated. Less attention has been paid, however, to how exchange affects the properties of quantum mechanical objects in the presence of a solvent. How important are spin statistics in determining the structure and dynamics of such objects? For instance, do fully solvent-supported single-electron states, such as solvated electrons, interact with each other in such a way that quantum mechanical exchange and correlation must be taken into account? That is, does the Pauli exclusion principle enhance or supress the formation of bound pairs of solvated electrons, so-called bipolarons, and what role does the solvent play? We have approached this question by performing mixed quantum/classical molecular (QM/CM) dynamics simulations of two excess electrons solvated by bulk liquid water. The mixed QM/CM molecular dynamics is performed at the level of the Born-Oppenheimer approximation, so that the water motions obey classical mechanics and the electronic degrees of freedom evolve on the ground state adiabatic energy surface. The two-electron adiabatic eigenstates are calculated with full configuration interaction (CI) using a highly efficient real-space method that we have recently introduced (Larsen, R. E.; Schwartz, B. J. J. Chem. Phys. 2003, 119, 7672) to compute the Coulomb and exchange interaction energies. Our calculations show that two excess electrons form dielectrons, that is, they are confined by the solvent to a single cavity for both singlet and triplet pairing of the electron spins. When the electrons' spins are singlet paired, the dielectron is confined to an aspherical, "potato-shaped" cavity, whereas when the electrons' spins are triplet paired, the dielectron occupies a "Peanut-shaped" cavity. We find that in both cases water molecules in the first solvation shell solvate the hydrated dielectron by pointing one of their O-H bonds directly toward the charge, just as occurs with a single hydrated electron. We examine the time evolution of various dielectron properties and compare and contrast the dielectron dynamics with the dynamics of a single hydrated electron. Finally, taking advantage of the fact that our CI calculation generates both ground and excited states, we have computed the optical absorption spectra of both singlet and triplet dielectrons. We discuss the significance of the predicted optical absorption spectra for the possible direct spectroscopic observation of hydrated dielectrons.