In recent years, surface segregation of doping elements in layered oxide positive electrode (cathode) materials for metal-ion batteries has drawn considerable attention. It was repeatedly shown that an increase of surface concentration of a particular element can have either detrimental or beneficial impact on the stability of the electrochemically active surface, manifesting declined or improved electrochemical performance. However, the physical and chemical reasons for segregation remain poorly understood. To explain the behavior of commercially important doping elements, such as Mg, Al, Ti, V, Cr, Mn, Fe, and Ni, we performed a density functional theory study of their segregation at the (104) low-energy surface of ${\mathrm{LiCoO}}_{2}$. By careful control of local oxidation states and magnetic moments of surface atoms, we find their most stable configurations. We discover that all elements, except Al and Cr, are prone to segregation that is primarily driven by the surface energies' difference between the host and solute lattices, which is explained through crystal-field stabilization energies. An additional contribution to segregation is caused by the elastic energy penalty to the ionic size mismatch effect. Finally, we rationalize the available experimental results and provide several predictions of highly segregating and nonsegregating dopants.