Rather than being free carriers or separated single-hole polarons, double holes in anatase TiO${}_{2}$ prefer binding with each other, to form an O-O dimer after large structural distortion. This pushes the hole states upward into the conduction band and traps the holes. Similar double-hole-induced O-O dimerization (a bipolaron) exists also in other transition metal oxides (TMOs) such as V${}_{2}$O${}_{5}$ and MoO${}_{3}$, which have the highest valence bands composed mainly of O 2p states, loose lattices, and short O-O distances. Since the dimerization can happen in impurity-free TMO lattices, independent of any extrinsic dopant, it acts as an intrinsic and general limit to the p-type conductivity in these TMOs.