  Based on a symmetry argument, we investigate the ground-state properties of
newly synthesized metal-halide ladder compounds
(C_8_H_6_N_4_)[Pt(C_2_H_8_N_2_)X]_2_(ClO_4_)_4_ 2H_2_O (X=Cl, Br, I). Employing
a fully dressed two-band Peierls-Hubbard model, we systematically reveal
possible charge- or spin-ordered states. Numerical phase diagrams demonstrate a
variety of competing Peierls and Mott insulators with particular emphasis on
the transition between two types of mixed-valent state of Pt^II^ and Pt^IV^
driven by varying interchain hopping integrals and Coulomb interactions.
