Abstract Experimental data show a number of plateaus of varying widths in the magnetic-field dependence of the electron-spin-polarization for fractional quantum Hall states. We have calculated the magnetic-field dependence of the spin polarization using a new theory. We start by adopting the Landau gauge and ignoring Coulomb interactions between electrons; then we construct single electron states in equally spaced orbitals. For a number of filling factors we have examined the many-electron states with electron configurations having minimum classical Coulomb energy. The residual Coulomb interactions in each many-electron state produce spin-exchange-forces. We have solved the eigenvalue problem of the interaction Hamiltonian composed of nearest neighbor spin-exchange-interactions. From the eigenvalues we have calculated the magnetic-field dependence of the spin polarization. Our results are in good accord with the magnetic-field dependence in experimental results, including the number and shape of the plateaus.