We study the formation of disk-dominated galaxies in a \Lambda CDM universe . Their existence is considered to be a challenge for the \Lambda CDM cosmology , because galaxy mergers isotropize stellar disks and trigger angular momentum transport in gas disks , thus fostering the formation of central stellar spheroids . Here , we postulate that the formation of stellar spheroids from gas-rich disks is controlled by two parameters that characterize galaxy mergers , the mass ratio of merging dark matter halos , and the virial velocity of the larger merging halo . We utilize merger histories generated from realizations of the cosmological density field to calculate the fraction of dark matter halos that have avoided spheroid formation , and compare the derived statistics with the spheroid occupation fractions in surveys of nearby galaxies . We find , for example , that the survival rate of disk-dominated galaxies in \Lambda CDM is just high enough to explain the observed fractional representation of disk-dominated galaxies in the universe if the only mergers which lead to central spheroid formation are those with mass ratios M _ { 2 } / M _ { 1 } > 0.3 and virial velocities V _ { vir, 1 } > 55 \textrm { km s } ^ { -1 } . We discuss the physical origin of this criterion .