Using exact diagonalization numerical methods, as well as analytical a
rguments, we show that for typical electron densities in chaotic and d
isordered dots the peak spacing distribution is not bimodal but Gaussi
an. This is in agreement with experimental observations. We attribute
this behavior to the tendency of an even number of electrons to gain o
n-sire interaction energy by removing the spin degeneracy. We predict
that the dot will show a nontrivial electron-number-dependent spin pol
arization. Experimental tests of this hypothesis based on the spin pol
arization measurements are proposed.