A negative mixed glass former effect (MGFE) in the Na+ ion conductivity of glass has been found in 0.5Na(2)S + 0.5[xGeS(2) + (1 - x)PS5/2] glasses where the Na+ ion conductivity is significantly smaller for all of the ternary glasses than either of the binary end-member glasses. The minimum conductivity of similar to 0.4 x 10(-6) (Omega cm)(-1) at 25 degrees C occurs for the x = 0.7 glass. Prior to this observation, the alkali ion conductivity of sulfide glasses at constant alkali concentration, but variable ratio of one glass former for another (x) ternary mixed glass former (MGF) glasses, has always produced a positive MGFE in the alkali ion conductivity; that is, the ternary glasses have always had higher ion conductivities that either of the end-member binary glasses. While the Na+ ion conductivity exhibits a single global minimum value, the conductivity activation energy exhibits a bimodal double maximum at x approximate to 0.4 and x approximate to 0.7. The modified Christensen-Martin-Anderson-Stuart (CMAS) model of the activation energies reveals the origin of the negative MGFE to be due to an increase in the dielectric stiffness (a decrease in relative dielectric permittivity) of these glasses. When coupled with an increase in the average Na+ ion jump distance and a slight increase in the mechanical stiffness of the glass, this causes the activation energy to go through maximum values and thereby produce the negative MGFE. The double maximum in the conductivity activation energy is coincident with double maximums in CMAS calculated strain, Delta E-S, and Coulombic, Delta E-C, activation energies. In these ternary glasses, the increase in the dielectric stiffness of the glass arises from a negative deviation of the limiting high frequency dielectric permittivity as compared to the binary end-member glasses. While the CMAS calculated total activation energies Delta E-act = Delta E-S + Delta E-C are found to reproduce the overall shape of the composition dependence of the measured Delta E-act values, they are consistently smaller than the measured values for all compositions x. The new concept of an effective Madelung constant for the Na+ ions in glass is introduced, M-D(Na+), to account for the difference. Calculated M-D (Na+) values necessary to bring the CMAS and experimental Delta E-act values into agreement are in excellent agreement with nominal values for typical oxide crystals containing Na+. New MD simulations of oxide glasses were performed and were used to calculate M-D(Na+) values for Na2O + SiO2 glasses for the first time and were found to agree quite well with the values for the sulfide glasses studied here. Insights from the current study have been used to predict and design new MGF systems that may lead to a positive MGFE in the ionic conductivity.