Electronegativity equalization in polyyne carbon chains with the composition X-(-C=C-)(N)-Y, where X, Y = H, F, or Na, and 1 less than or equal to N less than or equal to 5, has been studied at the MP2/6-31G** level of theory. In contrast to charges of individual atoms, charges of the X-C=C-, -C=C-, and -C=C-Y chain fragments are found to be highly additive. The observed additivity of fragment charges stems from the underlying additivity of the corresponding electronegativity vectors and softness matrices. Although the latter quantities are poorly transferable among polyyne carbon chains, they satisfy additive combination rules to a high degree of accuracy. Approximate models that involve either one-electron effective Hamiltonians or screened electrostatic interactions fail to reproduce the rigorously computed atomic softness matrices, indicating the complex nature of phenomena that control the electron flow in molecules.