Self-diffusion coefficients of the tungstosilicate anion SiW12O404- have been determined in an HClO4 medium of various concentrations by voltammetric measurements at a glassy carbon electrode. The results have been extrapolated to zero ionic strength using an analytical transport theory (mean spherical approximation (MSA) transport calculations). The electrical conductivity of aqueous sodium tungstosilicate solutions with and without added salt has been then calculated using both the MSA transport method and Brownian dynamics simulations. Calculations have been compared to our experimental data. It has been shown that the extrapolation at infinite dilution of the conductivity of sodium tungstosilicate solutions gives a value for the self-diffusion coefficient of the polyion consistent with the voltammetric determination. Moreover, the sodium tungstosilicate electrolyte exhibits a behavior similar to a simple electrolyte in aqueous solution, whereas the addition of a salt yields an ionic association phenomenon.