The behavior of the cross polar cap potential, ΦPC, under strong solar wind conditions is studied using global MHD simulations. Simulations using two typical values of the ionospheric Pedersen conductance in agreement with others show that the cross polar cap potential is reduced compared to the corresponding potential in the solar wind due to the stagnation of the magnetosheath flow and the existence of parallel potentials. However, it is the ionospheric conductance that affects the value of ΦPC the most: the transpolar potential saturates only for high enough ionospheric conductance. A mechanism in which the ionospheric conductance changes the properties of the magnetosheath flow is proposed. This mechanism assumes mapping of the electrostatic potential in the ideal MHD system and yields a self-consistent response of the reconnection and transpolar potentials to changes in the ionospheric conductance.