Who is left, who is right?

We propose a model to simulate the process of opinion formation in a society where the traditional division into leftists and rightists is not enough any longer. The model is based on the Ashkin-Teller idea to assign two Ising spins to each site (agent). The two states (up and down) of the first spin represent two possible opinions on any question in an economic area, and the two states of the second spin in a personal area. We assume that the mechanisms of opinion formation in both of these areas are different. The interaction between them is introduced in the form of a tolerance factor. It has been found, among others, that the formation of consensus between groups of agents which differ only in the economic area is quite simple, whereas if they differ in the personal area no consensus is possible.