3 parties would take up position around some population center, with some differentiation, but not too much. Probably they each move to the center of mass of th

3 parties would take up position around some population center, with some differentiation, but not too much. Probably they each move to the center of mass of the third of the population they represent, except that there's some incentive to be a little centrist of that to try and poach marginal voters from the other two parties. If a party moves too far out from center, centrist voters on their margins defect to the other two parties. I'm not sure what the penalty for being 'too centrist' is.