Two-party politics is not very different from one-party politics under certain assumptions

Imagine people's political opinions all lie on a single line from left to right and each political party chooses a point on this line. The people will choose the political party which has a point that is the closest to their political views on the line. We assume that people's political views uniformly distribute on this line. If there are only two parties in the game, the Nash equilibrium exists when both of the parties choose the central point. In this way, only the policies which match the central political view will be carried out no matter which political party is the dominant party. Therefore, even there are two political parties, however, both parties will choose the same policies. In this way, we cannot see that the difference between two-party politics and one-party politics. People may think that if there is only one party, one party can choose any policy it wants. It could be true. However, if the single party wants to maximise the country's total utility or satisfaction, it has to choose the middle point, if we assume that distance away from the point the party selects is negatively linearly corelated to that person's utility. Therefore, with assumption of when there are two parties, parties' priority is to maximise the number of their supporters and when there is only one party, the party wants to maximise the country's total satisifaction, both political structures will carry out the same result. If we have more than two political parties, there will be no pure strategy nash equilibrium, which means the political environment could be very unstable.