Problem of Legitimacy of a Government in a 2-Party Plurality Rule

Under the plurality voting rule we often see that a party forms the government by winning majority of the seats, without winning majority of the votes. In some situations a smaller party with lower vote share may win more seats than a party with larger vote share. A more problematic case is when in a two-party situation the party with smaller vote share wins majority of seats. In such situations often people question the legitimacy of the government which is formed with the minority vote share. Such a situation may occur if the population is distributed over constituencies in a way that is favourable towards the smaller party. Evidently, winnability of the party is dependent on the share of vote the party commands and the number of constituencies it needs to win. The paper tries to nd out under what circumstances a party with minority vote share may have a chance to win majority of the seats and under what condition such a situation can never happen