In democracies, there are commonly two different methods to elect legislature or parliament, which often results in who get to run the government as the executive branch (but not always, as seen in the US). The two ways are the single member district (SMD) aka plurality method and proportional representation. the French political scientist Maurice Duverger proposed a law and a hypothesis about the relationship between the number of parties in a country and its electoral system. The law was that ‘the simple majority, single ballot system favours the two-party system’; the hypothesis was that ‘both the simple-majority system with second ballot and proportional representation favour multi-partism’. The division of these two statements into one law and one hypothesis is due to Riker, who claims that the first is a generalization which can be backed by formal reasoning, whereas the second is an easily falsifiable contingent generalization about the cases actually studied by Duverger. The law is driven by the idea that in the long run rational politicians and voters will realize that it is hopeless to have more than two parties competing at national level. Although three parties may remain in contention for a few years, a party which begins to slide will rapidly disappear as everybody comes to realize that it will win no seats at all if its support is evenly dispersed. By contrast, the number of parties in a proportional electoral system may be determined more by social forces than by the system's opportunities to split without penalty: Austria and Germany are well-known examples of countries with PR but only three or four parties.
The reasoning behind Duverger's law seems good, so why has three-party competition been so hardy in Britain? Because the Liberals (now Liberal Democrats) have some local fortresses, they have never been entirely wiped out, so that votes for them are not always obviously wasted. A similar pattern of competition between two locally strong parties, which might be different parties in different parts of the country, persists in Canada. One view voiced by G. Tullock is that ‘Duverger's Law is true, but it may take 200 years to work itself out’.
The first one, SMD, is not too common among democracies, but it is present in big countries like the US, the UK and Canada. The essence of this method is that a country divides itself into several political districts, often referred to as constituencies, and then the inhabitants in each of the constituencies vote for the one they want to be represented by and the one who wins goes to the parliament/legislature. A person only need the most votes to win, not the majority of the votes.
For instance, person A could get 40% of the votes, person B 35% of the votes and person C the last 25% of the votes. Even though person A didn't get the majority of the votes, she got the plurality of the votes and therefore wins the election of that constituency. The other persons lose and get nothing. Thus this method is sometimes referred to as the "first-past-the-post" method. Person A wins even though the majority didn't want her to represent them, they wanted someone else to represent them. Not very democratic, is it? Also, the votes for person B and C get thrown away. This often results in that supporters of minority parties can't be bothered with voting in their constituencies when they know that their vote won't mean a thing. If party A consistently has won the election in a certain constituency, what is the point of voting for party B when…