In Political Parties (English edition 1954), 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? The struggle between the Liberals and the Labour Party to be the opposition to the Conservatives ran from 1918 to 1929, when it was won by Labour, and reopened in 1981. 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. The need to modify Duverger's law to allow for differing patterns of two‐party competition in different regions was pointed out by Douglas Rae (The Political Consequences of Electoral Laws, 1967). 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’.