What's the difference between a two-party system and a multi-party system

Multi party system:  

A multi-party system is a system in which multiple political parties have the capacity to gain control of government offices, separately or in coalition. The effective number of parties in a multi-party system is normally larger than two but lower than ten. In the vast majority of multi-party systems, numerous major and minor political parties hold a serious chance of receiving office, and because they all compete, a majority may not control the legislature, forcing the creation of a coalition. In some countries, every government ever formed since its independence has been by means of a coalition. Multi-party systems tend to be more common in parliamentary systems than presidential systems, and far more common in countries that use proportional representation compared to countries that use first past the post elections.

Party system :

A two-party system is a system where two major political parties dominate politics within a government. One of the two parties typically holds a majority in the legislature and is usually referred to as the majority party while the other is the minority party. The term has different senses. For example, in the United States, Jamaica, and Malta, the sense of two party system describes an arrangement in which all or nearly all elected officials only belong to one of the two major parties, and third parties rarely win any seats in the legislature. In such arrangements, two-party systems are thought to result from various factors like winner takes all election rules. In such systems, while chances for third party candidates winning election to major national office are remote, it is possible for groups within the larger parties, or in opposition to one or both of them, to exert influence on the two major parties. In contrast, in the United Kingdom and in other parliamentary systems and elsewhere, the term two-party system is sometimes used to indicate an arrangement in which two major parties dominate elections but in which there are viable third parties which do win seats in the legislature, and in which the two major parties exert proportionately greater influence than their percentage of votes would suggest.

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