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Longman Dictionary of Contemporary English
minority government
noun
EXAMPLES FROM CORPUS
▪ Chandra Shekhar's efforts at keeping his minority government afloat ended in March 1991.
▪ In other words, the position of a minority government can be made untenable if all the other parties combine against it.
▪ In spite of only a short period of minority government the Labour Party in the 1920s had also developed some ambitious long-term policies.
▪ Or he might aim for a minority government dependent on the votes of six Arab members of the Knesset.
▪ The following day Labor formed a minority government under Michael Field.
▪ We need electoral reform so that a minority government with a 100seat advantage can not implement the extremist policies of the Eighties again.
▪ When there is a minority government, however, the combination is far less stable.
Wiktionary
minority government

n. (context politics English) government by a political party or a coalition that does not have a majority of seats / votes in parliament

Wikipedia
Minority government

A minority government, or minority cabinet or minority parliament, is a cabinet formed in a parliamentary system when a political party or coalition of parties does not have a majority of overall seats in the parliament. It is sworn into office, with or without the formal support of other parties, to enable a government to be formed. Under such a government, legislation can only be passed with the support of enough other members of the legislature to provide a majority, encouraging multi-partisanship. In bicameral parliaments, the term relates to the situation in chamber whose confidence is considered most crucial to the continuance in office of the government.

A minority government tends to be much less stable than a majority government because, if they can unite for the purpose, opposing parliamentary members have the numbers to vote against legislation, or even bring down the government with a vote of no confidence.

Usage examples of "minority government".

The white-minority government made scattered concessions to nonwhites, but the basic dispute over the proper path of development remained.

We're employees of a foreign power conducting surveillance on behalf of a minority government so that their military can keep am eye on Islamic fanatics.