by-election (n.) An election held by itself, not at the time of a
general election.
Wikipedia
A by-election or bye-election is a type of special election. By-elections are used when a Member of Parliament dies or resigns while in political office. They are also used if a member of parliament is removed from office for some reason, for example he is guilty of a crime. The by-elections would take place to pick who would replaces the member of parliament.
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