An election held to fill a vacant post in the legislature due to the death or resignation of a member is called

Step 1: Analyze the question The question asks for the name of an election held to fill a vacant seat in the legislature. The seat became vacant because the member died or resigned, and it is not a general election.

Step 2: Explain the concepts

• Run-off election: A second round of voting between the top two candidates when no one gets the required majority in the first round.
• Electoral college: A body of electors chosen to elect a president or other officer (e.g., in the USA). Voters do not vote directly.
• By-election: An election held between general elections to fill a vacancy caused by death, resignation, or removal (e.g., recall or court order) of a member.
• Primary election: An election within a political party to choose its candidate for the main election.

Step 3: Match the definition

• The election is held to fill a vacant seat after a death or resignation, outside the normal general election cycle. That is exactly the definition of a by-election.
• A run-off needs a failed first round, which is not the case here.
• An electoral college and primaries are not about filling vacancies.

Step 4: Answer The correct option is C. by-election.

Tip: Think of "by" as meaning "on the side" or "in between." A by-election happens in between general elections. Also, in Nigeria, INEC conducts by-elections when a legislator dies, resigns, or is removed.