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People who do not register as a member of a political party when running for office are considered?

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Independent
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Answer :

People who do not register as a member of a political party when running for office are considered "Independents". They can choose to do this for many reasons, but usually it's to distinguish a candidate from the party mentality.

People who don't register as a member of a political party when running for office are known as 'independent'