A person or official who gives authorization or official approval (American spelling of 'authoriser').
From 'authorize' plus '-er' (Old English agent suffix). The American '-ize' spelling follows US conventions for verbs and their derivatives.
In medical and financial systems, your designated 'authorizer'—often a parent, guardian, or supervisor—literally has power over your life decisions, which is why questions of who gets to be an authorizer are deeply political and personal.
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